Optimal block-mode assignment and relocation in matrix polynomials for observer-based static and dynamic multivariable feedback compensators

Abstract This study introduces an observer-based dual strategy for optimizing block mode placement in matrix polynomial control systems, focusing on improving stability and performance in multivariable feedback applications. It introduces two approaches: a static state feedback compensator for a challenging Bidirectional Inductive Power Transfer (IPT) System, and a dynamic observer-based output feedback compensator for a defensive air-to-surface missile control problem. Both designs exploit the Grey Wolf Optimizer to solve the nonlinear convex optimization, associated with block mode selection. The dynamic plan employs Luenberger observer principles for unmeasured state estimation, ensuring system reliability through strict observability conditions. Simulation results reveal that the proposed optimal placement methods enhance tracking, boost stability margins, and substantially minimize control effort. Overall, this methodology offers an effective frame-work for robust controller design and state estimation across disparate, complex dynamic systems, while reducing computational burden and improving control efficiency.