Parameter Estimation and Pole-Placement Control of Time-Varying Plants

In this paper we consider the pole placement and adaptive pole placement control problem of linear time-varying plants with smooth parameters. First, we propose a new controller structure that guarantees the closed loop stability and meets the control objective exactly independent of the speed of variation of the plant parameters. We then design an adaptive estimator that can use any available a priori knowledge about the structure of the plant parameter variations to improve the quality of the parameter estimates. Finally, employing the certainty equivalence principle, we develop an indirect adaptive pole placement scheme for time-varying plants that guarantees the closed-loop stability, provided that only the variation of the unstructured (unknown) part of the parameters is slow, while the overall plant may be fast time-varying.