ON A CLASS OF OPTIMAL-CONTROL PROBLEMS WITH STATE JUMPS

In this paper, we consider a class of optimal control problems in whic h the dynamical system involves a finite number of switching times tog ether with a state jump at each of these switching times. The location s of these switching times and a parameter vector representing the sta te jumps are taken as decision variables. We show that this class of o ptimal control problems is equivalent to a special class of optimal pa rameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computatio nal algorithm is proposed. For illustration, a numerical example is in cluded.