Resilient control of uncertain dynamical systems.
The monograph consisting of seven chapters, appendix, references, and index deals with the design of non-fragile control and filtering for uncertain delayed dynamic systems. The fragility problem means that a robust controller can be very sensitive to even small changes in the controller coefficients. Chapter 1 introduces the fragility problem. Chapter 2 presents the state-space design of resilient dynamic output controllers for continuous-time (abbr. CT) uncertain state-delayed systems including guaranteed cost control and \(H_{\infty}\) approaches. Both norm-bounded and convex polytopic system uncertainties are included. Additive and multiplicative gain uncertainties are considered. Necessary and sufficient conditions for the robust quadratic stability of closed-loop CT systems are given. Chapter 3 is focused on the resilient controllers with both types of gain variations for discrete-time (abbr. DT) systems with norm-bounded uncertainties. Necessary and sufficient conditions for the robust quadratic stability of closed-loop DT systems are given. The stabilization schemes are based on guaranteed cost control and \(H_{\infty}\) approaches. Chapter 4 addresses the problem of resilient adaptive control for uncertain CT and DT state-delayed systems. Adaptive control schemes include both known and unknown gain perturbation bounds. Chapter 5 deals with robust non-fragile filtering for uncertain CT systems with norm-bounded uncertainties for both types of filter gain perturbations. A resilient \(\mathbf{L}_2-\mathbf{L}_{\infty}\) filter for uncertain state-delayed with polytopic uncertainties is presented. Resilient filter synthesis is developed for both delay-independent and delay-dependent cases. Chapter 6 is focused on delay-dependent methodologies for CT and DT systems. A descriptor approach to simultaneous \(H_2/H_{\infty}\) controller design is developed for CT systems with polytopic uncertainties and both types of gain perturbations. Feedback stabilization is presented for the DT state-delayed systems. Chapter 7 examines nonlinear CT and DT state-delayed systems. The robust stabilization using resilient control design is addressed. The trade-off between the size of controller gain and the bounds on nonlinearities is incorporated into the design. Some relevant mathematical tools are surveyed in the appendix. The monograph essentially contributes to a more comprehensive understanding of resilient control design and filtering. Unfortunately, there are some typos. A list of corrections would be useful. All results are given using the LMIs including numerous numerical examples. The book is an excellent self-contained up-to-date resource of working knowledge in the field. The monograph will be useful as graduate-level textbook in applied mathematics as well as control, electrical, civil, chemical, and mechanical engineering or a reference for researchers, practitioners, and interested readers interested in this challenging research subject.
scientific article; zbMATH DE number 2118883