Supervisory Control of Partially-Observed Discrete-Event Systems

Dr. Joseph Prosser, Applied Physics Laboratory

A discrete-event system (DES) is a dynamic system whose evolution in time is governed by the abrupt occurrence of physical events, at possibly irregular intervals. The study of such systems has become increasingly important in recent times because of the proliferation of human-made and computer-controlled systems that involve "discrete" quantities (e.g., how many parts are in an inventory, how many telephone calls are active, how many parts are in a buffer.) Many of these systems are driven by the instantaneous occurrences of "events" (e.g, the pushing of a button, hitting a keyboard key, or a traffic light turning green.)

We have found computationally efficient procedures for synthesizing supervisors that meet this objective, using both centralized and decentralized supervisory control architectures. In the new decentralized architecture, two or more supervisors simultaneously affect the operation of a single DES plant, and each supervisor makes its own local event-disabling decisions. The decisions then get fused into a single, global decision. We have applied these results to the problem of collision-free navigation of multiple robots in a maze.

General Input Balancing and Model Reduction for Linear and Nonlinear Systems

Prof. W. Steven Gray, Old Dominion University

Model reduction for linear state space systems has been investigated by many researchers over the past twenty years. Perhaps the most widely used methods in control applications are those related to the method of balance realizations introduced by Moore. In this context, a sufficient condition for a balanced realization to exist is minimality, i.e., joint controllability and observability, which can be determined independently from the class of admissible inputs. The input class, however, does play a role in the model reduction process. For example, a state may be strongly influenced by an input stimulus at a certain frequency and unaffected otherwise. Hence it could be deleted from the state variable model if this resonant input is never generated by the applied controller. In both the linear and nonlinear case, various notions of closed-loop balancing exist where the admissible inputs are assumed to be generated by specific controller types (LQG-optimal, H_inf-optimal, etc.).

In the nonlinear setting, the input class plays two roles. As in the linear case, it still plays a direct role in the state deletion decision, but it also plays a role in the observability property. In short, the choice of input class is linked to the existence of a balanced nonlinear realization. In the well known method due to Scherpen, the standing assumption is that the nonlinear system is zero-state observable, i.e., the zero-input is a universal input. In this talk, we present  a less restrictive notion of nonlinear balancing where observability is required only over the set of finite energy inputs. This idea leads naturally to a generalized notion of closed-loop balancing.

Semiglobal Output Regulation of Uncertain Nonlinear Systems

Prof. Alberto Isidori, University of Rome

This lecture will first summarize a recent approach  to the problem of structurally stable output regulation for nonlinear systems, in the presence of exosystem-generated disturbance inputs, which  unifies all earlier results on this subject and also provides a precise set of necessary and sufficient existence conditions. Then, it will be shown how recent design methods for semiglobal robust stabilization via output feedback can be used to address and solve the problem of semiglobal robust output regulation for a significant class of nonlinear systems.

Optical Sensors Based on  a Visual Sensory Model

Prof. Bahram Nabet, Drexel University

Biological visual sensory system can both inspire and guide the implementation of artificial optical sensory circuits. Massive parallelism, fault tolerance, simplicity of each processing unit, and regularity of the circuits make  optoelectronic implementation of these systems desirable. Integration of sensing and processing units on the same substrate increases the speed of operation and reduces the bandwidth necessary to transmit the sensed information to higher levels of processing. In this presentation, ionic conduction in excitable cells, the well-known "membrane equation," is shown to lead to analog electronic circuitry with rich processing and computational capabilities. We start  from simple components and demonstrates increasingly complicated processing by fusing the elements together. As an example of a mid-level processing system, a motion detector will be examined in some detail. Examples of more complicated higher level processing circuits for ultrasound  and night vision applications  will be presented.

