Model Predictive Controller for Piecewise Affine System

Abstract

This paper presents a hybrid procedure to solve Model Predictive Controller (MPC) for Piecewise Affine System (PWA) The approach presented here belong to the class of Branch and Bound (B&B) methods. The procedure uses the concepts of reachable set combined to the specific B&B methods, in order to reduce the number of Quadratic Problems (QP) needed to be solved by t he optimization algorithm.

Model predictive control techniques for hybrid systems

“…The structure of the MPC problem and the reachability analysis tools have been used in Peña et al (2003) to reduce the number of QP problems to be solved and for determining lower bounds to be used by branch and bounds algorithms in Peña et al (2005). Besides branch and bound methods, other solution methods have been investigated to implement MPC controllers.…”

Finite-horizon optimal control design for uncertain linear discrete-time systems

“…Therefore, existing works focus on searching for a feasible and suboptimal solution. Methods include graph search [17], [18], nonlinear programming [19], dynamic programming [20], model predictive control [8], and gradient decent [21]. For example, the study of optimal control of multi-region state-dependent switched systems appeared in [18] where the authors used branch-and-bound based model predictive control.…”

“…Methods include graph search [17], [18], nonlinear programming [19], dynamic programming [20], model predictive control [8], and gradient decent [21]. For example, the study of optimal control of multi-region state-dependent switched systems appeared in [18] where the authors used branch-and-bound based model predictive control. This combination of branch-and-bound and model predictive control still has a high computing demand.…”

Control Predictivo Sujeto a Restricciones Poliédricas No Convexas: Solución Explícita Y Estabilidad

“…A pesar de que existen diferentes métodos para realizar de manera eficiente la optimización anterior, como la basada en métodos Branch and Bound de [PCPC05], cuando el número de variables es elevado el coste computacional puede ser prohibitivo. Por ello, existen diferentes propuestas que tratan de obtener una solución explícita del problema de optimización, en analogía a lo realizado en la sección 2.3 para el control predictivo de sistemas lineales.…”