A pruning algorithm for managing complexity in the solution of a class of linear non-quadratic regulator problems

This paper develops an efficient computational method for solving a class of discrete time linear regulator problems, in which the payoff functions are not necessarily quadratic. The proposed method exploits the convexity of the payoff functions and approximates the attendant value function via a max-plus sum of affine functions. As the number of affine functions represented in this approximation can grow exponentially with the number of iterations of the computational method, effective pruning algorithms to manage complexity are essential. Two such algorithms are developed in this work. The utility of these algorithms is demonstrated via an example.