Learning Control of Linear System Having Unknown Random Variation of Dynamic Character

Abstract

The learning control synthesis is discussed for the noisy linear sampled-data system, the dynamic characteristics of which fluctuates in such a way as follows.
1) The form of the state-transition equation of the system fluctuates within the different forms which are given in advance.
2) The probability taking each one of the given forms is assumed to a random variable with an unknown probability density function.
The learning control problem is reduced to the stochastic control one with estimating the probability distribution of the random variables determining the form of the state-transition equtaion. In this paper, this probability distribution is determined from the joint probability density function of those random variables and the state variables of the system, and this joint probability density function is computed from a prior joint probability density function according to the Bayes rule.
By this learning control process, the system minimizes the conditional expectation of the quadratic form of state and control vectors.