Optimal control of impulsive systems using adaptive critic based neural networks

This dissertation presents systematic computational tools for the optimal control synthesis of fixed-time and variable-time impulsive systems. Necessary conditions for optimality have been derived for a fixed-time and a variable-time impulsive system using the calculus of variations method. Properties of the costates and the states relation are studied and presented in theorems for the optimal control of a linear fixed-time impulsive system. Optimal control of a variable-time impulsive problem is investigated. A single neural network adaptive critic (SNAC) method for an impulsive system is developed. Algorithms are presented for calculating the optimal impulsive solutions in finite and infinite horizon cases. Since the construction of the networks and the synthesis of the controllers are relatively free of problem-specific assumptions, the method presented here is suitable for a wide range of real life nonlinear impulsive systems. Linear and nonlinear examples of impulsive systems with continuous and impulsive dynamics are considered for the proposed method and algorithms. The given examples show that the proposed method provides the optimal solution for finite and infinite horizon cases.