Assessing Electromagnetic Environment  (EME) Effects on Flight-Critical Aircraft Control Computers

Dr. Celeste Belcastro, NASA Langley Research Center

Trends indicate that advanced aircraft are becoming increasingly dependent on electronic systems for safe flight.  Future advanced commercial aircraft may require systems for stability augmentation and flutter suppression, as well as guidance and control.  Such systems will be flight-critical, since safe flight of the aircraft will depend on their reliable operation.  The problem of verifying the integrity of the control computer in adverse, as well as nominal, operating environments is a key issue in the development, validation, certification, and operation of critical control systems. An adverse operating environment of particular concern for critical systems is caused by electromagnetic disturbances such as lightning and High Intensity Radiated Fields (HIRF).  These threats can cause common mode errors or upsets in critical systems whose fault tolerance is achieved through redundancy.  The current state-of-the-art  in electromagnetic environment (EME) effects testing is to perform laboratory tests on aircraft computers as well as full-scale aircraft testing.  Laboratory tests are primarily open-loop and static at a few operating points over the performance envelope of the equipment and do not consider system level effects.  Full-aircraft tests are also static with the aircraft situated on the ground and equipment powered on during exposure to electromagnetic energy.   These tests do not provide a means of validating system performance over the operating envelope or under various flight conditions. A process is presented for assessing the effects of electromagnetic environments on flight-critical aircraft control computers.  The assessment process is a combination of analysis, simulation, and tests and is currently under development for demonstration at the NASA Langley Research Center.  The assessment process is comprehensive in that it addresses (i) closed-loop operation of the controller under test, (ii) real-time dynamic detection of controller malfunctions that occur due to the effects of electromagnetic disturbances caused by lightning, HIRF, and electromagnetic interference and incompatibilities, and (iii) the resulting effects on the aircraft relative to the stage of flight, flight conditions, and required operational performance.

On Disturbance Attenuation Properties of Control Schemes for Euler-Lagrange Systems: Theoretical and Experimental Results

Prof. Jacquelien M. A. Scherpen, Technical University of Delft

Besides a more general introduction, the talk will consider the topic of the title, which is joint work with Romeo Ortega and Gerardo Escobar: We analyse the (local) disturbance attenuation properties of some asymptotically stabilizing nonlinear controllers for Euler-Lagrange systems reported in the literature. Our objective with this study is twofold: first, to compare the performance of these schemes from a perspective different from stabilizability; second, to quantify  the basic tradeoff between robust stability and robust performance for these designs. We consider passivity-based and feedback linearization schemes developed for the control of DC-to-DC converters and rigid robots. For the DC-to-DC problem we can show that for both controllers there exists a lower bound to the achievable attenuation level, i.e. a lower bound to the L2-gain of the closed loop operator from disturbance to regulated output, which is independent of the design parameters. Also, for the passivity based scheme we obtain an upper bound for the disturbance attenuation, which is insured provided we sacrifice the convergence rate. For rigid robots we show that both approaches yield arbitrarily good disturbance attenuation without compromising the convergence rate. The results are verified and analysed for the DC-to-DC converter in an experimental set-up

Research Progress on Gain Scheduling

Prof. Wilson "Jack" Rugh, Johns Hopkins University

After decades of silence on the subject, the academic research community in the 1990's has taken up the topic of gain scheduling for nonlinear control design with increasing interest. This has led to the formalization and clarification of some old ideas in gain scheduling, and to some new ideas that are quickly making their way into practice.

After a brief discussion of some very early examples of gain-scheduled control, a look at current requirements for nonlinear controllers, and a review of the salient features of gain-scheduled controllers, we will survey a number of current and future research directions.

Models for Film Growth and Methods for Model Reduction

Prof. P. S. Krishnaprasad, University of Maryland

The process of producing high quality thin (epitaxial, polycrystalline etc.) films of semiconductors (e.g. Si, SiGe) is governed by complex interplay of fluid flow, radiant heating, gas-phase and surface chemistry, and atomic scale phenomena that affect morphology of grown films. Models with predictive power that capture these different elements and provide useful guides for process control are of increasing interest. In this lecture, we discuss the types of models that arise from basic physical considerations of film growth in (commercial) rapid thermal reactors, and explore the problem of passing from these to low dimensional models of practical use in prediction.

