Abstract
This chapter presents online solutions to the optimal H∞ tracking of nonlinear systems to attenuate the effect of disturbance on the performance of the systems. To obviate the requirement of the complete knowledge of the system dynamics, reinforcement learning (RL) is used to learn the solutions to the Hamilton–Jacobi–Isaacs equations arising from solving the H∞ tracking problem. Off-policy RL algorithms are designed for continuous-time systems, which allows the reuse of data for learning and consequently leads to data efficient RL algorithms. A solution is first presented for the H∞ optimal tracking control of affine nonlinear systems. It is then extended to a special class of nonlinear nonaffine systems. It is shown that for the nonaffine systems existence of a stabilizing solution depends on the performance function. A performance function is designed to assure the existence of the solution to a class of nonaffine system, while taking into account the input constraints.
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