Optimal Control of Affine Nonlinear Continuous-time Systems

In this paper, the optimal regulation and tracking control of affine nonlinear continuous-time systems with known dynamics is undertaken using a novel single online approximator (SOL)-based scheme. The SOLA-based adaptive approach is designed to learn the infinite horizon continuous-time Hamilton-Jacobi-Bellman (HJB) equation and its corresponding optimal control input. A novel parameter tuning algorithm is derived which not only ensures the optimal cost (HJB) function and control input are achieved, but also ensures the system states remain bounded during the online learning process. Lyapunov techniques show that all signals are uniformly ultimately bounded (UUB) and the approximated control signal approaches the optimal control input with small bounded error. In the absence of OLA reconstruction errors, asymptotic convergence to the optimal control is shown. Simulation results illustrate the effectiveness of the approach.