Performance Risk Management in Servo Systems

Abstract

This chapter provides a concise and up-to-date analysis of the foundations of performance robustness of a linear-quadratic class of servo-systems with respect to variability in a stochastic environment. The dynamics of servo systems are corrupted by a standard stationary Wiener process and include input functions that are controlled by statistical optimal controllers. Basic assumptions are that the controllers have access to the current value of the states of the systems and are capable of learning about performance uncertainty of the systems that are now affected by stochastic elements, e.g., model deviations and exogenous disturbances. The controller considered here optimizes a multi-objective criterion over time where optimization takes place with high regard for sample realizations by the stochastic elements mentioned above. It is found that the optimal servo in the finite-horizon case is a novel two-degrees-of-freedom controller with: one, a feedback controller with state measurements that is robust against performance uncertainty and two, a model-following controller that minimizes the difference between the reference model and the system outputs.