Verifiable Adaptive Control with Analytical Stability Margins by Optimal Control Modification

This paper presents a verifiable model-reference adaptive control method based on an optimal control formulation for linear uncertain systems. A predictor model is formulated to enable a parameter estimation of the system parametric uncertainty. The adaptation is based on both the tracking error and predictor error. Using a singular perturbation argument, it can be shown that the closed-loop system tends to a linear time invariant model asymptotically under an assumption of fast adaptation. A stability margin analysis is given to estimate a lower bound of the time delay margin using a matrix measure method. Using this analytical method, the free design parameter n of the optimal control modification adaptive law can be determined to meet a specification of stability margin for verification purposes

Novel Observer-Based Suboptimal Digital Tracker for a Class of Time-Delay Singular Systems

This paper presents a novel suboptimal digital tracker for a class of time-delay singular systems. First, some existing techniques are utilized to obtain an equivalent regular time-delay system, which has a direct transmission term from input to output. The equivalent regular time-delay system is important as it enables the optimal control theory to be conveniently combined with the digital redesign approach. The linear quadratic performance index, specified in the continuous-time domain, can be discretized into an equivalent decoupled discrete-time performance index using the newly developed extended delay-free model. Additionally, although the extended delay-free model is large, its advantage is the elimination of all delay terms (which included a new extended state vector), simplifying the proposed approach. As a result, the proposed approach can be applied to a class of time-delay singular systems. An illustrative example demonstrates the effectiveness of the proposed design methodology

Approximation, analysis and control of large-scale systems - Theory and Applications

This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.Open Acces

Qualitative Properties of Hybrid Singular Systems

A singular system model is mathematically formulated as a set of coupled differential and algebraic equations. Singular systems, also referred to as descriptor or differential algebraic systems, have extensive applications in power, economic, and biological systems. The main purpose of this thesis is to address the problems of stability and stabilization for singular hybrid systems with or without time delay. First, some su cient conditions on the exponential stability property of both continuous and discrete impulsive switched singular systems with time delay (ISSSD) are proposed. We address this problem for the continuous system in three cases: all subsystems are stable, the system consists of both stable and unstable subsystems, and all subsystems are unstable. For the discrete system, we focus on when all subsystems are stable, and the system consists of both stable and unstable subsystems. The stability results for both the continuous and the discrete system are investigated by first using the multiple Lyapunov functions along with the average-dwell time (ADT) switching signal to organize the jumps among the system modes and then resorting the Halanay Lemma. Second, an optimal feedback control only for continuous ISSSD is designed to guarantee the exponential stability of the closed-loop system. Moreover, a Luenberger-type observer is designed to estimate the system states such that the corresponding closed-loop error system is exponentially stable. Similarly, we have used the multiple Lyapunov functions approach with the ADT switching signal and the Halanay Lemma. Third, the problem of designing a sliding mode control (SMC) for singular systems subject to impulsive effects is addressed in continuous and discrete contexts. The main objective is to design an SMC law such that the closed-loop system achieves stability. Designing a sliding surface, analyzing a reaching condition and designing an SMC law are investigated throughly. In addition, the discrete SMC law is slightly modi ed to eliminate chattering. Last, mean square admissibility for singular switched systems with stochastic noise in continuous and discrete cases is investigated. Sufficient conditions that guarantee mean square admissibility are developed by using linear matrix inequalities (LMIs)

Modeling and control of complex dynamic systems: Applied mathematical aspects

The concept of complex dynamic systems arises in many varieties, including the areas of energy generation, storage and distribution, ecosystems, gene regulation and health delivery, safety and security systems, telecommunications, transportation networks, and the rapidly emerging research topics seeking to understand and analyse. Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops. This special issue provides a platform for researchers to report their recent results on various mathematical methods and techniques for modelling and control of complex dynamic systems and identifying critical issues and challenges for future investigation in this field. This special issue amazingly attracted one-hundred-and eighteen submissions, and twenty-eight of them are selected through a rigorous review procedure

Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control

This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional-derivative control strategy is presented, where the derivative gain is to make the closed-loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods

A non-uniform predictor-observer for a networked control system

The final publication is available at Springer via http://dx.doi.org/10.1007/s12555-011-0621-5This paper presents a Non-Uniform Predictor-Observer (NUPO) based control approach in order to deal with two of the main problems related to Networked Control Systems (NCS) or Sensor Networks (SN): time-varying delays and packet loss. In addition, if these delays are longer than the sampling period, the packet disordering phenomenon can appear. Due to these issues, a (scarce) nonuniform, delayed measurement signal could be received by the controller. But including the NUPO proposal in the control system, the delay will be compensated by the prediction stage, and the nonavailable data will be reconstructed by the observer stage. So, a delay-free, uniformly sampled controller design can be adopted. To ensure stability, the predictor must satisfy a feasibility problem based on a time-varying delay-dependent condition expressed in terms of Linear Matrix Inequalities (LMI). 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