Stochastic adaptive control of a continuous-time, linear periodic system with unknown baseline shift

Considers the problem of optimal control for a linear, time-varying system with periodic coefficients and quadratic cost in the case when an unknown periodic baseline shift is present. The author studies the estimation of this periodic parameter under arbitrary control inputs using a time-weighted least squares procedure. The author proves that the estimator converges a.s. to a piecewise constant approximation of the true parameter. The author then studies the problem of adaptive control using a certainty-equivalent controller based on this estimator. The author proves that this adaptive control is both admissible and ε-optimal. Finally, a simulation is included to illustrate the results herein