Single network adaptive critic aided nonlinear dynamic inversion

Abstract

Approximate Dynamic Programming (ADP) offers a systematic method of optimal control design for nonlinear systems. Of the many architectures based on ADP, Adaptive Critic (AC) is the most popular. An AC consists of two neural networks that interactively train each other to arrive at the optimal control solution. Single Network Adaptive Critic (SNAC) is an improvement over the AC. As the name suggests, it consists of only one network but, at the same time, achieves faster convergence to the optimal solution. The advantages of SNAC have been harnessed very well in optimal state regulation applications. However, literature concerning the direct use of SNAC in command following applications seems sparse. This is probably because of the fact that it is practically difficult to anticipate a proper training domain to train the SNAC neural network when the commands are not known a-priori. Nonlinear Dynamic Inversion (NDI) is a sub-optimal, nonlinear control design method that offers a closed form solution. The ease of implementation and the ability to use NDI control readily for regulating and command following applications make it a very popular control design method in a wide area of applications. However, it lacks the formalism and advantages of optimal control design principles. In this dissertation, we present a novel hybrid technique of nonlinear design that retains the advantages of both SNAC and NDI and, at the same time, makes SNAC extendable to command following applications to achieve near-optimal responses and relates NDI to optimal control design principles. We also present in this dissertation an extended architecture that adapts online to system inversion errors, parameter estimation error and reduced control effectiveness. The versatility of the new technique is demonstrated by considering five nonlinear systems of increasing complexity, including the longitudinal aircraft system.