Contemporary Issues in Systems Stability and Control with Applications
A Workshop in Honor of Anthony N. Michel
Notre Dame, Indiana
April 5, 2003


  1. Approximation of Input-Output Maps Using Gaussian Radial Basis Functions
    Irwin W. Sandberg, University of Texas at Austin
    Radial basis functions are of interest in connection with a variety of approximation problems in the neural networks area, and in other areas as well. Here we show that the members of some interesting families of shift-varying input-output maps, that take a function space into a function space, can be uniformly approximated, over an infinite time or space domain, in a certain special way using gaussian radial basis functions.

  2. Neural Architectures with Learning Mechanisms in Integrated CMOS Chips
    Khurram Waheed, Michigan State University
    Fathi M. Salem, Michigan State University
    This talk presents a comprehensive exposition of our work on modeling of neural networks and their hardware implementations. In this effort we discuss several architectures and their hardware implementations leading to the latest layered system architecture, named micro-learner, which integrates digital/analog neuro-processing, memory, A/D and D/A conversions. The chip only requires external counter to proceed through three phases of learning, (weight) storing, processing, or (weight) reading/writing to external unit. The chip is envisioned to mount on a probe or probe array for on-line processing or control without the interface with external platforms. Finally, contributions of Tony Michel in regard to foundational and analytical basis of neural networks and large scale systems and their impact on the modeling of neural networks will be discussed.

  3. Direct Neural Dynamic Programming
    Lei Yang, Arizona State University
    Russell Enns, The Boeing Company
    Yu-Tsung Wang, Scientific Monitoring, Inc.
    Jennie Si, Arizona State University
    This talk is about approximate dynamic programming, which has gone by many different names, such as "reinforcement learning", "adaptive critics", "neuro-dynamic programming", "adaptive dynamic programming" or more broadly, approximate dynamic programming. Years of research have shown that these apparently diverse areas are actually addressing much the same issue: optimization over time by using learning and approximation to handle problems that severely challenge conventional methods due to their very large scale and/or lack of sufficient prior knowledge. In the present paper, we first address the results and challenges in a unified fashion of some of the most important results under the scope of approximate dynamic programming, to provide an introduction to results obtained in respective areas such as neural networks, adaptive/optimal/robust control, computer science/machine learning, decision theory (especially the study of Markov decision processes), engineering and operations research. Then we present results developed and tested by the authors. We introduce the fundamentals and the basic framework of our direct NDP. We address the generalization issue by demonstrating a continuous state complex control problem. Specifically we will provide details of how to use direct NDP to perform stabilization, command tracking, and re-configuration for an Apache helicopter. This is probably one of the first studies that an ADP type of algorithm has been applied to a complex, realistic, continuous state problem. Until now, reinforcement learning has been mostly successful in discrete state space problems. On the other hand, prior ADP based approaches to controlling continuous state space systems have all been limited to smaller, or linearized, or decoupled problems. Therefore the work presented here compliments and advances the existing literature in the general area of learning approaches in approximate dynamic programming.

  4. Chemical Plume Tracing with Autonomous Underwater Vehicles
    Jay Farrell, University of California, Riverside
    Olfactory-based mechanisms have been hypothesized for a variety of biological behaviors: homing by Pacific salmon, homing by green sea turtles, foraging by Antarctic procellariiform seabirds, foraging by lobsters, foraging by blue crabs, and mate-seeking and foraging by insects. Typically, olfactory-based mechanisms proposed for biological entities combine a large-scale orientation behavior based in part on olfaction with a multisensor local search in the vicinity of the source. Long-range olfactory based search is documented in moths at ranges of 100-1000 m and in Antarctic procellariiform seabirds over thousands of kilometers. This presentation considers the development of algorithms to replicate these feats in autonomous vehicles. The goal of the autonomous vehicle will be to locate the source of a chemical that is transported in a turbulent fluid flow. Autonomous vehicle with such capabilities possess applicability in searching for environmentally interesting phenomena, unexploded ordinance, undersea wreckage, and sources of hazardous chemicals or pollutants. This talk will discuss the chemical plume tracing problem, discuss aspects of the problem that make it challenging, present a solution to the problem, and present results from in-water experiments.

