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We present a set of model-free, reduced-dimensional reinforcement learning(RL) based optimal control designs for linear time-invariant singularlyperturbed (SP) systems. We first present a state-feedback and output-feedbackbased RL control design for a generic SP system with unknown state and inputmatrices. We take advantage of the underlying time-scale separation property ofthe plant to learn a linear quadratic regulator (LQR) for only its slowdynamics, thereby saving a significant amount of learning time compared to theconventional full-dimensional RL controller. We analyze the sub-optimality ofthe design using SP approximation theorems and provide sufficient conditionsfor closed-loop stability. Thereafter, we extend both designs to clusteredmulti-agent consensus networks, where the SP property reflects throughclustering. We develop both centralized and cluster-wise block-decentralized RLcontrollers for such networks, in reduced dimensions. We demonstrate thedetails of the implementation of these controllers using simulations ofrelevant numerical examples and compare them with conventional RL designs toshow the computational benefits of our approach.

Reduced-Dimensional Reinforcement Learning Control using Singular Perturbation Approximations