Optimal Control for Positive Systems Using Linear Programming

This brief presents a class of optimal control for positive systems with linear nonnegative costs. First, a novel approach combining value iteration and policy iteration is presented to solve the optimal problems. The conditions are provided under which the solutions to Bellman function are unique. Then, the controller is proposed to reach the positivity and stability of the system by linear programming. In addition, a model-based reinforcement learning algorithm is developed to be insensitive to probing noise. Finally, an illustrative example is given to validate the efficacy of the proposed design.