The task of producing reduced order models from complex models has a long history in statistical analysis and in control theory under various names such as principal component analysis (PCA), Karhunen-Loeve decomposition, balancing etc.. In the setting of nonlinear systems the techniques are less well-developed, in part due to a lack of effective algorithms for determining the necessary `ignorable' coordinates. In this lecture, we will present some techniques for finding such coordinates. A first illustration of these ideas in connection with pure sensor data will be given (joint work with T. Kugarajah and S. Johnson). This will be followed by a numerical implementation of Morse's Lemma in the critical point theory of functions, for use in model reduction via balancing  of nonlinear dynamical systems (joint work with A.J. Newman).

An Optical Chopper Using Sliding Control

Prof. Stephen D. Goodman, West Virginia Institute of Technology

An optical chopper can be  made with an interferometer, a movable mirror, and a light detector.  The principle of operation is that the output of the light detector is a feedback signal that ultimately moves the mirror by means of a controller and an external, binary reference signal that indicates whether the interferometer should be constructively interfering or destructively interfering.  The controller uses sliding control to activate a power amplifier that in turn applies a voltage to a piezo-crystal which moves the mirror.  All aspects of the design are presented, including the interferometer, controller, and power amplifier. The results of the system are also presented in terms of the largest average contrast ratio of maximum to minimum output light intensity as well as the frequency response of the chopper.

Lyapunov and Operator Methods for Stability Analysis of Differential-Delay Systems

Prof. Erik I. Verriest, Georgia Institute of Technology

Delays occur in systems due to computation- communication- and/or transportation lags. In this presentation an overview of the stability analysis methods for delay systems will be given.

The Lyapunov-Krasovskii theory is used to obtain sufficient conditions for the robust stability (independent of the delay) of linear differential delay systems. These sufficient conditions are interesting in the sense that they involve the existence of a triple of positive definite matrices satisfying a certain Riccati equation, and are therefore more algebraic in nature. The approach is fruitful as it is readily generalized to other cases.  This includes time varying linear systems (with time varying delay), distributed delay systems, the stochastic stability of random delay systems, systems with nonlinearities and the discrete equivalent to the delay system.  On the design side, the conditions for stability have been exploited to derive stabilizability conditions under state and output feedback.  The existence proofs are constructive, and hence lead to the prescription of a whole class of stabilizing gains.

The Lyapunov-Razumikhin approach leads to delay-dependent (sufficient) criteria for stability. Among the other new methods, an operator method yielding necessary conditions for a subclass will be reported.

Some Recent Developments in Nonlinear Programming

Prof. André Tits, University of Maryland

The numerical solution of nonlinear constrained optimization problems will be considered. The focus will be on methods that generate a sequence of iterates entired contained in the feasible set, i.e., such that the constraints are satisfied at each iteration. The advantages of ``interior points'' methods (which were first studied in the real of linear programming) and of ``feasible'' sequential quadratic programming (FSQP) will be contrasted. Recent work on FSQP will be discussed, including application to problems with a large number of inequality constraints, such as finely discretized semi-infinite problems.

On Input-to-State Stability and Detectability

Prof. Yuan Wang, Florida Atlantic University

The study of input-to-state stability aims at understanding the dependence of state trajectories on the magnitude of inputs. This is especially relevant when the inputs in question represent disturbances acting on a system.  For linear systems, this leads to the consideration of gains and the operator-theoretic approach, including the formulation of H_inf control.  For nonlinear systems, a candidate for such a formulation is the property called input-to-state stability (ISS).  Since introduced by E.D.Sontag in the late 80's, this property has been widely used by various authors in studies ranging from robust control to highly nonlinear small-gain theorems.  This talk will discuss some characterizations of the ISS property.  We will show the equivalence between the ISS property and several (apparent) variations proposed in the related literature.
 

