Predictive Control for Linear and Hybrid Systems [Bookshelf

Abstract

This book offers new insight in the realm of predictive control. The authors demonstrate how predictive control can be implemented in applications that were thought to be impossible when they started their collaboration about two decades ago. The book not only contains mature, and tried and tested, material but also the fundamentals necessary for understanding recent methods that have been receiving considerable interest in academia and industry. Depending on your perspective, predictive control can be seen as a subset or superset of classical optimal control or as something completely different. Here, predictive control is viewed as a modern optimal control method that builds on classical optimal control results, when possible. The main thesis in predictive control is that most practical control problems are naturally formulated as a sequence of infinite-dimensional, constrained, nonlinear optimal control problems, which are often impossible to solve. For example, in most applications, the optimal controller is not simply a linear, finite-dimensional dynamical system, as in proportional-integral-derivative, linear-quadratic Guassian, or H-infinity control, even if the model of the controlled system is linear and finite dimensional. The optimal control policy can be discontinuous, even if all the functions used to define the optimal control problem are smooth. Researchers in predictive control aim to understand these and other fundamental problems that naturally arise in applications, while finding practical and approximate solutions with appropriate guarantees. The book's emphasis is on the use of multiparametric programming to compute the explicit solution to the FHOCPs. It is divided into five parts: I) Basics of Optimization, II) Multiparametric Programming, III) Optimal Control, IV) Constrained Optimal Control of Linear Systems, and V) Constrained Optimal Control of Hybrid Systems. If readers started at the beginning and worked all the way to the end, they will have been introduced to a variety of fundamental and interesting topics in optimization, geometry, control, and dynamical systems theory that could be applied in a number of areas. In terms of a target audience, the book is suitable for both advanced undergraduate engineering students and in some cases, engineering postgraduates and above.