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Structural Minimum Controllability Problem for Linear Continuous-Time Switching Systems  [PDF]
Sergio Pequito,George J. Pappas
Mathematics , 2015,
Abstract: This paper addresses a problem on the structural design of control systems, and explicitly takes into consideration the possible application to large-scale systems. More precisely, we aim to determine the minimum number of manipulated/measured state variables ensuring structural controllability/ observability of the linear continuous-time switching system. Further, the solution can be determined by an efficient procedure, i.e., polynomial in the number of state variables.
Structural Controllability of Switched Linear Systems  [PDF]
Xiaomeng Liu,Hai Lin,Ben M. Chen
Mathematics , 2011,
Abstract: This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the traditional controllability concept for dynamical systems, and purely based on the interconnection relation between the state variables and inputs through non-zero elements in the state matrices. In order to illustrate such a relationship, two kinds of graphic representations of switched linear systems are proposed, based on which graph theory based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented. Finally, the paper concludes with discussions on the results and future work.
Distributed Verification of Structural Controllability for Linear Time-Invariant Systems  [PDF]
Joao Carvalho,Sergio Pequito,A. Pedro Aguiar,Soummya Kar,Karl H. Johansson
Mathematics , 2015,
Abstract: Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work we study controllability in the structural system theoretic sense, structural controllability. In other words, instead of focusing on a specific numerical system realization, we provide guarantees for equivalence classes of linear time-invariant systems on the basis of their structural sparsity patterns, i.e., location of zero/nonzero entries in the plant matrices. To this end, we first propose several necessary and/or sufficient conditions to ensure structural controllability of the overall system, on the basis of the structural patterns of the subsystems and their interconnections. The proposed verification criteria are shown to be efficiently implementable (i.e., with polynomial time complexity in the number of the state variables and inputs) in two important subclasses of interconnected dynamical systems: similar (i.e., every subsystem has the same structure), and serial (i.e., every subsystem outputs to at most one other subsystem). Secondly, we provide a distributed algorithm to verify structural controllability for interconnected dynamical systems. The proposed distributed algorithm is efficient and implementable at the subsystem level; the algorithm is iterative, based on communication among (physically) interconnected subsystems, and requires only local model and interconnection knowledge at each subsystem.
Structural Observability of Controlled Switching Linear Systems
International Journal of Control Science and Engineering , 2012, DOI: 10.5923/j.control.20120205.05
Abstract: In this paper, a new methodology for analysis of structural observability of controlled switching linear systems modelled by bond graphs is proposed. Causal manipulations on the bond graph model enable to determine graphically the observable subspace. A novel definition of observability is proposed. Finally, two sufficient conditions of observability are derived. The proposed method, based on a bond graph theoretic approach, assumes only the knowledge of the systems structure. These conditions can be implemented by classical bond graph theory algorithms based on finding particular paths and cycles in a bond graph.
Strong Structural Controllability and Observability of Linear Time-Varying Systems  [PDF]
Gunther Reissig,Christoph Hartung,Ferdinand Svaricek
Mathematics , 2013, DOI: 10.1109/TAC.2014.2320297
Abstract: In this note we consider continuous-time systems x'(t) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t), as well as discrete-time systems x(t+1) = A(t) x(t) + B(t) u(t), y(t) = C(t) x(t) + D(t) u(t) whose coefficient matrices A, B, C and D are not exactly known. More precisely, all that is known about the systems is their nonzero pattern, i.e., the locations of the nonzero entries in the coefficient matrices. We characterize the patterns that guarantee controllability and observability, respectively, for all choices of nonzero time functions at the matrix positions defined by the pattern, which extends a result by Mayeda and Yamada for time-invariant systems. As it turns out, the conditions on the patterns for time-invariant and for time-varying discrete-time systems coincide, provided that the underlying time interval is sufficiently long. In contrast, the conditions for time-varying continuous-time systems are more restrictive than in the time-invariant case.
Observability and Detectability of Linear Switching Systems: A Structural Approach  [PDF]
Elena De Santis,Maria Domenica Di Benedetto,Giordano Pola
Mathematics , 2008,
Abstract: We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable choice of the control input. We derive a necessary and sufficient condition for observability that can be verified computationally. A characterization of control inputs ensuring observability of switching systems is given. Moreover, we prove that checking detectability of a linear switching system is equivalent to checking asymptotic stability of a suitable switching system with guards extracted from it, thus providing interesting links to Kalman decomposition and the theory of stability of hybrid systems.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method  [cached]
Qiang Ma
International Journal of Modern Education and Computer Science , 2011,
Abstract: In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix) of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.
Graph-Theoretic Characterizations of Structural Controllability for Multi-Agent System with Switching Topology  [PDF]
Xiaomeng Liu,Hai Lin,Ben M. Chen
Computer Science , 2012,
Abstract: This paper considers the controllability problem for multi-agent systems. In particular, the structural controllability of multi-agent systems under switching topologies is investigated. The structural controllability of multi-agent systems is a generalization of the traditional controllability concept for dynamical systems, and purely based on the communication topologies among agents. The main contributions of the paper are graph-theoretic characterizations of the structural controllability for multi-agent systems. It turns out that the multi-agent system with switching topology is structurally controllable if and only if the union graph G of the underlying communication topologies is connected (single leader) or leader-follower connected (multi-leader). Finally, the paper concludes with several illustrative examples and discussions of the results and future work.
Controllability and null controllability of linear systems
I Davies, P Jackreece
Journal of Applied Sciences and Environmental Management , 2005,
Abstract: This paper establishes sufficient conditions for the controllability and null controllability of linear systems. The aim is to use the variation of constant formula to deduce our controllability grammiam, by exploiting the properties of the grammiam and the asymptotic stability of the free system, we achieved our results. Journal of Applied Sciences and Environmental Management Vol. 9(3) 2005: 31-36
Controllability and reachability of singular linear discrete time systems  [PDF]
Charalambos P. Kontzalis,Grigoris Kalogeropoulos
Mathematics , 2014,
Abstract: The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be established through selection of the proper state variables. Time domain analysis is the method of analyzing the system based on this description equation, through which we may gain a fair understanding of the system's structural features as well as its internal properties. Using time domain analysis, this article studies the fundamentals in system theory such as reachability and controllability.
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