Modeling and Statistical Analysis of Multipath Fading Wireless Channels

Prof. Charalambos "Bambos" Charalambos, Ottawa University
 
In a typical wireless communication channel, propagation of electro-magnetic energy over large areas arrives at the receiver through many paths, by way of reflection, diffraction and scattering from surfaces, producing a distorted version of the transmitted wave. Distortions occur due to (i) severe signal envelope fluctuations  over local areas, known as short-term fading, and (ii) less severe mean signal envelope fluctuations which are due to topographic based changes, known as long-term fading. In general, such channels are modeled by impulse responses which experience time-spread as well as time-variations.

This talk is aimed at introducing  detailed stochastic dynamical models which characterize both the short-term and the long-term effects of the channel at a macroscopic level. This is done under a diversified set of conditions, which are  consistent with the mechanics of energy propagation. The  distributions of the received signal power of each path are derived. These  are geneneralizations of the well-known Rayleigh, Rician, Nakagami and Log-Normal distributions, to their time-varying analogs. In addition, the statistical  properties the received signal are examined and  a central limit theorem is derived, which implies Gaussianity of the channel impulse response.

Statistical Learning Control of Uncertain Systems: It is Better Than It Seems

Prof. Chaouki Abdallah, University of New Mexico
 
Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to "difficult" control problems. Unfortunately, the number of samples required in order to guarantee stringent performance levels may be prohibitively large. This talk introduces bootstrap learning methods and the concept of stopping times to drastically reduce the bound on the number of samples required to achieve a performance level. We then apply these results to obtain more efficient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems.

Geometric Aspects in Modeling, Analysis, and Control of Mechanical Systems

Prof. Francesco Bullo, University of Illinois at Urbana-Champaign
 
This talk discusses some aspects of an emerging geometric control theory for mechanical system. The use of a Riemannian geometric formalism is advocated in modeling, analysis, and design problems. First, I will review some modeling ideas for systems with constraints and symmetries. Then, I will consider two analysis problems: (i) how to describe and construct kinematic reductions for mechanical systems, and (ii) how to describe the evolution of a mechanical system under low or high amplitude oscillatory controls. Finally, I will discuss some implications for the design of stabilizing controllers and motion planning algorithms.

Chemotaxis: A Control Engineer's Perspective on Signal Transduction Pathways in Biology

Prof. Pablo A. Iglesias, Johns Hopkins University
 
Biological signaling pathways are composed of large "networks" of interconnected molecular components, many of which involve considerable feedback and are highly nonlinear. The subsystems comprising the network are subject to control by many independent events, and thus defy attempts to describe clear cut cause-and-effect relationships. Because of these features, the complete understanding of how these systems work presents a problem of daunting complexity to researchers. The traditional approach has been to "break" these networks into their components to study them separately. This reductionist paradigm has led to many breakthroughs, but alone cannot provide a full understanding of the system. Only recently has it begun to be appreciated that new techniques and approaches are needed to understand these networks. Feedback control theory is commonly used in engineering practice as a means of regulating man-made systems. In this talk we discuss how a study of biological signaling pathways using the tools of control systems may lead to special insight into our understanding of how biology works.

Nonsmooth Feedback Design for Genuinely Nonlinear Systems That Cannot be Smoothly Controlled

Prof. Wei Lin, Case Western Reserve University
 
This lecture will give an overview of some exciting developments and advances over the last few years in the areas of global stabilization, output tracking and adaptive control using nonsmooth feedback for a significant class of inherently nonlinear systems with nonlinear parameterization, which cannot be dealt with or controlled by any smooth state feedback, even locally. In this talk, we will also discuss some major open and challenging problems on which the research is currently progressing.

