Design of penalty functions for optimal control of linear dynamical systems under state and input constraints

Paul Malisani (1, 2) , François Chaplais (1) , Nicolas Petit (1)

1 CAS - Centre Automatique et Systèmes
2 EDF R&D ENERBAT - Energie dans les Bâtiments et les Territoires

This paper addresses the problem of solving a constrained optimal control for a general single-input single output linear time varying system by means of an unconstrained method. The exposed methodology uses a penalty function approach, commonly considered in finite dimensional optimization problem, and extended here it to the considered infinite dimensional (functional optimization) case. The main novelty is that both the bounds on the control variable and on a freely chosen output variable are considered and studied theoretically. It is shown that a relatively simple and constructive choice of penalty functions allows to completely alleviate the usual difficulties of handling such constraints in optimal control. An illustrative example is provided to show the potential of the method.

Domaines: Automatique / Robotique

Paul Malisani, François Chaplais, Nicolas Petit. Design of penalty functions for optimal control of linear dynamical systems under state and input constraints. 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 2011, Dec 2011, Orlando, United States. pp.6697 - 6704, ⟨10.1109/CDC.2011.6160718⟩. ⟨hal-00676305⟩