Optimal guaranteed cost control of uncertain non-linear systems using adaptive dynamic programming with concurrent learning

In this study, the authors study the optimal guaranteed cost control problem for a class of non-linear uncertain systems based on adaptive dynamic programming (ADP) with concurrent learning. A neural network-based approximate optimal guaranteed cost control design is developed not only to ensure the system stability for all admissible uncertainties but also to achieve a minimal guaranteed cost. First, the optimal guaranteed cost control problem is transformed into an optimal control problem of the nominal system by properly modifying the cost function to account for all possible uncertainties. Then based on ADP, an adaptive optimal learning algorithm is proposed for the nominal system by using a single critic network with concurrent learning to approximate the solution of Hamilton-Jacobi-Bellman equation. To relax the demands of the persistence of excitation condition, the recorded past data are used simultaneously with the current data for the adaptation of the critic network weights. Besides, an additional adjusting term is employed to stabilise the system and relax the requirement for an initial stabilising control. Moreover, uniform ultimate boundedness of the closed-loop system is guaranteed by using the Lyapunov approach. Finally, three simulation examples are provided to demonstrate the effectiveness of the proposed approach.