H2, fixed architecture, control design for large scale systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1990.Includes bibliographical references (p. 227-234).by Mathieu Mercadal.Ph.D

Robust Distributed Stabilization of Interconnected Multiagent Systems

Many large-scale systems can be modeled as groups of individual dynamics, e.g., multi-vehicle systems, as well as interconnected multiagent systems, power systems and biological networks as a few examples. Due to the high-dimension and complexity in configuration of these infrastructures, only a few internal variables of each agent might be measurable and the exact knowledge of the model might be unavailable for the control design purpose. The collective objectives may range from consensus to decoupling, stabilization, reference tracking, and global performance guarantees. Depending on the objectives, the designer may choose agent-level low-dimension or multiagent system-level high-dimension approaches to develop distributed algorithms. With an inappropriately designed algorithm, the effect of modeling uncertainty may propagate over the communication and coupling topologies and degrade the overall performance of the system. We address this problem by proposing single- and multi-layer structures. The former is used for both individual and interconnected multiagent systems. The latter, inspired by cyber-physical systems, is devoted to the interconnected multiagent systems. We focus on developing a single control-theoretic tool to be used for the relative information-based distributed control design purpose for any combinations of the aforementioned configuration, objective, and approach. This systematic framework guarantees robust stability and performance of the closed-loop multiagent systems. We validate these theoretical results through various simulation studies

Optimal nonlinear control and estimation using global domain linearization

Alan Turing teaches that cognition is symbol processing. Norbert Wiener teaches that intelligence rests on feedback control. Thus, there are discrete symbols and continuous sensory-motor signals. Sensorimotor dynamics are well-represented by nonlinear differential equations. A possible construction of symbols could be based on equilibria. Language is a symbol system and is one of the highest expressions of cognition. Much of this comes from spatial reasoning, which requires embodied cognition. Spatial reasoning derives from motor function. This thesis introduces a novel generalized non-heuristic method of linearizing nonlinear differential equations over a finite domain. It is used to engineer optimal convergence to target sets, a general form of spatial reasoning. Ordinary differential equations are ubiquitous models in physics and engineering that describe a wide range of phenomena including electromechanical systems. This thesis considers ordinary differential equations expressed in state-space form. For a given initial state, these equations generate signals that are continuous in both time and state. The control engineering objective is to find input functions that steer these states to desired target sets using only the measured output of the system. The state-space domain containing the target set, along with its cost, can be thought of as a symbol for high-level planning. Consider a basis state equal to a vector of nonlinear basis functions, computed from the state, where the state is generated from a multivariate nonlinear dynamic system. The basis state derivative can be expressed as a linear dynamic system with an additional error term. This thesis describes radial basis functions that minimize the error over the entire state-space domain, where the basis state equals zero if and only if the state is in a desired target set. This gives an approximate linear-dynamic system, and if the basis state goes to zero, then the state goes to the target set. This form of linear approximation is global over the domain. Careful selection of the basis gives a fully generalizable relationship between linear stability and nonlinear stability. This form of linearization can be applied to optimal state feedback and state estimation problems. This thesis carefully introduces optimal state feedback control with an emphasis on optimal infinite horizon solutions to linear-dynamic systems that have quadratic cost. A thorough introduction is also given to the optimal output feedback of linear-dynamics systems. The detectable and stabilizable subspaces of a linear-dynamic system are expressed in a generalized closed form. After introducing optimal control for linear systems, this thesis explores adaptive control from several different perspectives including: tuning, system identification, and reinforcement learning. Each of these approaches can be characterized as an optimal nonlinear output feedback problem. In each case, generalized representations can be found using a single layer of appropriately chosen nonlinear basis functions with linear parameterization. The primary focus of this thesis is to select these basis functions, in a fully generalized way, so that they have linear-dynamics. When this can be achieved, infinite horizon state feedback and state estimation can be computed using well-known closed-form solutions. This thesis demonstrates how multivariate nonlinear dynamic systems defined on a finite domain can be approximated by computationally equivalent high-dimensional linear-dynamic systems using a generalized basis state. This basis state is computed with a single layer of biologically inspired radial basis functions. The method of linearization is described as "global domain linearization" because it holds over a specified domain, and therefore provides a global linear approximation with respect to that domain. Any optimal state estimation or state feedback is globally optimal over the domain of linearization. The tools of optimal linear control theory can be applied. In particular, control and estimation problems involving under-actuated under-measured nonlinear systems with generalized nonlinear reward can be solved with closed-form infinite horizon linear-quadratic control and estimation. The controllable, uncontrollable, stabilizable, observable, unobservable, and detectable subspaces can all be described in a meaningful generalized way. State estimation and state feedback can then be implemented in computationally efficient low-dimensional highly nonlinear form. Generalized optimal state estimation and state feedback for continuous-time continuous-state systems is necessary machinery for any high-level symbolic planning that might involve unstable electromechanical systems. Symbols naturally form in the presence of more than one target state. This could provide a natural method of language acquisition. Given a state, all symbolic domains that intersect the state would have equilibrium and cost. These intersections define the legal grammar of symbol transition. An engineer or agent can design these symbols for high-level planning. Generalized infinite horizon state feedback and state estimation can then be computed for the continuous system that each symbol represents using traditional linear tools with domain linearization