Auxiliary Signal Design for Failure Detection

Prof. Stephen L. Campbell, North Carolina State University
 
Failure detection has been the subject of many studies. Most of this work has concerned passive failure detection. In the passive approach, for material or security reasons, the detector monitors the system but has no way of acting upon it. A major drawback with the passive approach is that failures can be masked by the operation of the system. This is true, in particular, for controlled systems where the desirable robustness of control systems tends to mask abnormal behaviors of the systems. In contrast, active detection consists in acting upon the system using a test signal in order to detect abnormal behaviors which would otherwise remain undetected during normal operation. There are many requirements on a test signal during the test period including the desire that the system should continue to operate in a reasonable manner, the test period should be short, and the effect of the auxiliary signal on the system minimal. This talk will describe a recently developed approach for optimal auxiliary signal design for guaranteed detection in the presence of model uncertainties.

Dropouts and Quantization in Networked Control Systems

Prof. Michael Lemmon, University of Notre Dame
 
In recent years there has been considerable interest in controlling dynamical systems over communication networks. We refer to these as networked control systems and these systems are found in a variety of applications that include industrial automation, military command-and-control, and infrastructure systems such as the electric power grid. This talk focuses on a networked control system that consists of a generalized regulator whose feedback path is implemented over a non-deterministic network. Being non-deterministic, the network is free to randomly drop feedback measurements. We pose the following questions: How do data dropouts affect overall system stability and performance? How does measurement quantization affect overall system stability and performance? Can we use such knowledge to design better network scheduling protocols and synthesize better controllers? Answers have been obtained to many of these questions and they provide a tantalizing picture characterizing the minimum information required to support a control system. This talk reviews that prior work to provide a cross-layered view of networked systems in which control algorithms and network protocols work together in a coordinated manner.

Geometry, Algebra, and Combinatorics of Noncommuting Flows

Prof. Matthias Kawski, Arizona State University
 
Noncommuting flows are a distinguishing feature of geometric control theory. They also have important uses in computational mathematics, physics, and various other areas. Lie-theoretic tools have been a mainstay of differential geometric control for several decades. But recent insights point to deeper underlying geometric and algebraic structures that are formalized by chronological algebras (these are "dual" to Leibniz algebras). This presentation highlights the dramatic simplifications resulting from the combination of geometric work such as Sussmann's exponential product expansion of the Chen series, the chronological calculus of Gamkrelidze and Agrachev, and explicit algebraic combinatorial formulae for the dual PBW-bases built on Hall-Viennot bases of a free Lie algebra (Melancon, Reutenauer). The resulting "continuous Campbell-Baker-Hausdorff formula" promises to have applications reaching far beyond control.

Algebraic Approach to Nonlinear System Interconnections

Dr. Yaqin Li, Old Dominion University
 
In many engineering applications, systems are interconnected in a variety of ways. Understanding the nature of these interconnections is important for both system analysis and design. For a large-scale system, it is convenient to first decompose it into subsystems, and then to analyze the whole system by considering the subsystem interconnections. For linear systems, some beautiful and complete results for the interconnections are now standard subjects, however, the interconnections of nonlinear systems are not so well understood. Our specific interest is the interconnection of analytic input-output systems represented as Fliess operators. A broad range of analytic nonlinear systems can be described by a Fliess operator or its associated formal power series. The four basic interconnections considered are the parallel, product, cascade and feedback connections. A fairly complete algebraic theory can be constructed to describe these interconnections. Motivated by this theory, the formal Laplace-Borel transform is defined, and the algebraic structures it induces on formal power series and Fliess operators are characterized.

