Minimum cost constrained input-output and control configuration co-design problem: A structural systems approach

Pequito, Sérgio; Kar, Soummya; Pappas, George J.

doi:10.1109/acc.2015.7171972

Cited by 28 publications

(48 citation statements)

References 34 publications

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“…Hence one can conclude if generic arbitrary pole placement is possible in a structural system in polynomial time. However, optimal selection of input-output set that guarantee arbitrary pole placement cannot be solved in polynomial time unless P = NP [5].…”

Section: Definitionmentioning

confidence: 99%

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Approximating constrained minimum cost input–output selection for generic arbitrary pole placement in structured systems

2019

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This paper is about minimum cost constrained selection of inputs and outputs in structured systems for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states that each output can sense is pre-specified. Our goal is to optimally select an input-output set that the system has no structurally fixed modes. Polynomial time algorithms do not exist for solving this problem unless P = NP. To this end, we propose an approximation algorithm by splitting the problem in to three sub-problems: a) minimum cost accessibility problem, b) minimum cost sensability problem and c) minimum cost disjoint cycle problem. We prove that problems a) and b) are equivalent to the weighted set cover problem. We also show that problem c) can be solved using a minimum cost perfect matching algorithm. Using these, we give an approximation algorithm which solves the minimum cost generic arbitrary pole placement problem. The proposed algorithm incorporates an approximation algorithm to solve the weighted set cover problem to solve a) and b) and a minimum cost perfect matching algorithm to solve c). Further, we show that the algorithm has polynomial complexity and gives an order optimal O(logn) approximate solution to the minimum cost input-output selection for generic arbitrary pole placement problem, where n denotes the number of states in the system.

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Section: Definitionmentioning

confidence: 99%

“…Note that for this class of systems Problem 1 is not NP-hard [5]. Pequito.et al addressed Problem 1 along with costs for feedback edges in [5] and obtained a polynomial time optimal algorithm. In the following result we prove that the polynomial time algorithm given in this paper also gives an optimal solution to Problem 1.…”

Section: A Irreducible Systemsmentioning

confidence: 99%

Approximating constrained minimum cost input–output selection for generic arbitrary pole placement in structured systems

2019

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“…Input selection with different inputs and constraints has been considered in [11], [12], [13], [14], [5]. In [11], the authors study the problem of minimizing total control effort for a given state transfer while ensuring controllability.…”

Section: Related Workmentioning

confidence: 99%

Minimal input selection for robust control

Liu

Clark

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a discrete optimization problem with bounded submodularity ratio, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system.

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“…The same algorithm is then employed in [28] for SSA selection with simpler H 2 /H ∞ formulations. The SA selection with control configuration selection problem is formulated in [25] using structural design and graph theory, which is proven to be NP-hard. Although this particular problem is similar to the SSASP with SOFC given in (2), the problem proposed in [25], along with the algorithms, are based on the information of structural pattern of the dynamic matrix.…”

Section: Introductionmentioning

confidence: 99%

“…The other drawback of this method is that arbitrary convex constraints on the binary selection variables are not easy to include. Finally, the algorithm proposed in [25]-which interestingly runs in polynomial-time if the structure of the dynamic matrix is irreducible-only computes the structure and the corresponding costs of the feedback matrix (along with the sets of selected SA).…”

Section: Introductionmentioning

confidence: 99%

Algorithms for joint sensor and control nodes selection in dynamic networks

et al. 2019

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The problem of placing or selecting sensors and control nodes plays a pivotal role in the operation of dynamic networks. This paper proposes optimal algorithms and heuristics to solve the simultaneous sensor and actuator selection problem in linear dynamic networks. In particular, a sufficiency condition of static output feedback stabilizability is used to obtain the minimal set of sensors and control nodes needed to stabilize an unstable network. We show the joint sensor/actuator selection and output feedback control can be written as a mixed-integer nonconvex problem. To solve this nonconvex combinatorial problem, three methods based on (1) mixed-integer nonlinear programming, (2) binary search algorithms, and (3) simple heuristics are proposed. The first method yields optimal solutions to the selection problem-given that some constants are appropriately selected. The second method requires a database of binary sensor/actuator combinations, returns optimal solutions, and necessitates no tuning parameters. The third approach is a heuristic that yields suboptimal solutions but is computationally attractive. The theoretical properties of these methods are discussed and numerical tests on dynamic networks showcase the trade-off between optimality and computational time.

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Minimum cost constrained input-output and control configuration co-design problem: A structural systems approach

Cited by 28 publications

References 34 publications

Approximating constrained minimum cost input–output selection for generic arbitrary pole placement in structured systems

Approximating constrained minimum cost input–output selection for generic arbitrary pole placement in structured systems

Minimal input selection for robust control

Algorithms for joint sensor and control nodes selection in dynamic networks

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