A nearly optimal control approach for uncertainty input-delay systems based on adaptive dynamic programming

This paper concerned with a nearly optimal control approach based on adaptive dynamic programming technique to solve robust control problem of the neutral type time-delay systems, taking parameter uncertainties and input delay into account. Based on the neural network (NN)-based adaptive dynamic programming and Lyapunov-Razumikhin theorems, the robust control design problem can be equivalently transformed into a nearly optimal control problem, and the amount of matched uncertainties are indirectly reflected in the performance index. A nearly optimal control is designed to approximate the costate function of the Hamilton-Jacobi-Isaaca (HJI) equation by NN-based adaptive dynamic programming scheme. By algebraic inequalities and appropriate uncertainty descriptions, sufficient conditions are derived under which not only the uncertain input-delay dynamical systems can achieve asymptotic stability, but also acquire the guaranteed level of performance for regulation. Simulation example is performed to demonstrate the effectiveness of the proposed approaches.