Performance Analysis of Recoverable Flight Control Systems Subject to Neutron-Induced Upsets Using Hybrid Dynamical Models

Dr. Hong Zhang, Old Dominion University
 
It has been observed that atmospheric neutrons can produce single-event upsets in digital flight control hardware. Potentially, they can reduce system performance and introduce a safety hazard. One experimental system-level approach investigated to help mitigate the effects of these upsets is NASA Langley's Recoverable Computer System. It employs rollback error recovery using dual-lock-step processors together with new fault-tolerant architectures and communication subsystems. In this talk, a class of stochastic hybrid dynamical models, which consists of a jump-linear system and a stochastic finite-state automaton, is used to describe the performance of a Boeing 737 aircraft system in closed-loop with a Recoverable Computer System. The jump-linear system models the switched dynamics of the closed-loop system due to the presence of controller recoveries. Each dynamical model in the jump-linear system was obtained separately using system identification techniques and high fidelity flight simulation software. The stochastic finite-state automaton approximates the recovery logic of the Recoverable Computer System. The upsets process is modeled by either an independent, identically distributed process or a first-order Markov chain. Mean-square stability and output tracking performance of the recoverable flight system are analyzed theoretically via a model-equivalent Markov jump-linear system of the stochastic hybrid model. The model was validated using data from a controlled experiment at NASA Langley, where simulated neutron-induced upsets were injected into the system at a desired rate. The effects on the output tracking performance of a simulated aircraft were then directly observed and quantified. The model was then used to analyze a neutron-based experiment on the Recoverable Computer System at the Los Alamos National Laboratory. This model predicts that the experimental flight control system, when functioning as designed, will provide robust control performance in the presence of neutron induced single-event upsets at normal atmospheric levels.

Packet Scheduling in Wireless LAN and Wireless Sensor Networks

Dr. Zhenghao Zhang, State University of New York at Stony Brook
 
Packet scheduling is to find smart schedules to send packets to improve the performance of a communication system. In this talk we will first describe our ongoing research on packet scheduling in Wireless Local Area Networks (LAN) enhanced with the Multiple Packet Transmission (MPT) technique. With MPT, the sender can send two distinct packets to two receivers simultaneously, which will greatly improve the downlink throughput of a Wireless LAN. Since not all pairs of receivers can receive from the sender at the same time, careful packet scheduling is needed. We will mainly discuss a new linear time algorithm for finding faster schedules, which is based on matching theories in graphs. Second, we will describe our research in heterogeneous wireless sensor networks, in which two types of nodes are deployed, the cluster head nodes and the basic sensor node. The cluster head node organizes sensors around it into a cluster and can use polling to get the data packets from the sensors. We focus on finding energy-efficient polling schedules and show that the problem of finding a minimum time contention-free schedule is NP-hard under virtually all scenarios. We then give a fast on-line algorithm to find sub-optimal schedules and show that the sensors lifetime can be greatly improved with the polling scheme, compared with other existing random-access methods. At the end of the talk we will briefly describe future research plans on cross-layer design in wireless networks.

Space-Time Coding with Feedback

Dr. Haiquan Wang, University of Waterloo
 
In this presentation, I will give some basic coding criteria for a Multiple-Input, Multiple-Output (MIMO) system with feedback. A MIMO system without feedback has been proposed and well-understood from capacity view and from coding view. In this system, by using multiple transmit and receive antennas and time delay slots, coded signals can be spread on multiple paths and at different time slots, hence, multiple independently faded replicas of the same data information can be obtained at the receiver. Thus, `space diversity' and `time diversity' can be generated. Based on the pair-wise error probability analysis, criteria for designing a code which effectively utilizes space diversity and time diversity have been introduced. Now assume that the MIMO system has an error-free, zero-delay feedback channel with infinite or limited bandwidth from the receiver to the transmitter. Using this feedback channel, the receiver can send back the instant channel information to the transmitter completely or partially according to the limitation on bandwidth of the feedback channel, and the transmitter can utilize these information to code transmit signals to improve the performance of the system. The problem is how to do coding, that is, how to exploit the space and time diversities and utilize channel information at the transmit side to design transmitted signals such that the performance of the whole system can be improved. To do so, some good criteria for designing transmitted signals are needed. In this presentation, I will give some basic coding criteria for this system. In the case that complete feedback from the receiver to the transmitter is available, the optimal structure of the codes is shown to have the form cu^*, where c is a T-dimensional complex vector (T is a time delay), and u is a unit-norm eigenvector corresponding to the largest eigenvalue of matrix HH^* (H is the channel matrix and y means the transpose and conjugate). Moreover, criterion for designing vector c is obtained. In the case that only finite-bit feedback is available, the optimal structure of the codes is proved to have the form cp^*, where c is also a T-dimensional complex vector and p is a M-dimensional vector with unit-norm (M is the transmit number of the system). Furthermore, criteria for designing vectors c and p are given. A Lloyd-like algorithm to approach p is introduced.

