Minimized Tracking Error Randomness Control for Nonlinear Multivariate and Non-Gaussian Systems Using the Generalized Density Evolution Equation

In this technical note, a new stochastic control algorithm is presented for nonlinear and non-Gaussian continuous-time systems. Based on the recently developed generalized density evolution equation, which is more tractable than the classical Liouville equation, the relationship is established among the probability density function (PDF) of tracking error, control input and disturbances. An improved performance index is then constructed for this stochastic control strategy, which includes quadratic information potential of the tracking error, mean value of squared tracking error and constraints on the control input energy. By minimizing the performance index, a recursive optimal control algorithm is obtained using the gradient descent method. Moreover, the statistical linearization technique is adopted to formulate the boundedness condition of the closed-loop system. An illustrative example is given to demonstrate the validity and efficiency of the proposed stochastic optimal control methodology.