Fully probabilistic adaptive control with arbitrary density functions of forward models and inverse controllers

Robust controllers for nonlinear systems with non Gaussian random inputs and uncertain parameters can be reliably designed using probabilistic methods. In this paper, a design approach based on the combination of robust stochastic adaptive method and mixture density network (MDN) is proposed for general nonlinear ARMAX models with uncertain parameters and with non-Gaussian random inputs. Using MDNs, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In simulations, we see that the proposed MDN stochastic adaptive control algorithm outperforms the conventional stochastic adaptive control methods.