  5. Evolutionary Multiobjective Optimization: Qualitative Analysis and Design Implementation
    Gary G. Yen, Oklahoma State University
    In this talk, we propose a new evolutionary approach to multiobjective optimization problems--the Dynamic MultiObjective Evolutionary Algorithm (DMOEA). In our DMOEA, a novel cell-based rank and density estimation strategy is proposed to efficiently compute dominance and diversity information when the population size dynamically increases or decreases. In addition, a population growing strategy and a population declining strategy are designed to determine if an individual will be survived or eliminated based on some qualitative indicators. Meanwhile, an objective space compression strategy is devised to continuously refine the quality of the resulting Pareto front. By examining the selected performance metrics on three recently designed benchmark functions, DMOEA is found to be competitive with, or even superior to five state-of-the-art MOEAs in terms of keeping the diversity of the individuals along the trade-off surface, tending to extend the Pareto front to new areas and finding a well-approximated Pareto optimal front. Moreover, DMOEA is evaluated by using different parameter settings on the chosen test functions to verify its robustness of converging to an optimal population size, if it exists. From simulation results, DMOEA has shown the potential of autonomously determining the optimal population size, which is found insensitive to the initial population size chosen.

  6. Trajectory Sensitivity Theory in Nonlinear Dynamical Systems: Power System Applications
    M. A. Pai, Univ. of Illinois at Urbana-Champaign
    Trong B. Nguyen, Pacific Northwest National Lab
    Trajectory sensitivity analysis (TSA) has been applied in control system problems for a long time in such areas as optimization, adaptive control etc. Applications in power systems in conjunction with Lyapunov/transient energy functions first appeared in the 80's. More recently, it has found applications on its own by defining a suitable metric on the trajectory sensitivities with respect to the parameters of interest. In this talk we present the theoretical as well as practical applications of TSA for dynamic security applications in power systems. We also discuss the technique to compute critical values of any parameter that induces stability in the system using trajectory sensitivities.

  7. Emergency Control and Special Protection Systems in Electric Power Systems
    Vijay Vittal, Iowa State University
    Power systems are being operated closer to the stability limit nowadays as deregulation introduces many more economic objectives for operation. As open access transactions increase, weak connections, unexpected events, hidden failures in protection system, human errors and other reasons may cause the system to lose balance and even lead to catastrophic failures. As a result several innovative emergency control procedures and special protection systems are being introduced to maintain the reliability of the system. The control approaches fall under the category of corrective control and are initiated after the occurrence of the disturbance. This talk addresses the topic of designing a corrective control strategy after large disturbances. When a power system is subjected to large disturbances such as simultaneous loss of several generating units or major transmission lines, and the vulnerability analysis indicates that the system is approaching a catastrophic failure, control actions need to be taken to limit the extent of the disturbance. In our approach, the system is separated into smaller islands at a slightly reduced capacity. The basis for forming the islands is to minimize the generation-load imbalance in each island, thereby facilitating the restoration process. An analytical approach to forming the islands using a two time scale procedure is developed. Then by exploring a carefully designed load shedding scheme based on the rate of frequency decline, we limit the extent of the disruption, and we are able to restore the system rapidly. We refer to this corrective control scheme as controlled islanding followed by load shedding based on the rate of frequency decline. Traditionally power system control design has largely been based on a model based approach. Currently several innovations in the area of synchronized phasor measurements have significantly improved the availability of real time signals over a wide portion of the network. As a result several new control approaches based on measurements are feasible. These approaches will be examined. A new class of controls called special protection systems (SPS) in now finding greater acceptance in power systems with the enhanced need to provide reliability in a competitive restructured utility environment. These systems are triggered only when large disturbances occur. They provide a degree of safety in preventing cascading outages. The SPS being explored will be presented and their potential for greater use will be examined.

