Robust control of linear systems: a min-max reinforcement learning formulation

In this paper, an online robust controller based on a min-max reinforcement learning approach for linear systems is discussed. Disturbances are represented by external signals coupled with the control input which are assumed to be bounded within a set of admissible disturbances. The proposed controller implements a min-max approach which realizes a smooth transition between optimal and robust controllers. Lyapunov stability theory is used to assess the stability and boundedness of the min-max robust formulation. A neural reinforcement learning architecture is used to obtain an approximation of the parameters associated to the optimal cost. Simulations are carried out to validate the proposed approach.