Online Algorithms and Policies Using Adaptive and Machine Learning Approaches

This paper considers the problem of real-time control and learning in dynamic systems subjected to parametric uncertainties. A combination of Adaptive Control (AC) in the inner loop and a Reinforcement Learning (RL) based policy in the outer loop is proposed such that in real-time the inner-loop AC contracts the closed-loop dynamics towards a reference system, and as the contraction takes hold, the RL in the outerloop directs the overall system towards optimal performance. Two classes of nonlinear dynamic systems are considered, both of which are control-affine. The first class of dynamic systems utilizes equilibrium points with expansion forms around these points and employs a Lyapunov approach while second class of nonlinear systems uses contraction theory. AC-RL controllers are proposed for both classes of systems and shown to lead to online policies that guarantee stability using a high-order tuner and accommodate parametric uncertainties and magnitude limits on the input. In addition to establishing a stability guarantee with real-time control, the AC-RL controller is also shown to lead to parameter learning with persistent excitation for the first class of systems. Numerical validations of all algorithms are carried out using a quadrotor landing task on a moving platform. These results point out the clear advantage of the proposed integrative AC-RL approach.