Fixed final-time near optimal regulation of nonlinear discrete-time systems in affine form using output feedback

In this paper, the fixed final-time near optimal output regulation of affine nonlinear discrete-time systems with unknown system dynamics is considered. First, a neural network (NN)-based observer is proposed to reconstruct both the system state vector and control coefficient matrix. Next, actor-critic structure is utilized to approximate the time-varying solution of the Hamilton-Jacobi-Bellman (HJB) equation or value function. To satisfy the terminal constraint, a new error term is defined and incorporated in the NN update law so that the terminal constraint error is also minimized over time. A NN with constant weights and time-dependent activation function is employed to approximate the time-varying value function which subsequently is utilized to generate the fixed final time near optimal control policy due to NN reconstruction errors. The proposed scheme functions in a forward-in-time manner without offline training phase. The effectiveness of the proposed method is verified via simulation.