Optimal control of hybrid systems with polynomial impulses
We address an optimal control problem for a measure driven hybrid dynamical system. The impulsive dynamics is due to the BV -relaxation (the compactification of the trajectory tube in the weak topology of the space BV of functions of bounded variation) of a dynamical system with polynomial dependence on a control variable in the right-hand side under the constraint on the norm of a control in the Lebesgue space Lp. The relaxed system is described by a certain measure differential equation. The hybrid feature is expressed in the presence of “nonstandard mixed constraints”. The latter term is used to name asymptotic constraints relating the state and the measure, and these conditions are formulated as constraints on one-sided limits of a solution to the measure differential equation. The main result is an equivalent transformation of the considered model to a usual optimal control problem. To this end we propose a special space-time transformation technique.
CYBERNETICS AND PHYSICS, Vol. 4, No. 1. 2015, 11-16.