  8. Power Systems Stability: New Opportunities for Control
    Anjan Bose, Washington State University
    The power system networks in North America and Europe are the largest man-made interconnected systems in the world. The Eastern Interconnection in North America that stretches from the East Coast to the Rocky Mountains is the largest in terms of geographic area covered, total installed generation capacity and total length of transmission lines. Moreover, all the rotating generators in one network rotate synchronously producing alternating current at the same frequency, that is, all the generators operate together in dynamic equilibrium. Any unbalance in the energy distribution of the system caused by disturbances tends to perturb the system. Large disturbances, usually caused by short circuits of high voltage equipment, can make the power system become unstable. Large power systems exhibit a large range of dynamical characteristics, very slow to very fast, and various controllers have been developed over time to control various phenomena. Many of the controls are on-off switches (circuit breakers) that can isolate short-circuited or malfunctioning equipment, or shed load or generation. Other controls are discrete like tap-changers in transformers or switching of capacitor/reactor banks. Still others are continuous control like voltage controllers and power system stabilizers in rotating generators or the newer power electronic controls in FACTS devices (Flexible AC Transmission Systems refers to modern electronic devices such as High Voltage DC Transmission or Static VAR Controllers that can control power flows or voltage). However, all the controls (especially the fast ones) are local controls, that is, the input and the control variables are in the same locale (substation). Most dynamic phenomena in the power system, on the other hand, are regional or sometimes system-wide. Thus designers of power system control have been constrained to handle system-wide stability problems with local controllers. The only system-wide control in the power system is the balancing of the slowly changing system electrical load by adjusting generation levels; this slow dynamical phenomenon allows a slow communication system to reach all the generators in the system in time for the adjustments to be effective. The only other way to implement non-local control has been to dedicate a communication channel between the input variable in one substation to the control variable in another, an expensive proposition that has limited its use. The tremendous breakthroughs in computer communications of the last decade, both in cost and bandwidth, have opened opportunities that are yet to be fully utilized in the control of power systems. The availability of many new control devices, e.g., FACTS devices, and of accurate time synchronizing signals through the GPS are also factors in this new equation. It is certainly possible now to design fast system-wide controls. However, much research and development is needed to bring such designs to fruition. In this talk, we first survey the state of the art in stability control of power systems. Then we outline the new technologies that can be brought to bear on this problem. Finally, we lay out a possible development path from system-wide controls in which simple extensions of existing controls can start helping power system operations right away to concepts that will require significant time and effort to control more complex phenomena. The goal, as always, is to provide more efficient operation, that is, be able to transmit more power over existing transmission lines with more flexibility.

  9. Data Fusion Modeling for Groundwater Systems Using Generalized Kalman Filtering
    David W. Porter, Johns Hopkins University Applied Physics Lab
    Engineering projects involving hydrogeology are faced with uncertainties because the earth is heterogeneous, and typical data sets are fragmented and disparate. In theory, predictions provided by computer simulations using calibrated models constrained by geological boundaries provide answers to support management decisions, and geostatistical methods quantify safety margins. In practice, currently existing methods are limited by the data types and models that can be included, computational demands, or simplifying assumptions. Data fusion modeling (DFM) removes many of the limitations and is capable of providing data integration and model calibration with quantified uncertainty for a variety of hydrological, geological, and geophysical data types and models. The benefits of DFM for waste management, water supply, and geotechnical applications are savings in time and cost through the ability to produce visual models that fill in missing data and predictive numerical models to aid management optimization. DFM has the ability to update field-scale models in real time using PC or workstation systems and is ideally suited for parallel processing implementation. DFM is a spatial state estimation and system identification methodology that uses three sources of information: measured data, physical laws, and statistical models for uncertainty in spatial heterogeneities. What is new in the present DFM is the solution of the causality problem in the data as simulation Kalman filter methods to achieve computational practicality. The Kalman filter is generalized by introducing information filter methods due to Bierman coupled with a Markov random field representation for spatial variation. A Bayesian penalty function is implemented with Gauss-Newton methods. This leads to a computational problem similar to numerical simulation of the partial differential equations PDEs of groundwater. As a matter of fact, extensions of PDE solver ideas to break down computations over space form the computational heart of DFM. State estimates and uncertainties can be computed for heterogeneous hydraulic conductivity fields in multiple geological layers from the usually sparse hydraulic conductivity data and the often more plentiful head data. Further, a system identification theory is derived based on statistical likelihood principles. A maximum likelihood theory is provided to estimate statistical parameters such as Markov model parameters that determine the geostatistical variogram. Field-scale application of DFM at the DOE Savannah River Site is presented and compared with manual calibration. DFM calibration runs converge in less than 1 hour on a Pentium PC for a 3D model with more than 15,000 nodes. Run time is approximately linear with the number of nodes. Furthermore, conditional simulation is used to quantify the statistical variability in model predictions such as contaminant breakthrough curves.