Development and evaluation of a Kalman-filter algorithm for terminal area navigation using sensors of moderate accuracy

Translational state estimation in terminal area operations, using a set of commonly available position, air data, and acceleration sensors, is described. Kalman filtering is applied to obtain maximum estimation accuracy from the sensors but feasibility in real-time computations requires a variety of approximations and devices aimed at minimizing the required computation time with only negligible loss of accuracy. Accuracy behavior throughout the terminal area, its relation to sensor accuracy, its effect on trajectory tracking errors and control activity in an automatic flight control system, and its adequacy in terms of existing criteria for various terminal area operations are examined. The principal investigative tool is a simulation of the system

State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates

State estimation is a fundamental problem when monitoring and controlling dynamical systems. Engineering systems interconnect sensing and computing devices over shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. Often, the dynamics of these systems are affected by external factors. In certain cases, these factors would lead the system to switch between different modes. In other cases, they would affect the dynamics of the system continuously in time without leading to explicit mode transitions. In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error bounds. Our approach relies on the notion of topological entropy and uses techniques from control under limited information. Since the computation of these entropies is hard in general, we compute corresponding upper bounds. Additionally, we design a state estimation algorithm for switched systems when their modes cannot be observed. We show that the average bit rate used by the algorithm is optimal in the sense that the efficiency gap is within an additive constant from the gap between the entropy of the considered system and its computed upper-bound. Finally, we apply our theory and algorithms to linear and nonlinear models of systems such as a glycemic index for diabetic patients, a controller of a Harrier jet and a Pendulum

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Observability and observer design for switched linear systems

Hybrid vehicles, HVAC systems in new/old buildings, power networks, and the like require safe, robust control that includes switching the mode of operation to meet environmental and performance objectives. Such switched systems consist of a set of continuous-time dynamical behaviors whose sequence of operational modes is driven by an underlying decision process. This thesis investigates feasibility conditions and a methodology for state and mode reconstruction given input-output measurements (not including mode sequence). An application herein considers insulation failures in permanent magnet synchronous machines (PMSMs) used in heavy hybrid vehicles. Leveraging the feasibility literature for switched linear time-invariant systems, this thesis introduces two additional feasibility results: 1) detecting switches from safe modes into failure modes and 2) state and mode estimation for switched linear time-varying systems. This thesis also addresses the robust observability problem of computing the smallest structured perturbations to system matrices that causes observer infeasibility (with respect to the Frobenius norm). This robustness framework is sufficiently general to solve related robustness problems including controllability, stabilizability, and detectability. Having established feasibility, real-time observer reconstruction of the state and mode sequence becomes possible. We propose the embedded moving horizon observer (EMHO), which re-poses the reconstruction as an optimization using an embedded state model which relaxes the range of the mode sequence estimates into a continuous space. Optimal state and mode estimates minimize an L2-norm between the measured output and estimated output of the associated embedded state model. Necessary conditions for observer convergence are developed. The EMHO is adapted to solve the surface PMSM fault detection problem

Active Perception by Interaction with Other Agents in a Predictive Coding Framework: Application to Internet of Things Environment

Predicting the state of an agent\u27s partially-observable environment is a problem of interest in many domains. Typically in the real world, the environment consists of multiple agents, not necessarily working towards a common goal. Though the goal and sensory observation for each agent is unique, one agent might have acquired some knowledge that may benefit the other. In essence, the knowledge base regarding the environment is distributed among the agents. An agent can sample this distributed knowledge base by communicating with other agents. Since an agent is not storing the entire knowledge base, its model can be small and its inference can be efficient and fault-tolerant. However, the agent needs to learn -- when, with whom and what -- to communicate (in general interact) under different situations.This dissertation presents an agent model that actively and selectively communicates with other agents to predict the state of its environment efficiently. Communication is a challenge when the internal models of other agents is unknown and unobservable. The proposed agent learns communication policies as mappings from its belief state to when, with whom and what to communicate. The policies are learned using predictive coding in an online manner, without any reinforcement. The proposed agent model is evaluated on widely-studied applications, such as human activity recognition from multimodal, multisource and heterogeneous sensor data, and transferring knowledge across sensor networks. In the applications, either each sensor or each sensor network is assumed to be monitored by an agent. The recognition accuracy on benchmark datasets is comparable to the state-of-the-art, even though our model has significantly fewer parameters and infers the state in a localized manner. The learned policy reduces number of communications. The agent is tolerant to communication failures and can recognize the reliability of each agent from its communication messages. To the best of our knowledge, this is the first work on learning communication policies by an agent for predicting the state of its environment

