Projeto de controladores com complexidade reduzida para sistemas lineares sujeitos a restrições usando análise de agrupamentos de dados

Abstract

Controller design for discrete-time linear systems subject to constraints can be carried out based on the concept of invariant sets, together with the solution of multiparametric programming problems. Such a solution is represented by a set of polyhedral regions associated to a Piecewise Affine (PWA) control law. However, for high-order systems, the multiparametric linear programming technique may result in controllers of high complexity, which require a hardware with great storage capacity in the memory and high processing power due to the a high number of polyhedral regions defining the PWA law. In this work we propose a number of numerical methods which aim to reduce the complexity of such controllers. To this end, the concept of invariant sets and the K q-flat data cluster analysis algorithm are applied. First, we show that the K q-flat algorithm can be used to establish a smaller number of polyhedral regions associated to a PWA state feedback control law. Then, this approach is extended to the design of static output feedback controllers for constrained systems and of state observers with error limitation. In addition, optimization problems are proposed to compute a suboptimal PWA law capable of further reducing the number of polyhedral regions. The results we present show that the proposed approaches are able to compute PWA laws with a smaller number of polyhedral regions when compared with the multiparametric solution, strongly reducing the computational cost associated to their implementation.