OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

 Design of set-invariant observers for linear discrete-time systems

Carlos E. T. Dorea
Universidade Federal da Bahia, Brazil

The concept of set-invariance has been intensively used the last years to solve control problems with constraints. In particular, if the constraints are given by a set of linear inequalities, it is possible to construct a controlled invariant set contained in the polyhedron defined by the constraints, such that a suitable sequence of control inputs can be computed to enforce the constraints along the state trajectory.

Based on this concept, we recently proposed a solution for the dual problem, i.e. the design of full-order state observers with limitation of the estimation error. Conditions were established under which a given polyhedral set defined on the estimation error space is invariant, in the sense that the error trajectory can be kept in this set by means of a suitable output injection. Then, we addressed the problem of computing an invariant polyhedron which bounds as much as possible the trajectory of the estimation error, given a polyhedral set of possible initial states.

In this talk, we present the basic technique and discuss some important issues, such as convergence and computational effort of the proposed algorithms, minimality of the computed invariant sets and the computation of the output injection. We conclude by discussing the potential application of the results to the solution of control problems with constraints via output feedback.

Slides