Optimal stochastic adaptive control with quadratic index

Abstract

The discrete-time stochastic control system with complete observation is considered with quadratic loss function when the constant coefficients of the system are unknown. The parameter estimates given by the recursive least-squares method are used to define the feedback gain, and the adaptive control is taken to be either a linear-state feedback disturbed by a sequence of random vectors with variances tending to zero or only the disturbance without the feedback term in accordance with stopping times defined on the trajectory of the system. It is proved that the parameter estimates are strongly consistent and the loss function reaches its minimum, i.e. the adaptive control is optimal.