Decentralized control of uncertain interconnected time-delay systems

In this thesis, novel stability analysis and control synthesis methodologies are proposed for uncertain interconnected time-delay systems. It is known that numerous real-world systems such as multi-vehicle flight formation, automated highway systems, communication networks and power systems can be modeled as the interconnection of a number of subsystems. Due to the complex and distributed structure of this type of systems, they are subject to propagation and processing delays, which cannot be ignored in the modeling process. On the other hand, in a practical environment the parameters of the system are not known exactly, and usually the nominal model is used for controller design. It is important, however, to ensure that robust stability and performance are achieved, that is, the overall closed-loop system remains stable and performs satisfactorily in the presence of uncertainty. To address the underlying problem, the notion of decentralized fixed modes is extended to the class of linear time-invariant (LTI) time-delay systems, and a necessary and sufficient condition is proposed for stabilizability of this type of systems by means of a finite-dimensional decentralized LTI output feedback controller. A near-optimal decentralized servomechanism control design method and a cooperative predictive control scheme are then presented for uncertain LTI hierarchical interconnected systems. A H {592} decentralized overlapping control design technique is provided consequently which guarantees closed-loop stability and disturbance attenuation in the presence of delay. In particular, for the case of highly uncertain time-delay systems, an adaptive switching control methodology is proposed to achieve output tracking and disturbance rejection. Simulation results are provided throughout the thesis to support the theoretical finding

Optimization-based Robustness and Stabilization in Decentralized Control

This dissertation pertains to the stabilization, robustness, and optimization of Finite Dimensional Linear Time Invariant (FDLTI) decentralized control systems. We study these concepts for FDLTI systems subject to decentralizations that emerge from imposing sparsity constraints on the controller. While these concepts are well-understood in absence of an information structure, they continue to raise fundamental interesting questions regarding an optimal controller, or on suitable notions of robustness in presence of information structures. Two notions of stabilizability with respect to decentralized controllers are considered. First, the seminal result of Wang & Davison in 1973 regarding internal stabilizability of perfectly decentralized system and its connection to the decentralized fixed-modes of the plant is revisited. This seminal result would be generalized to any arbitrary sparsity-induced information structure by providing an inductive proof that verifies and shows that those mode of the plant that are fixed with respect to the static controllers would remain fixed with respect to the dynamic ones. A constructive proof is also provided to show that one can move any non-fixed mode of the plant to any arbitrary location within desired accuracy provided that they remain symmetric in the complex plane. A synthesizing algorithm would then be derived from the inductive proof. A second stronger notion of stability referred to as "non-overshooting stability" is then addressed. A key property called "feedthrough consistency" is derived, that when satisfied, makes extension of the centralized results to the decentralized case possible. Synthesis of decentralized controllers to optimize an H_Infinity norm for model-matching problems is considered next. This model-matching problem corresponds to an infinite-dimensional convex optimization problem. We study a finite-dimensional parametrization, and show that once the poles are chosen for this parametrization, the remaining problem of coefficient optimization can be cast as a semidefinite program (SDP). We further demonstrate how to use first-order methods when the SDP is too large or when a first-order method is otherwise desired. This leaves the remaining choice of poles, for which we develop and discuss several methods to better select the most effective poles among many candidates, and to systematically improve their location using convex optimization techniques. Controllability of LTI systems with decentralized controllers is then studied. Whether an LTI system is controllable (by LTI controllers) with respect to a given information structure can be determined by testing for fixed modes, but this gives a binary answer with no information about robustness. Measures have already been developed to determine how far a system is from having a fixed mode when one considers complex or real perturbations to the state-space matrices. These measures involve intractable minimizations of a non-convex singular value over a power-set, and hence cannot be computed except for the smallest of the plants. We replace these problem by equivalent optimization problems that involve a binary vector rather than the power-set minimization and prove their equality. Approximate forms are also provided that would upper bound the original metrics, and enable us to utilize MINLP techniques to derive scalable upper bounds. We also show that we can formulate lower bounds for these measures as polynomial optimization problems,and then use sum-of-squares methods to obtain a sequence of SDPs, whose solutions would lower bound these metrics