NSF Optimal Reference Tracking, the Next Step in the Design of Controllers for Markovian Jump Linear Systems

The research develops the first collection of methods, for designing controllers that achieve optimal reference tracking, for randomly time-varying systems. As a first step, the PI adopts a Markovian jump linear system formulation because it retains the tractability of the linear deterministic case, while featuring a stochastic variation of its underlying structure. Recent results provide solutions to the H2 and H_inf optimal regulator (no reference) problems, for Markovian jump linear systems. However, the paradigm described in this proposal, where a reference has to be tracked, has not been investigated and it cannot be addressed by methods based on classical adaptations of optimal regulation theory, such as the internal model principle. The PI expects that an efficient design methodology will rely on a new framework for the joint design of the state-estimator, the state-feedback controller and the feedforward terms, using linear matrix inequality techniques. The research will also unveil structural properties of servomechanisms that achieve optimal reference tracking, in the presence of random or intermittent failures.

Optimal Reference Tracking, the Next Step in the Design of Controllers for Markovian Jump Linear Systems is a two-year, $97K grant.