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Wei Kang - One of the best experts on this subject based on the ideXlab platform.
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Controllability and local accessibility - a normal form approach
IEEE Transactions on Automatic Control, 2003Co-Authors: Wei Kang, Mingqing Xiao, I. Amadou TallAbstract:Given a system with an Uncontrollable linearization at the origin, we study the controllability of the system at equilibria around the origin. If the Uncontrollable Mode is nonzero, we prove that the system always has other equilibria around the origin. We also prove that these equilibria are linearly controllable provided a coefficient in the normal form is nonzero. Thus, the system is qualitatively changed from being linearly Uncontrollable to linearly controllable when the equilibrium point is moved from the origin to a different one. This is called a bifurcation of controllability. As an application of the bifurcation, systems with a positive Uncontrollable Mode can be stabilized at a nearby equilibrium point. In the last part of this paper, simple sufficient conditions are proved for local accessibility of systems with an Uncontrollable Mode. Necessary conditions of controllability and local accessibility are also proved for systems with a convergent normal form.
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Resonant terms and bifurcations of nonlinear control systems with one Uncontrollable Mode
Systems & Control Letters, 2003Co-Authors: Boumediene Hamzi, Wei KangAbstract:In this paper we provide a simple algorithm of feedback design for systems with Uncontrollable linearization with only quadratic degeneracy, such as transcritical and saddle-node bifurcations. This approach avoids the computation of nonlinear normal forms. It is based only on quadratic invariants which can be determined directly from the quadratic terms in the Uncontrollable dynamics.
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Bifurcation Control via State Feedback for Systems with a Single Uncontrollable Mode
SIAM Journal on Control and Optimization, 2000Co-Authors: Wei KangAbstract:The state feedback control of bifurcations with quadratic or cubic degeneracy is addressed for systems with a single Uncontrollable Mode. Based on normal forms and invariants, the classification of bifurcations for systems with a single Uncontrollable Mode is obtained (Table 1). Using invariants, stability characterizations are derived for a family of bifurcations, including saddle-node bifurcations, transcritical bifurcations, pitchfork bifurcations, and bifurcations with a cusp or hysteresis phenomenon. Bifurcations in systems under perturbed feedbacks are also addressed. In the case of a saddle-node bifurcation, continuous but not differentiable feedbacks are introduced to locally remove the bifurcation and to achieve the stability.
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Bifurcation for discrete time parameterized systems with Uncontrollable linearization
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Boumediene Hamzi, J-p. Barbot, Wei KangAbstract:In this paper we study bifurcation problems for discrete time parameterized nonlinear control systems which possess one Uncontrollable Mode in their linearization. First, we classify equilibrium sets, then we study controllability and stabilizability near bifurcation points.
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Normal forms for discrete time parameterized systems with Uncontrollable linearization
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Boumediene Hamzi, J-p. Barbot, Wei KangAbstract:We determine quadratic normal forms for discrete time parameterized nonlinear control systems which possess one Uncontrollable Mode in their linearization. These normal forms are the simplest elements of the equivalence class of the group of transformations by quadratic change of coordinates and quadratic feedback.
Boumediene Hamzi - One of the best experts on this subject based on the ideXlab platform.
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Resonant terms and bifurcations of nonlinear control systems with one Uncontrollable Mode
Systems & Control Letters, 2003Co-Authors: Boumediene Hamzi, Wei KangAbstract:In this paper we provide a simple algorithm of feedback design for systems with Uncontrollable linearization with only quadratic degeneracy, such as transcritical and saddle-node bifurcations. This approach avoids the computation of nonlinear normal forms. It is based only on quadratic invariants which can be determined directly from the quadratic terms in the Uncontrollable dynamics.
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Nonlinear discrete-time control of systems with a Naimark-Sacker bifurcation
Systems & Control Letters, 2001Co-Authors: Boumediene Hamzi, Jean-pierre Barbot, Salvatore Monaco, Dorothée Normand-cyrotAbstract:In this paper we study the problem of the stabilization of nonlinear control system with one complex Uncontrollable Mode. We find normal forms and quadratic invariants; then we compute center manifolds, and use bifurcation theory to synthesize quadratic controllers.
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Bifurcation for discrete time parameterized systems with Uncontrollable linearization
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Boumediene Hamzi, J-p. Barbot, Wei KangAbstract:In this paper we study bifurcation problems for discrete time parameterized nonlinear control systems which possess one Uncontrollable Mode in their linearization. First, we classify equilibrium sets, then we study controllability and stabilizability near bifurcation points.
