Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

Linear robust H-infinity stochastic control theory on the insurance premium-reserve processes

This thesis deals with the stability analysis of linear discrete-time premium-reserve (P-R) systems in a stochastic framework. Such systems are characterised by a mixture of the premium pricing process and the medium- and long- term stability in the accumulated reserve (surplus) policy, and they play a key role in the modern actuarial literature. Although the mathematical and practical analysis of P-R systems is well studied and motivated, their stability properties have not been studied thoughtfully and they are restricted in a deterministic framework. In Engineering, during the last three decades, many useful techniques are developed in linear robust control theory. This thesis is the first attempt to use some useful tools from linear robust control theory in order to analyze the stability of these classical insurance systems. Analytically, in this thesis, P-R systems are first formulated with structural properties such that time-varying delays, random disturbance and parameter uncertainties. Then as an extension of the previous literature, the results of stabilization and the robust H-infinity control of P-R systems are modelled in stochastic framework. Meanwhile, the risky investment impact on the P-R system stability condition is shown. In this approach, the potential effects from changes in insurer's investment strategy is discussed. Next we develop regime switching P-R systems to describe the abrupt structural changes in the economic fundamentals as well as the periodic switches in the parameters. The results for the regime switching P-R system are illustrated by means of two different approaches: markovian and arbitrary regime switching systems. Finally, we show how robust guaranteed cost control could be implemented to solve an optimal insurance problem. In each chapter, Linear Matrix Inequality (LMI) sufficient conditions are derived to solve the proposed sub-problems and numerical examples are given to illustrate the applicability of the theoretical findings

Secondary frequency stochastic optimal control in independent microgrids with virtual synchronous generator-controlled energy storage systems

With the increasing proportion of renewable energy in microgrids (MGs), its stochastic fluctuation of output power has posed challenges to system safety and operation, especially frequency stability. Virtual synchronous generator (VSG) technology, as one effective method, was used to smoothen frequency fluctuation and improve the system’s dynamic performance, which can simulate the inertia and damping of the traditional synchronous generator. This study outlines the integration of VSG-controlled energy storage systems (ESSs) and traditional synchronous generators so they jointly participate in secondary frequency regulation in an independent MG. Firstly, a new uncertain state-space model for secondary frequency control is established, considering the measurement noises and modelling error. Then, an improved linear quadratic Gaussian (LQG) controller is designed based on stochastic optimal control theory, in which the dynamic performance index weighting matrices are optimized by combining loop transfer recovery (LTR) technology and the distribution estimation algorithm. On the issue of secondary frequency devices’ output power allocation, the dynamic participation factors based on the ESS’s current state of charge (SOC) are proposed to prevent the batteries’ overcharging and overdischarging problems. The energy storage devices’ service life can be prolonged and OPEX (operational expenditure) decreased. Multiple experimental scenarios with real parameters of MGs are employed to evaluate the performance of the proposed algorithm. The results show that, compared with the lead-compensated-proportional-integral-derivative (LC-PID) control and robust μ-control algorithms, the proposed stochastic optimal control method has a faster dynamic response and is more robust, and the fluctuations from renewable energy and power loads can be smoothened more effectively

Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation

Copyright [2001] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.We investigate the robust filter design problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, unknown state time-delay, parameter uncertainties, and unknown nonlinear disturbances, which are all often encountered in practice and the sources of instability. The aim of this problem is to design a linear, delayless, uncertainty-independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the existence of desired robust exponential filters, which are derived in terms of the solutions to algebraic Riccati inequalities. The developed theory is illustrated by numerical simulatio

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited