Stability Analysis for Incremental Adaptive Dynamic Programming with Approximation Errors

This paper provides a convergence and stability analysis of the incremental value iteration algorithm under the influence of various errors. Incremental control is firstly used to linearize the continuous-time nonlinear system, recursive least squares (RLS) identification is then introduced to identify the incremental model online. Based on the incremental model, the value iteration algorithm is used to design an optimal adaptive controller, with an analytical optimal control law. Moreover, the convergence of the developed incremental value iteration algorithm is proved. The stability of the controller is analyzed using Lyapunov stability theory. Finally, a flight control simulation verifies the robustness of the controller to various initial conditions, as well as adaptation to actuator faults.