Coefficient Matrix Decomposition Method and BIBO Stabilization of Stochastic Systems with Time Delays

The mean square BIBO stabilization is investigated for the stochastic control systems with time delays and nonlinear perturbations. A class of suitable Lyapunov functional is constructed, combined with the descriptor model transformation and the decomposition technique of coefficient matrix; thus some novel delay-dependent mean square BIBO stabilization conditions are derived. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Finally, three numerical examples are given to demonstrate that the derived conditions are effective and much less conservative than those given in the literature

Robust load frequency control of interconnected grids with electric vehicles

This thesis presents new load frequency controls of interconnected grids, using electric vehicles to assist power plants in providing stability, which fluctuates with load demands and renewable powers. New robust control schemes for comprehensive power systems with electric vehicles, diverse transmission links, network-induced time delays and uncertainties are investigated.<br /

Optimization methods for deadbeat control design: a state space approach

This thesis addresses the synthesis problem of state deadbeat regulator using state space techniques. Deadbeat control is a linear control strategy in discrete time systems and consists of driving the system from any arbitrary initial state to a desired final state infinite number of time steps. Having described the framework for development of the thesis which is in the form of a lower linear-fractional transformation (LFT), the conditions for internal stability based on the notion of coprime factorization over the set of proper and stable transfer matrices, namely RH, is discussed. This leads to the derivation of the class of all stabilizing linear controllers, which are parameterized affinely in terms of a stable but otherwise free parameter Q, usually known as the Q-parameterization. In this work, the classical Q- parameterization is generalized to deliver a parameterization for the family of deadbeat regulators. Time response characteristics of the deadbeat system are investigated. In particular, the deadbeat regulator design problem in which the system must satisfy time domain specifications and minimize a quadratic (LQG-type) performance criterion is examined. It is shown that the attained parameterization for deadbeat controllers leads to the formulation of the synthesis problem in a quadratic programming framework with Q regarded as the design variable. The equivalent formulation of this objective as a quadratic integral in the frequency domain provides the means for shaping the frequency response characteristics of the system. Using the LMI characterization of the standard H problem, a new scheme for shaping the system frequency response characteristics by minimizing the infinity norm of an appropriate closed-loop transfer function is introduced. As shown, the derived parameterization of deadbeat compensators simplifies considerably the formulation and solution of this problem. The last part of the work described in this thesis is devoted to addressing the synthesis problem of deadbeat regulators in a robust way, when the plant is subject to structured norm-bounded parametric uncertainties. A novel approach which is expressed as an LMI feasibility condition has been proposed and analysed

Learning Stable Koopman Models for Identification and Control of Dynamical Systems

Learning models of dynamical systems from data is a widely-studied problem in control theory and machine learning. One recent approach for modelling nonlinear systems considers the class of Koopman models, which embeds the nonlinear dynamics in a higher-dimensional linear subspace. Learning a Koopman embedding would allow for the analysis and control of nonlinear systems using tools from linear systems theory. Many recent methods have been proposed for data-driven learning of such Koopman embeddings, but most of these methods do not consider the stability of the Koopman model. Stability is an important and desirable property for models of dynamical systems. Unstable models tend to be non-robust to input perturbations and can produce unbounded outputs, which are both undesirable when the model is used for prediction and control. In addition, recent work has shown that stability guarantees may act as a regularizer for model fitting. As such, a natural direction would be to construct Koopman models with inherent stability guarantees. Two new classes of Koopman models are proposed that bridge the gap between Koopman-based methods and learning stable nonlinear models. The first model class is guaranteed to be stable, while the second is guaranteed to be stabilizable with an explicit stabilizing controller that renders the model stable in closed-loop. Furthermore, these models are unconstrained in their parameter sets, thereby enabling efficient optimization via gradient-based methods. Theoretical connections between the stability of Koopman models and forms of nonlinear stability such as contraction are established. To demonstrate the effect of the stability guarantees, the stable Koopman model is applied to a system identification problem, while the stabilizable model is applied to an imitation learning problem. Experimental results show empirically that the proposed models achieve better performance over prior methods without stability guarantees

Contributions to Passivity Theory and Dissipative Control Synthesis

This thesis contains contributions to some relevant problems in the field of control theory and controller design technology, namely to the areas of passivity analysis and dissipative control synthesis for linear and nonlinear dynamical systems. The first of our contributions consists in presenting a solution to a problem which had been unsolved for many years: the problem of the equivalence between the notions of strict positive realness and strict passivity of linear systems. Both properties imply the asymptotic stability of a linear system, although the former is a frequency-domain concept and the latter is a time-domain concept. Subsequently, we approach the equally classical topic of static output feedback stabilization of linear systems, a problem to which a definite solution remains to be given. We present a new necessary and sufficient LMI condition for stabilization based on the notion of strict dissipativity, and we propose a new noniterative strategy for controller design which consists in solving a single convex optimization problem. In addition, we also introduce a new dissipativity-based strategy for feedback stabilization of nonlinear systems using the notion of linear annihilators and the celebrated Finsler’s Lemma. This approach allows for analysing the dissipativity properties of rational nonlinear plants in terms of a polytopic LMI condition. A new stabilizability condition that would not be feasible in the case of a passive representation of the system is presented as well, making it possible to derive a closed-form expresion for the controller’s feedthrough term as a direct consequence of the local dissipativity analysis of the plant. This feature simplifies the remaing steps of the controller design procedure considerably, both in the case of a static or a dynamic output feedback

Proceedings of the Workshop on Applications of Distributed System Theory to the Control of Large Space Structures

Two general themes in the control of large space structures are addressed: control theory for distributed parameter systems and distributed control for systems requiring spatially-distributed multipoint sensing and actuation. Topics include modeling and control, stabilization, and estimation and identification