Output feedback design for discrete-time constrained systems subject to persistent disturbances via bilinear programming

• Published in: Journal of the Franklin Institute Vol. 358; no. 18; pp. 9741 - 9770
• Main Authors: Brião, Stephanie L., Castelan, Eugênio B., Camponogara, Eduardo, Ernesto, Jackson G.
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.12.2021; Elsevier Science Ltd
• Subjects: Constraints; Discrete time systems; Disturbances; Feedback control systems; Invariance; Invariants; Numerical analysis; Optimization; Output feedback; Polyhedra
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2021.10.024

•Algebraic invariance property of a polyhedron from which system trajectories converge in finite-time to a bounded polyhedron.•Synthesis of static and dynamic output feedback control laws with structural constraints such as controller decentralization.•Bilinear optimization for solving an associated constrained control problem under persistent bounded disturbances.•Numerical analysis compared with existing techniques show the efficiency of control synthesis with bilinear optimization. In this work, we use the Δ-Invariance property of polyhedral sets to design a stabilizing Static Output Feedback (SOF) for linear discrete-time systems subject to persistent disturbances, assuring the states and control constraints fulfillment. We deduce new algebraic conditions to guarantee that any trajectory emanating from the Δ-Invariant polyhedron remains in it and converges in finite-time to another polyhedral set around the origin, where the trajectory remains ultimately bounded. Thus, the proposed SOF solution for the constrained control problem also requires determining the Δ-invariant and the ultimately bounded polyhedra. Therefore, the proposal considers a bilinear optimization problem whose objective function weighs the two associated polyhedral sets’ size and whose constraints are formed by the invariance relation. Moreover, an efficient non-linear optimization solver is used to tackle the present bilinearities. Numerical examples showcase the effectiveness and potential of our proposal.