An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints

The paper develops a robust control approach for nonaffine nonlinear continuous systems with input constraints and unknown uncertainties. Firstly, this paper constructs an affine augmented system (AAS) within a pre-compensation technique for converting the original nonaffine dynamics into affine dynamics. Secondly, the paper derives a stability criterion linking the original nonaffine system and the auxiliary system, demonstrating that the obtained optimal policies from the auxiliary system can achieve the robust controller of the nonaffine system. Thirdly, an online adaptive dynamic programming (ADP) algorithm is designed for approximating the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, the gradient descent approach and projection approach are employed for updating the actor-critic neural network (NN) weights, with the algorithm’s convergence being proven. Then, the uniformly ultimately bounded stability of state is guaranteed. Finally, in simulation, some examples are offered for validating the effectiveness of this presented approach.