Adaptive controller design and disturbance attenuation for SISO linear systems with noisy output measurements and partly measured disturbances

Abstract

In this article, we present robust adaptive controller design for SISO linear systems with noisy output measurements and partly measured disturbances. Using the worst-case analysis approach, we formulate the robust adaptive control problem as a non-linear H ^∞-optimal control problem under imperfect state measurements and solve it using game theory. The design paradigm is the same as (Pan, Z. and Başar, T., 1998, Adaptive Controller Design for Tracking and Disturbance Attenuation for SISO Linear Systems with Noisy Output Measurements, CSL report, Urbana, IL: University of Illinois at Urbana-Champaign) with the only difference being the treatment of the measured disturbances. The same result as (Pan and Başar l998) is achieved. In addition, when the relative degrees from the measured disturbances to the output are no less than that from the control input, the controller designed achieves the zero disturbance attenuation level with respect to the measured disturbance inputs. The asymptotic tracking objective is achieved even if the measured disturbance is only uniformly bounded, without requiring it to be of finite energy. This strong robustness property is then illustrated by numerical examples.

Keywords:

• non-linear H ^∞ control
• cost-to-come function
• integrator backstepping
• adaptive control
• measured disturbances

Acknowledgement

This research was supported in part by the National Science Foundation under CAREER Award ECS-0296071.