An Online Nonlinear Optimal Controller Synthesis for Aircraft with Model Uncertainties

Abstract

In this paper, a new neural network approach/architecture, called the ―Cost Function Based Single Network Adaptive Critic (J-SNAC)‖ is presented to solve difficult nonlinear control problems. This approach is applicable to a wide class of nonlinear systems where the optimal control equation can be explicitly expressed in terms of the state and cost variables. After the training‘, the output of the neural network represents the optimal cost for a quadratic cost function. This neural network is synthesized by solving the equations associated with an optimal control problem for a control-affine nonlinear system. Optimal control is obtained by finding the derivatives of the output of the network with respect to its input and using it in the expression for optimal control. Development of this algorithm is presented in paper with an approximate dynamic programming (ADP) formulation. Synthesis of an optimal neurocontroller for the nominal system is described first. The optimal controller synthesis includes an approximated system‘ which contains with an estimate of the uncertainties. The cost network is updated at every step to account for the uncertainties and help provide optimal control for the changed plant. An aircraft control problem has been solved with the J-SNAC approach in this paper. Flight control of an F-16 short-period mode is synthesized in which the dynamic nonlinearities are dependent not only on the states of the system, but also on the control inputs.