Research ArticleImproved single neuron controller for multivariable stochastic systems with non-Gaussianities and unmodeled dynamics

- (h,ϕ)-entropy is adopted to formulate the generalized MEE criterion.
- The stochastic estimation of (h,ϕ)-entropy is obtained using “sliding window” technique.
- Stochastic gradient method is used to get the optimal weighting matrix.
- The presented approach relies on system measurements instead of the plant model.

In this paper, a new adaptive control approach is presented for multivariate nonlinear non-Gaussian systems with unknown models. A more general and systematic statistical measure, called (h,ϕ)-entropy, is adopted here to characterize the uncertainty of the considered systems. By using the “sliding window” technique, the non-parameter estimate of the (h,ϕ)-entropy is formulated. Then, the improved neuron based controllers are developed for multivariate nonlinear non-Gaussian systems by minimizing the entropies of the tracking errors in closed loops. The condition to guarantee the strictly decreasing entropy of tracking error is presented. Moreover, the convergence in the mean-square sense has been analyzed for all the weights in the neural controllers. Finally, the comparative simulation results are presented to show that the performance of the proposed algorithm is superior to that of PID control strategy.