An Improved Adaptive Optimal Regulation Framework with Robust Control Synthesis

In this chapter, we focus on developing adaptive optimal regulators for a class of continuous-time nonlinear dynamical systems through an improved neural learning mechanism. The main objective lies in that establishing an additional stabilizing term to reinforce the traditional training process of the critic neural network, so that to reduce the requirement with respect to the initial stabilizing control, and therefore, bring in an obvious convenience to the adaptive-critic-based learning control implementation. It is exhibited that by employing the novel updating rule, the adaptive optimal control law can be obtained with an excellent approximation property. The closed-loop system is constructed and its stability issue is handled by considering the improved learning criterion. After that, we apply the adaptation-oriented approximate optimal control strategy to perform robust stabilization when including complex nonlinearity and uncertainty. By considering the dynamical uncertainties, it is proven that the developed near-optimal control law can achieve uniform ultimate boundedness of the closed-loop state vector, thereby guaranteeing a certain extent of robustness for the uncertain nonlinear plant. Simulation for a classical nonlinear system and experiment on an overhead crane are conducted to verify the efficient performance of the present design methods, especially the major role that the stabilizing term performed.