Interference Mitigation in Future Generation Wireless Systems

Prof. Dimitrie C. Popescu, The University of Texas at San Antonio
 
Worldwide success of cellular telephones during the past decade has prompted demand for additional services and systems in which mobility is a key factor like for example wireless data systems providing access to the Internet, or mobile ad-hoc networks (MANET) and sensor networks that can be used for monitoring, surveillance, and homeland security applications. In this context, future generation wireless systems are expected to provide a wide range of services that will enable greater user mobility and reduce networking costs. However, their performance will be affected by interference, which is inherent to wireless communications due to the shared nature of the communication medium, the electromagnetic frequency spectrum. As a consequence, interference mitigation will be extremely important in future generation wireless systems to ensure operation under Quality of Service (QoS) constraints implied by the various applications. In this talk we will discuss new methods for interference mitigation in future generation wireless systems. A new algorithm for joint power and data rate control in wireless systems that was developed using a game-theoretic approach will be presented, followed by an overview of interference avoidance methods, an area in which the speaker made numerous fundamental contributions. Interference avoidance provides distributed iterative algorithms for transmitter optimization which minimize interference and maximize system capacity, and which are applicable to a wide variety of wireless communication systems and scenarios. We will also discuss Ultra Wideband (UWB) systems and present a new method for mitigating narrowband interference in OFDM-based UWB systems.

Input-Output Behavior and Realization Theory of Hybrid Systems: A Formal Power Series Approach

Dr. Mihaly Petreczky, Johns Hopkins University
 
Hybrid systems are dynamical systems which exhibit both continuous and discrete behavior. Such systems arise naturally in a number of fields, including control theory, signal processing, computer vision, communication networks and even biotechnology. Our goal is to find a mathematical model of a hybrid system based on its input-output behavior. That is, we assume that the hybrid system takes in input signals and emits output signals. By the input-output behavior we mean the map, which for each input signal fed in to the system tells us the output signal generated by the system under the specified input signal. The mathematical model we want to find should be a hybrid state-space representation. A hybrid state-space representation consists of a finite collection of differential equations and a finite state automaton. One assumes that the system switches from one state of the automaton to another one and between the switches the state changes according to the differential equation associated with the corresponding state of the automaton. Notice that the input-output behavior can also be viewed as a mathematical model of the hybrid system, but state-space representations are much more useful for solving practical and theoretical problems. In this talk we will address the following questions: 1. Under which conditions does an input-output behavior admit a hybrid state-space representation? 2. When is a hybrid state-space representation of an input-output behavior minimal (i.e. it contains the least number of variables), does such a minimal hybrid state-space representation exist, is it unique? 3. How to compute/construct a (preferably minimal) hybrid state-space representation of an input-output behavior? The questions of the type described above are known as the realization problem and the solution is known under the term realization theory. Realization theory provides the theoretical foundations for the solution of such practically relevant problems as systems identification, state estimation, filtering, etc. Our main mathematical tool will be the theory of rational formal power series.

