Optimal Guaranteed Cost Tracking of Uncertain Nonlinear Systems Using Adaptive Dynamic Programming with Concurrent Learning

Abstract

In this paper, based on adaptive dynamic programming (ADP) with concurrent learning, the problem of optimal guaranteed cost tracking is studied for a class of uncertain continuous-time nonlinear systems. First, the original uncertain system and a reference system are combined into an augmented uncertain system, and the performance index is transformed into the corresponding augmented form. Afterwards, the solution of the optimal control problem consisting of the nominal augmented system with the modified performance index is proven to be the optimal guaranteed cost tracking control law of the original uncertain system. Moreover, a concurrent learning tuning algorithm based on ADP is presented to approximate the solution of corresponding Hamilton-Jacobi-Bellman (HJB) equation, which relaxes the condition of persistent excitation (PE). A neural network-based approximate optimal guaranteed cost tracking design is developed not only to ensure tracking error convergence to zero for all admissible uncertainties but also to achieve the minimal guaranteed cost. Finally, two simulation examples are considered to verify the effectiveness of the theoretical results.