Combined $\mathcal{H}_{\infty}$ linear parameter varying control design and optimal sensor/actuator selection

Abstract

This paper presents an approach to co-design H∞ dynamic output feedback controllers for linear parametervarying (LPV) systems with optimal selection of sensors and actuators. This concurrent design problem is formulated as a Mixed Boolean Semi-Definite Programming (MBSDP) optimization problem. By means of the Big-M reformulation, the boolean decision variables related to the selection of sensors and actuators are decoupled from the SDP problem underlying the H∞ controller synthesis. This reformulation allows us to solve the initial NP-hard problem efficiently using a Branch and Bound (BNB) algorithm. The concurrent design of an LPV vibration controller and optimal actuator selection for a smart composite plate serves as a case study to validate the developed approach.

Feedback control of linear systems with optimal sensor and actuator selection

“…The LPV combined control design in our article is applied to the optimal sensor and actuator selection. This is an extension of our previous work (Singh et al, 2019), where the combined control design was applied with only actuator selection for a composite plate.…”

“…This article tackles the combined design problem for LTI and LPV control design with optimal sensor and actuator selection. Here, the Boolean and the semidefinite programming (SDP) variables are decoupled using Big-M reformulations which were discussed in our previous work (Singh et al, 2018a(Singh et al, , 2018b for LTI controller synthesis and were introduced in Singh et al (2019) for LPV controller synthesis. We formulate the combined design problem by representing the LMIs generalized for LTI and LPV controller synthesis as an optimization problem.…”

Concurrent design of an active vibration feedback controller and actuator/sensor selection for a composite plate

“…They are compared with an exhaustive search for the same application in order to analyze the optimality of the solution and computation time required to attain the solution. The vibration control application is discussed in [16], however it is for a linear parameter varying (LPV) system and the number of sensors and actuators is not very high.…”