Controle por realimentação de saída de sistemas lineares sob restrições com redução do conjunto terminal

Abstract

Controlled invariant sets have been widely used to solve constrained systems problems. Although it has already been well studied in state feedback control, the use of controlled invariant sets for output feedback still lacks further exploration. Since in many situations, system states are not available, the theory of invariant sets has been extended to the output feedback structure, and necessary and sufficient conditions have been established to assess whether a given polyhedral set is invariant under output feedback. In addition to the static output feedback strategy, it is also possible to apply a dynamic output feedback, a strategy in which a state observer is incorporated into the compensator structure, in order to obtain a dynamic compensator. In this case it is possible to build an output feedback controlled invariant set from a conditioned invariant set and a controlled invariant set, so it is possible to reduce the uncertainty of states using the contraction of the conditioned invariant set In this work we propose an improvement in the design of output feedback controllers using invariant sets. A possible control strategy for the output feedback is to minimize, one step ahead, the distance of the admissible states to the origin. Here we propose the optimization of this strategy by using the result of the linear programming problem as an additional information to compute the next control action. By doing that it is possible to reduce the set of possible states and, as a consequence, improve the states convergence. There will be presented the results obtained from the optimization strategy using a hypercube around the origin and a homothetic set in relation to the controlled invariant set as a target for the optimization of the distance to the origin. First, the theory of invariant sets and its application in state feedback control will be presented. Then, the strategies for static and dynamic output feedback will be presented without the use of additional information on the computation of the control action. Finally, the design of dynamic and static output feedback controllers using the optimization strategies with the additional information of the hypercube and the homothetic set will be presented. The results obtained through these strategies will be ilustrated by nnumerical examples.