Self-learning optimal guaranteed cost control of input-affine continuous-time nonlinear systems under uncertain environment

In this paper, we investigate the self-learning optimal guaranteed cost control problem of input-affine continuous-time nonlinear systems possessing dynamical uncertainty. The cost function related to the original uncertain system is discussed sufficiently, with the purpose of developing the optimal guaranteed cost and the corresponding feedback control input. Through theoretical analysis, the optimal guaranteed cost control problem is transformed into designing an optimal controller of the nominal system with a newly defined cost function. The policy iteration algorithm is employed to conduct the learning process and a critic neural network is built, serving as the approximator, to implement the algorithm conveniently. The main idea comes from adaptive dynamic programming (ADP), which is regarded as a self-learning optimal control approach with a certain degree of human brain intelligence. The performance of the control strategy is verified via a simulation example. The established method provides a combination of ADP and robust control design, which enhances the scope of ADP study to nonlinear systems under uncertain environment.