A neuro‑observer‑based optimal control for nonaffine nonlinear systems with control input saturations

In this study, an adaptive neuro-observer-based optimal control (ANOPC) policy is introduced for unknown nonaffinenonlinear systems with control input constraints. Hamilton–Jacobi–Bellman (HJB) framework is employed to minimize anon-quadratic cost function corresponding to the constrained control input. ANOPC consists of both analytical and algebraicparts. In the analytical part, first, an observer-based neural network (NN) approximates uncertain system dynamics,and then another NN structure solves the HJB equation. In the algebraic part, the optimal control input that does not exceedthe saturation bounds is generated. The weights of two NNs associated with observer and controller are simultaneouslyupdated in an online manner. The ultimately uniformly boundedness (UUB) of all signals of the whole closed-loop systemis ensured through Lyapunov’s direct method. Finally, two numerical examples are provided to confirm the effectiveness ofthe proposed control strategy.