Resilient Control-Continuous Case

Abstract

An integral part of robust control system design methods has been based on using a fixed quadratic Lyapunov function in order to guarantee robust stability [17, 73]. An implicit assumption inherent in these design methods is that the controller will be implemented exactly. In the presence of uncertain parameters, it is often desirable to perform the control system design not only to ensure stability but also to guarantee an adequate level of system performance. This brings about the notion of guaranteed cost control (GCC) [103] and H8-control [17]. When attending to the controller implementation based on different control design methods, it turns out that the controllers are very sensitive ”fragile” with respect to errors in the controller coefficients. This is due to imprecision in analog-digital conversion, fixed word length, finite resolution instrumentation and numerical roundoff errors. It is considered beneficial that the designed (nominal) controllers should be capable of tolerating some level of controller gain variations. This illuminates the controller fragility problem as discussed in Chapter 1 and in the discussions to follows we address methods to overcome this problem.