Single Network Adaptive Critic aided nonlinear dynamic inversion for suboptimal command tracking

Using the Approximate Dynamic Programming (ADP) approach, nonlinear optimal control problems can be solved by using a dual neural network architecture called the Adaptive Critic (AC). A Single Network Adaptive Critic (SNAC) architecture has been shown to have much faster convergence than AC. Even though the SNAC offers a systematic optimal control design method for optimal state regulation for a class of nonlinear control systems, it lacks the generality necessary for command tracking as it is practically difficult to anticipate a proper training domain in state space when the command sequence is not known a priori. Dynamic Inversion (DI), on the other hand, is a very popular nonlinear control design method for both output regulation and command tracking that offers a closed form expression for control. However, it lacks the interpretation and advantages of optimal control design. In this paper we propose a systematic technique for selecting the DI gains with the help of a pre-synthesized SNAC network in order that the resulting DI solution closely mimics the SNAC solution for output regulation and can be extended to command tracking problems. Moreover, it retains all the benefits of DI design. The potential of this new methodology of near-optimal dynamic inversion design is demonstrated in this paper by considering a benchmark nonlinear system.