Optimal controller synthesis of variable-time impulsive problems using single network adaptive critics

This paper presents a systematic approach to solve for the optimal control of a variable-time impulsive system. First, optimality condition for a variable-time impulsive system is derived using the calculus of variations method. Next, a single network adaptive critic technique is proposed to numerically solve for the optimal control and the detailed algorithm is presented. Finally, two examples-one linear and one nonlinear-are solved applying the conditions derived and the algorithm proposed. Numerical results demonstrate the power of the neural network based adaptive critic method in solving this class of problems.