Analysis and Approximation of the Infinite Horizon Problem With Impulsive Controls
Fabio Camilli, Maurizio Falcone · 1996
In this paper we study an infinite horizon control problem where the dynamics involves an ordinary control v, an impulsive control u and its derivative u. A new reparametrization of the problem is introduced adding one variable to the state space. The new system can be treated with the techniques developed for optimal control problems involving only controls in L 1 and its value function coincides with the value function of the original problem. This correspondence also helps in the construction of an approximation scheme, based on a discrete dynamic programming principle, which will be proved to converge to the value function. 1991 Subject Classification. Primary 49N25; Secondary 65M12, 49L20. Key words. Impulsive control, viscosity solutions, approximation schemes. 1 Introduction We will consider a slow growth control problem with controlled dynamics in IR n given by ae x(t) = f(x; u; v; u) t 2 [0; +1[ x(0) = x; u(0) = u (1) where u : [0; +1[! U and v : [0; +1[! V are ...