Stability Analysis of Hybrid Jump Linear Systems with Markov Inputs

Dr. Arturo Tejada, Old Dominion University
 
In the past two decades, the number of applications that make use of supervisory algorithms to control complex continuous-time or discrete-time systems has increased steadily. Typical examples include air traffic management, digital control systems over networks, and flexible manufacturing systems. A common feature of these applications is the intermixing of the continuous dynamics of the controlled plant, and the logical and discrete dynamics, of the supervising algorithms. These so-called hybrid systems are the focus of much ongoing research. When the plant is a discrete-time process or is represented by one, there exist few mathematical models to study the effect of the supervising algorithms. To mitigate this problem, this dissertation addresses the following three main objectives. To introduce a new modeling framework for discrete-time stochastic hybrid systems suitable for stability analysis; to derive testable stability conditions for these models; and to demonstrate that these models are suitable to study real-world applications. To attain the first objective, the Hybrid Jump Linear System model is introduced. Although it has the same modeling capabilities as other formalisms in the literature (e.g. Discrete Stochastic Hybrid Automata), it possesses the unique advantage of representing the dynamics of both the controlled plant and the supervising algorithm in the same analysis framework: stochastic difference equations. This enables the study of their joint properties such as, for example, mean square stability. The second objective is addressed by developing a suite of testable sufficient mean square stability conditions. These tests were developed by applying, successively, switched systems' techniques, singular value analysis, and a second moment lifting technique. The last objective will be achieved by developing a hybrid jump linear system model of an AFTI-F16 flight controller deployed on a fault tolerant computer with rollback and cold-restart capabilities and studying its stability properties.

Fault Tolerance for Safety-Critical Systems: The Scalable Processor-Independent Design for Extended Reliability (SPIDER)

Dr. Paul Miner, NASA Langley Research Center
 
The Scalable Processor-Independent Design for Extended Reliability (SPIDER) is a family of fault-tolerant architectures developed at NASA Langley Research Center. Each member of the SPIDER family provides a general-purpose integrated modular avionics platform. The goal of the design is to provide a flexible set of architectural solutions capable of satisfying a wide range of performance and reliability requirements, while preserving a consistent interface to applications. The central feature of the SPIDER architecture is the Reliable Optical Bus (ROBUS). The ROBUS provides a set of guaranteed services to attached nodes, in the presence of a bounded number of physical faults. These services include interactive consistency (Byzantine Agreement), distributed diagnosis (group membership), and clock synchronization. The ROBUS also guarantees recovery from a bounded number of transient faults. Furthermore, it includes a restart mechanism for recovery from correlated transient upsets. Finally, the ROBUS design supports a mechanism for real-time updates to the communication schedule, while still preserving the guaranteed services. Devices attached to the ROBUS may include general-purpose processors, remote data concentrators, sensors, or actuators. Using the guaranteed services from the ROBUS, the attached nodes can implement higher-level services. In addition to the synchronization and membership services derived directly from the ROBUS, the attached nodes can be combined to provide both fail-operational and fail-stop capabilities. The redundancy management capabilities at this level are flexible; they can be adapted to support dissimilar processors while preserving the strong fault-masking guarantees. The combination of these capabilities provides a family of integrated modular avionics platforms that supports a range of application and reliability demands.

Modeling and Stability Analysis of Nonlinear Sampled-data Systems with Embedded Recovery Algorithms

Dr. Heber Herencia-Zapana, National Institute of Aerospace
 
Computer control systems for safety critical systems are designed to be fault tolerant and reliable, however, soft errors triggered by harsh environments can affect the performance of these control systems. The soft errors of interest which occur randomly, are nondestructive and introduce a failure that lasts a random duration. To minimize the effect of these errors, safety critical systems with error recovery mechanisms are being investigated. The main goals of this dissertation are to develop modeling and analysis tools for sampled-data control systems that are implemented with such error recovery mechanisms. First, the mathematical model and the well-posedness of the stochastic model of the sampled-data system are presented. Then this mathematical model and the recovery logic are modeled as a dynamically colored Petri net (DCPN). For stability analysis, these systems are then converted into piecewise deterministic Markov processes (PDP). Using properties of a PDP and its relationship to discrete-time Markov chains, a stability theory is developed. In particular, mean square equivalence between the sampled-data and its associated discrete- time system is proved. Also conditions are given for stability in distribution to the delta Dirac measure and mean square stability for a linear sampled-data system with recovery logic.