Stability and optimization of control systems

Abstract

This project aims at studying two classes of control systems:classical control problems and impulsive control systems. Asregards classical control systems the purpose is look at optimalproblems with mixed constraints in the state and in the controlvariables and provide necessary optimality conditions in the formof the strong maximum principle of Pontryagin for problems withfinite horizon. Then look at problems of the same kind but withinfinite horizon and extend the necessary conditions to this classof problems. Regarding the second class of problems, the impulsiveones, we first aim at proving existence of smooth impulsivefeedback control for the impulsive control system and secondlyproviding necessary optimality conditions for the impulsivecontrol problem. This part will depend on the optimalityconditions obtained for the classical optimal control problem withmixed constraints. (AU)