Feedback control of linear systems with optimal sensor and actuator selection

Abstract

This article demonstrates a combined [Formula: see text] feedback control design for linear time-invariant and linear parameter-varying systems and optimal sensors and actuator selection. The combined design problem is systematically constructed as a mixed Boolean semidefinite programming optimization problem. We impose Big-M reformulations to the non-deterministic polynomial-time-hard coupled problem to be solved as a convex optimization problem using the branch and bound algorithm. The combined design of dynamic output feedback control along with optimal actuator selection for a linear time-invariant seismic rejection controller design serves as an application for validation by simulation. In addition, active vibration control of a smart composite plate along with optimal sensor and actuator selection validates the developed approach for linear parameter-varying controller synthesis. On comparing this approach with exhaustive search, it is observed that mixed Boolean semidefinite programming approaches have faster computation time, and comparing with the iterative reweighted ℓ1 norm algorithm and mixed Boolean semidefinite programming using outer approximations, mixed Boolean semidefinite programming yields a global solution.