On Statistical Control of Stochastic Servo-Systems: Performance-Measure Statistics and State-Feedback Paradigm

This paper 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 controllers. Basic assumptions will be that controllers have access to the current value of the states of the systems and would like to learn about performance uncertainty of the systems that is now affected by other noncooperative learners, i.e. model deviations and environmental disturbances named Nature. The controller considered here optimizes a multi-objective criterion over time where optimization takes place with high regard for possible random sample realizations by Nature who may more likely not be acting in concert. 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; two, a model-following controller that minimizes the difference between the reference model and the system outputs.