Nonlinear static output feedback controller design for uncertain polynomial systems: An iterative sums of squares approach

This paper examines the problem of designing a nonlinear static output feedback controller for uncertain polynomial systems via an iterative sums of squares approach. The derivation of the static output feedback controller is given in terms of the solvability conditions of state dependent bilinear matrix inequalities (BMIs). An iterative algorithm based on the sum of squares (SOS) decomposition is proposed to solve these state-dependent BMIs. Finally, numerical examples are provided at the end of the paper as to demonstrate the validity of the proposed design techniqu

Robust L2–L∞ control of uncertain differential linear repetitive processes

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdFor two-dimensional (2-D) systems, information propagates in two independent directions. 2-D systems are known to have both system-theoretical and applications interest, and the so-called linear repetitive processes (LRPs) are a distinct class of 2-D discrete linear systems. This paper is concerned with the problem of L2–L∞ (energy to peak) control for uncertain differential LRPs, where the parameter uncertainties are assumed to be norm-bounded. For an unstable LRP, our attention is focused on the design of an L2–L∞ static state feedback controller and an L2–L∞ dynamic output feedback controller, both of which guarantee the corresponding closed-loop LRPs to be stable along the pass and have a prescribed L2–L∞ performance. Sufficient conditions for the existence of such L2–L∞ controllers are proposed in terms of linear matrix inequalities (LMIs). The desired L2–L∞ dynamic output feedback controller can be found by solving a convex optimization problem. A numerical example is provided to demonstrate the effectiveness of the proposed controller design procedures.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Robust de-centralized control and estimation for inter-connected systems

The thesis is concerned with the theoretical development of the control of inter-connected systems to achieve the whole overall stability and specific performance. A special included feature is the Fault-Tolerant Control (FTC) problem for the inter-connected system in terms of local subsystem actuator fault estimation. Hence, the thesis describes the main FTC challenges of distributed control of uncertain non-linear inter-connected systems. The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control with unmatched components including uncertainties and disturbances. The second controller dealing with matched components including uncertainties and actuator faults. The main contributions of the thesis are summarised as follows: - The non-linear inter-connected systems are controlled by two controllers. The linear part via a linear matrix inequality (LMI) technique and the discontinuous part by using Integral Sliding Mode Control (ISMC) based on state feedback control. - The development of a new observer-based state estimate control strategy for non-linear inter-connected systems. The technique is applied either to every individual subsystem or to the whole as one shot system. - A new proposal of Adaptive Output Integral Sliding Mode Control (AOISMC) based only on output information plus static output feedback control is designed via an LMI formulation to control non-linear inter-connected systems. The new method is verified by application to a mathematical example representing an electrical power generator. - The development of a new method to design a dynamic control based on an LMI framework with Output Integral Sliding Mode Control (OISMC) to improve the stability and performance. - Using the above framework, making use of LMI tools and ISMC, a method of on-line actuator fault estimation has been proposed using the Proportional Multiple Integral Observer (PMIO) for fault estimation applicable to non-linear inter-connected systems

Robust de-centralized control and estimation for inter-connected systems

The thesis is concerned with the theoretical development of the control of inter-connected systems to achieve the whole overall stability and specific performance. A special included feature is the Fault-Tolerant Control (FTC) problem for the inter-connected system in terms of local subsystem actuator fault estimation. Hence, the thesis describes the main FTC challenges of distributed control of uncertain non-linear inter-connected systems. The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control with unmatched components including uncertainties and disturbances. The second controller dealing with matched components including uncertainties and actuator faults.The main contributions of the thesis are summarised as follows:- The non-linear inter-connected systems are controlled by two controllers. The linear part via a linear matrix inequality (LMI) technique and the discontinuous part by using Integral Sliding Mode Control (ISMC) based on state feedback control.- The development of a new observer-based state estimate control strategy for non-linear inter-connected systems. The technique is applied either to every individual subsystem or to the whole as one shot system.- A new proposal of Adaptive Output Integral Sliding Mode Control (AOISMC) based only on output information plus static output feedback control is designed via an LMI formulation to control non-linear inter-connected systems. The new method is verified by application to a mathematical example representing an electrical power generator.- The development of a new method to design a dynamic control based on an LMI framework with Output Integral Sliding Mode Control (OISMC) to improve the stability and performance.- Using the above framework, making use of LMI tools and ISMC, a method of on-line actuator fault estimation has been proposed using the Proportional Multiple Integral Observer (PMIO) for fault estimation applicable to non-linear inter-connected systems