Introduction

Abstract

The ultimate goal of a control system designer is to build a system that will work in a real environment. Since the real environment may change and operating conditions may vary from time to time, the control system must be able to withstand these variations. Even if the environment does not change, other factors of life are the model uncertainties as well as noises. Any mathematical representation of a system often involves simplifying assumptions. Nonlinearities are either unknown and hence unmodeled, or are modeled and later ignored in order to simplify analysis. High frequency dynamics are often ignored at the design stage as well. In consequence, control systems designed based on simplified models may not work on real plants in real environments. The particular property that a control system must possess for it to operate properly in realistic situations is commonly called robustness. Mathematically, this means that the controller must perform satisfactorily not just for one plant, but for a family of plants. If a controller can be designed such that the whole system to be controlled remains stable when its parameters vary within certain expected limits, the system is said to possess robust stability. In addition, if it can satisfy performance specifications such as steady state tracking, disturbance rejection and speed of response requirements, it is said to possess robust performance. The problem of designing controllers that satisfy both robust stability and performance requirements is called robust control. Optimization theory is one of the cornerstones of modern control theory and was developed in an attempt to solve such a problem. In a typical control system design, the given specifications are at first transformed into a performance index, and then control laws which would minimize some norm, say H ₂ or H _∞ norm of the performance index are sought. This book focusses on the H _∞ optimal control theory.