  10. Wave-Digital Concepts and Relativity Theory
    Alfred Fettweis, Ruhr-Universitaet Bochum
    The wave-digital approach to numerical integration owes its advantageous behavior partly to the use of wave concepts, in particular however to the use of passivity and losslessness properties that occur naturally in physical systems. For handling nonlinear such systems, one is naturally led to certain formulations that turn out to be of fundamental physical significance, yet are violated by some basic relations in special relativity theory. By starting from the classical relativistic kinematics and making some assumptions that are at least not a priori physically unreasonable, however, one is led to a modified version of relativistic dynamics that is in complete accord with the formulations just mentioned, yields expressions of appealing elegance (including a four-vector, thus a Lorentz-invariant quadruplet, that is of immediate physical significance and coincides with a four-vector already considered by Minkowski), and is, at least at first sight, in good agreement with some reasonable analytic expectations. In this alternative approach, Newton's second law is altered in a slightly different way than in classical relativity, and, as a consequence, Newton's third law, which is taken over untouched in classical theory, has also to be subjected to some modification. For problems concerning collisions of particles or action of fields (electromagnetic, gravitational) upon particles the alternative approach yields exactly the same dynamic behavior as the classical theory. Corresponding experiments are thus unable to differentiate, and the same holds for some other available experimental results. The present talk builds on the same basic concepts as those that have previously been published and, in some respect, expands them. On the other hand, an unnecessary additional earlier requirement that had led to an unavoidable factor 1/2 in the expression for the equivalence between mass and energy is abandoned. This way, e.g., a remarkable agreement with certain results in electromagnetics is obtained. For further testing the validity, the crucial issue to be considered now appears to be the kinetic energy of fast particles. A classical experiment by Bertozzi addresses this issue, but it is not yet sufficiently clear how the results obtained there should properly be interpreted in the present context. It is hoped that the present talk can contribute to clarifying some of the issues involved, even if the conventional theory should in the end be confirmed, by accurate and unequivocal measurements, to be the one agreeing best with reality.

  11. Time, Systems and Control: Qualitative Properties and Methods
    Lyubomir T. Gruyitch, University of Technology Belfort
    The goal is to present some not widely known original recent results and new ones in the areas in which Professor Anthony N. Michel has been a world leading scientist. Properties of time are summarized. They are linked with the features of physical variables expressed by the Physical Continuity and Uniqueness Principle implying the Time Continuity and Uniqueness Principle. They appear important for modeling of physical systems and for studies of their qualitative dynamical properties. The complete transfer function matrix is defined for MIMO time-invariant linear continuous-time and discrete-time systems.\ It is crucial for zero-pole cancellation, system minimal realization, synthesis of stabilizing, tracking and/or optimal control for the systems. A new Lyapunov methodology for nonlinear systems, called the consistent Lyapunov methodology, enables us to establish the necessary and sufficient conditions for: i) asymptotic stability, ii) a direct construction of a Lyapunov function for a given nonlinear dynamical system, and iii) for a set to be the exact domain of asymptotic stability. They are not expressed in terms of the existence of a Lyapunov function. The extended concepts of definite vector functions and of vector Lyapunov functions open new directions for studies of complex nonlinear dynamical systems and for their control synthesis. This is shown by sythesizing stabilizing (output) tracking control for time-invariant nonlinear 2D systems.

  12. Asymptotic Stability of Multibody Attitude Systems
    Jinglai Shen, University of Michigan
    Amit K. Sanyal University of Michigan

    N. Harris McClamroch, University of Michigan
    A rigid base body, supported by a fixed pivot point, is free to rotate in three dimensions. Multiple elastic subsystems are rigidly mounted on the rigid body; the elastic degrees of freedom are constrained relative to the rigid base body. A mathematical model is developed for this multibody attitude system that exposes the dynamic coupling between the rotational degrees of freedom of the base body and the deformation or shape degrees of freedom of the elastic subsystems. The models are used to assess passive dissipation assumptions that guarantee asymptotic stability of an equilibrium solution. These results are motivated and inspired by a 1980 publication of R. K. Miller and A. N. Michel.

  13. Robust Regulation of Polytopic Uncertain Linear Hybrid Systems with Networked Control System Applications
    Hai Lin, University of Notre Dame
    Panos J. Antsaklis, University of Notre Dame
    In this talk, a class of discrete time uncertain linear hybrid systems, affected by both parameter variations and exterior disturbances, is considered. The main question is whether there exists a controller such that the closed loop system exhibits desired behavior under dynamic uncertainty and exterior disturbances. The notion of {\em attainability} is introduced to refer to the specified behavior that can be forced to the plant by a control mechanism. We give a method for attainability checking that employs the predecessor operator and backward reachability analysis, and a procedure for controller design that uses finite automata and linear programming techniques. Finally, Networked Control Systems (NCS) are proposed as a promising application area of the results and tools developed here, and the ultimate boundedness control problem for the NCS with uncertain delay, package dropout and quantization effects is formulated as a regulation problem for an uncertain hybrid system.

  14. Stable Cooperative Resource Allocation
    Kevin Passino, The Ohio State University
    Resource allocation involves partitioning of resources (e.g., processor time or machine processing capacity) and dedication of these to tasks (jobs in a computer system or parts in a manufacturing system) in order to optimize some performance objective (e.g., maximize task completion throughput rate). Such resource allocation functionalities are commonly found in parallel and distributed computing systems and flexible manufacturing systems, but can also represent biological attentional processes in humans. Distributed multi-processor resource allocation demands that multiple processors each decide how to allocate their resources (e.g., computing power) to multiple task types. Network-based cooperative resource allocation involves having multiple processors work together over an imperfect communication network to share the processing load in order to optimize throughput. Here, we will show that one class of network-based cooperative schedulers exhibit stable behavior (i.e., result in bounded buffer levels). Simulation results will be provided to provide insights into scheduler performance and resource allocation dynamics.

  15. The Cosmology of Zeros
    Michael K. Sain, University of Notre Dame
    For a transfer function which is the ratio, say, of two polynomials with real coefficients, it is clear that the number of zeros in the extended complex plane is equal to the number of poles in the extended complex plane. A matrix of such transfer functions does not, in general, enjoy the same property. In particular, when the matrix is deficient in either row or column rank, such an accounting does not give equality. To recapture the essence of the above classical equality, one may take into account the kernel and the cokernel of the matrix of transfer functions, and recast the ideas of poles and zeros in terms of spaces. In this talk we summarize these notions and show how they can apply to the well known systems theory problem of exact model matching, where they provide surprising insights about pole and zero "cancellation." The exposition takes place in the "cosmo-logical space" of vectors, modules, and mappings.

  16. The Adaptive Dynamic Programming Theorem
    John J. Murray State University of New York at Stony Brook
    Chadwick J. Cox, Accurate Automation Corp.

    Richard E. Saeks, Accurate Automation Corp.
    The centerpiece of Dynamic Programming is the Hamilton Jacobi Bellman (HJB) Equation which can be used to solve for the optimal cost functional for a nonlinear optimal control problem, while one can solve a second partial differential equation for the corresponding optimal control law. Although the direct solution of the Hamilton Jacobi Bellman Equation is computationally untenable. The Adaptive Dynamic Programming Algorithm, one starts with an initial cost functional/control law pair, and constructs a sequence of cost functional/control law pairs in real-time. The goal of the present talk is to provide a proof for the Adaptive Dynamic Programming Theorem to the effect that (with the appropriate technical assumptions) this process is:
    • globally convergent to the optimal cost functional, and
    • stepwise stable; i.e., the controller is a stabilizing controller at every iteration of the algorithm;
    for a prescribed nonlinear optimal control problem with unknown input affine state dynamics and input quadratic performance measure.

  17. Reliability of SCADA Systems in Offshore Oil and Gas Platforms
    Kelvin T. Erickson, University of Missouri-Rolla
    E. Keith Stanek, University of Missouri-Rolla
    Egemen Cetinkaya, Sprint PCS
    Shari Dunn-Norman, University of Missouri-Rolla
    Ann Miller, University of Missouri-Rolla

    Supervisory control and data acquisition (SCADA) systems are commonly used in the offshore oil and gas industry for remote monitoring and control of offshore platforms. Using a generalized platform system architecture, the reliability of the entire system is estimated. The outcome of this reliability assessment is an estimate of
    • mean time between failures (MTBF);
    • system availability; and
    • probability of facility damage or pollution release.
    The reliability was estimated using probabilistic risk assessment. A fault tree was constructed to show the effect of contributing events on system-level reliability. Probabilistic methods provide a unifying method to assess physical faults, contributing effects, human actions, and other events having a high degree of uncertainty. The probability of various end events, both acceptable and unacceptable, is calculated from the probabilities of the basic initiating failure events.

  18. Power Control and Call Admission Control for DS-CDMA Cellular Networks
    Derong Liu, University of Illinois at Chicago
    Yi Zhang, University of Illinois at Chicago
    Sanqing Hu, University of Illinois at Chicago
    In this talk, we consider call admission control algorithms for SIR-based power-controlled DS-CDMA cellular networks. We consider networks that handle multiple classes of services. When a new call (or a handoff call) arriving at a base station requesting for admission, our algorithms will calculate the desired power control set points for the new call and all existing calls. We will provide necessary and sufficient conditions under which the power control algorithm will have a feasible solution. These conditions are obtained through deriving the inverse of the matrix used in the calculation of power control set points. If there is no feasible solution to power control or if the desired power levels to be received at the base station for some calls are larger than the maximum allowable power limits, the admission request will be rejected. Otherwise, the admission request will be granted. When higher priority is desired for handoff calls, we will allow different thresholds for new calls and handoff calls. We will develop an adaptive algorithm that adjusts these thresholds in real-time as environment changes. The performance of our algorithms will be shown through computer simulation and compared with existing algorithms.