MTN Optimal Control of SISO Nonlinear Time-varying Discrete-time Systems for Tracking by Output Feedback

MTN optimal control scheme of SISO nonlinear time-varying discrete-time systems based on mufti-dimensional Taylor network (MTN) is proposed to achieve the real-time output tracking control for a given reference signal. Firstly, an ideal output signal is selected and Pontryagin minimum principle adopted to obtain the numerical solution of the optimal control law for the system relative to the ideal output signal, with the corresponding optimal output termed as desired output signal. Then, MTN optimal controller (MTNC) is generated automatically to fit the optimal control law, and the conjugate gradient (CG) method is employed to train the weight parameters of MTNC offline to acquire the initial weight parameters of MTNC for online training that guarantees the stability of dosed-loop system. Finally, a four-term back propagation (BP) algorithm with a second order momentum term and error term is proposed to adjust the weight parameters of MTNC adaptively to implement the output tracking control of the systems in real time; the convergence conditions for the four-term BP algorithm are determined and proved. Simulation results show that the proposed MTN optimal control scheme is valid; the system's actual output response is capable of tracking the given reference signal in real time.