Optimal output-feedback tracking of SISO stochastic nonlinear systems using multi-dimensional Taylor network

The randomness and nonlinearity of stochastic nonlinear systems increase computational complexity and impede their tracking performance. However, randomness and nonlinearity are inevitable in practical applications, and the existing methods can hardly achieve the desirable control effect, especially in real-time control. For this end, a new network control strategy based on multi-dimensional Taylor network (MTN), whose design depends only on the system output, is put forward to solve the optimal output-feedback tracking problem of the SISO stochastic nonlinear systems. The network structure of the MTN is given first, and its approximation properties are proven. Based on the quadratic cost function design learning algorithm, the tracking error is minimized to update the controller parameters, and the desired tracking performance is obtained. Using the Lyapunov stability theorem, it is proved that the corresponding closed-loop system is bounded in the sense of probability and it can be ensured that the output tracking error converges to a small residual set around the origin in the sense of probability. An example is provided to illustrate the effectiveness of the proposed design approach. Comparative simulation study reveals that the proposed solution promises desirable real-time dynamic performance.