Dynamic Multiobjective Control for Continuous-Time Systems Using Reinforcement Learning

This paper presents an extension of the reinforcement learning algorithms to design suboptimal control sequences for multiple performance functions in continuous-time systems. The first part of the paper provides the theoretical development and studies the required conditions to obtain a state-feedback control policy that achieves Pareto optimal results for the multiobjective performance vector. Then, a policy iteration algorithm is proposed that takes into account practical considerations to allow its implementation in real-time applications for systems with partially unknown models. Finally, the multiobjective linear quadratic regulator problem is solved using the proposed control scheme and employing a multiobjective optimization software to solve the static optimization problem at each iteration.