Optimal actuator/sensor selection through dynamic output feedback

Abstract

Abstract-This paper is devoted to the problem of optimal selection of a subset of available actuators/sensors through a multi-channel H 2 dynamic output feedback controller for continuous linear time invariant systems. Incorporating two extra terms for penalizing the number of actuators and sensors into the optimization objective function, we develop an iterative process to identify the favorable row/column-wise sparse DOF gains. Employing the identified structure, we solve the constructed row/column structured multi-channel H 2 DOF problem in order to derive a gain that exploits optimum number of sensors/actuators by which the closed-loop stability is maintained and the performance degradation of the closedloop system is restricted. Through an example we demonstrate the remarkable performance and broad applicability of the proposed approach.Index Terms-Simultaneous actuator/sensor selection, multichannel H 2 row-column-sparse dynamic output feedback (DOF) problem, linear matrix inequality. I. INTRODUCTIONThe number of components (actuators or sensors) in modern control systems can be very large, and hence, it is often not very feasible to manually find a subset of all available components to meet a specific control objective. Hence, the problem of selecting a configuration of actuators (sensors) from the set of all available actuators (sensors), while the control performance remains in an acceptable level compared to the non-sparse performance, is a well-known problem in the literature of control theory; see e.g. [1]-[6]. This problem can equivalently be considered as the design of a row (column) sparse feedback gain for the underling system. This paper aims to develop a unified framework to systematically design a sparse row-wise and columnwise dynamic output feedback (DOF) gain via convex optimization, while satisfying multi-channel H 2 performance specifications. One immediate application of this issue will be in the over-actuated (over-sensed) systems [7]. It is known that one method for reconfiguration strategy of fault tolerant control is usually to build an over-actuated (over-sensed) system first and then design a nominal controller using some of the available components. Hence whenever a fault happens in the system, the configuration of the control system is changed by using some of the redundant components in order to attain the nominal control objective [8].This problem leads to a difficult combinatorial optimization problem. There are a large number of investigations in

Performance guarantees for greedy maximization of non-submodular controllability metrics

“…Topology design problems have also been considered for specific classes of networks, including leader selection and communication network design [21], [22]. Various optimization methods have been proposed for topology design, including greedy algorithms [8], [9], [17], [18], [21], convex relaxation heuristics with sparsity inducing regularization [13]- [16], [23], and mixed-integer semidefinite programming methods [19], [20]. These methods are all heuristic approximations to extremely difficult combinatorial optimization problems.…”

Time-Varying Sensor and Actuator Selection for Uncertain Cyber-Physical Systems

“…More elaborate quantitative notions based on Gramians [6]- [14] and classical optimal and robust control Ahmad F. Taha and estimation problems [15]- [22] for linear systems have also been studied. For selecting SaAs based on these metrics, several optimization methods are proposed in this literature, including combinatorial greedy algorithms [8], [9], [19], [21], [23], convex relaxation heuristics using sparsity-inducing ℓ 1 penalty functions [15]- [18] and reformulations to mixedinteger semidefinite programming via the big-M method or McCormick's relaxation [13], [22], [24]. As a departure from control-theoretic frameworks, the authors in [25] explore an optimization-based method for reconstructing the initial states of nonlinear dynamic systems given (a) arbitrary nonlinear model, while (b) optimally selecting a fixed number of sensors.…”

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

“…Another approach explores the design of static output feedback H ∞ /H 2 feedback control [8] and [9] with sensors or actuator selection. [10] solves the combined problem by taking uncertainty into account using approximations of the 0 norm in terms of (weighted) 1 norms [11].…”