Adaptive Near-Optimal Control of Uncertain Systems with Application to Underactuated Surface Vessels

In this paper, a unified online adaptive near-optimal control framework is proposed for linear and nonlinear systems with parameter uncertainty. Under this framework, auxiliary systems converging to the unknown dynamics are constructed to approximate and compensate the parameter uncertainty. With the aid of the auxiliary system, future outputs of the controlled system are predicted recursively. By utilizing a predictive time-scale approximation technique, the nonlinear dynamic programming problem for optimal control is significantly simplified and decoupled from the parameter learning dynamics: the finite-horizon integral-type objective function is simplified into a quadratic one relative to the control action and there is no need to solve time-consuming Hamilton equations. Theoretical analysis shows that closed-loop systems are asymptotically stable. It is also proved that the proposed adaptive near-optimal control law asymptotically converges to the optimal. The efficacy of the proposed framework and the theoretical results are validated by an application to underactuated surface vessels.