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Normal forms for discrete time parameterized systems with Uncontrollable linearization
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Boumediene Hamzi, J-p. Barbot, Wei KangAbstract:We determine quadratic normal forms for discrete time parameterized nonlinear control systems which possess one Uncontrollable Mode in their linearization. These normal forms are the simplest elements of the equivalence class of the group of transformations by quadratic change of coordinates and quadratic feedback.
Tong Zhou - One of the best experts on this subject based on the ideXlab platform.
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ACC - Relations between Controllability and Structure of a Networked Dynamic System
2019 American Control Conference (ACC), 2019Co-Authors: Yuan Zhang, Tong ZhouAbstract:Dependence of controllability of a networked dynamic system (NDS) on its structure is investigated in this paper. Each subsystem is permitted to have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation (LFT), to allow rational function dependence of system matrices on the first principle parameters. It is proven that controllability keeps to be a generic property for this kind of NDSs. Results are at first established for structural controllability of LFT-parameterized plants under a diagonalization assumption. Necessary and sufficient conditions are then established respectively for the NDS to have a fixed Uncontrollable Mode, to have a parameter-dependent Uncontrollable Mode, and to be structurally controllable, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and give some insights on how the NDS controllability is influenced by subsystem input-output relations, subsystem Uncontrollable Modes and subsystem interconnection topology.
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Structural Controllability of an NDS With LFT Parameterized Subsystems
IEEE Transactions on Automatic Control, 2019Co-Authors: Yuan Zhang, Tong ZhouAbstract:This paper studies structural controllability for a networked dynamic system (NDS), in which each subsystem may have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation. It is proven that controllability keeps to be a generic property for this kind of NDSs. Some necessary and sufficient conditions are then established, respectively, for them to be structurally controllable, to have a fixed Uncontrollable Mode, and to have a parameter-dependent Uncontrollable Mode, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and in their verifications, all arithmetic calculations are performed separately on each subsystem. In addition, these conditions also reveal influences on NDS controllability from subsystem input–output relations, subsystem Uncontrollable Modes, and subsystem interconnection topology. Based on these observations, the problem of selecting the minimal number of subsystem interconnection links is studied under the requirement of constructing a structurally controllable NDS. A heuristic method is derived with some provable approximation bounds and a low computational complexity.
J-p. Barbot - One of the best experts on this subject based on the ideXlab platform.
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Bifurcation for discrete time parameterized systems with Uncontrollable linearization
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Boumediene Hamzi, J-p. Barbot, Wei KangAbstract:In this paper we study bifurcation problems for discrete time parameterized nonlinear control systems which possess one Uncontrollable Mode in their linearization. First, we classify equilibrium sets, then we study controllability and stabilizability near bifurcation points.
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Normal forms for discrete time parameterized systems with Uncontrollable linearization
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1Co-Authors: Boumediene Hamzi, J-p. Barbot, Wei KangAbstract:We determine quadratic normal forms for discrete time parameterized nonlinear control systems which possess one Uncontrollable Mode in their linearization. These normal forms are the simplest elements of the equivalence class of the group of transformations by quadratic change of coordinates and quadratic feedback.
Yuan Zhang - One of the best experts on this subject based on the ideXlab platform.
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ACC - Relations between Controllability and Structure of a Networked Dynamic System
2019 American Control Conference (ACC), 2019Co-Authors: Yuan Zhang, Tong ZhouAbstract:Dependence of controllability of a networked dynamic system (NDS) on its structure is investigated in this paper. Each subsystem is permitted to have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation (LFT), to allow rational function dependence of system matrices on the first principle parameters. It is proven that controllability keeps to be a generic property for this kind of NDSs. Results are at first established for structural controllability of LFT-parameterized plants under a diagonalization assumption. Necessary and sufficient conditions are then established respectively for the NDS to have a fixed Uncontrollable Mode, to have a parameter-dependent Uncontrollable Mode, and to be structurally controllable, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and give some insights on how the NDS controllability is influenced by subsystem input-output relations, subsystem Uncontrollable Modes and subsystem interconnection topology.
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Structural Controllability of an NDS With LFT Parameterized Subsystems
IEEE Transactions on Automatic Control, 2019Co-Authors: Yuan Zhang, Tong ZhouAbstract:This paper studies structural controllability for a networked dynamic system (NDS), in which each subsystem may have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation. It is proven that controllability keeps to be a generic property for this kind of NDSs. Some necessary and sufficient conditions are then established, respectively, for them to be structurally controllable, to have a fixed Uncontrollable Mode, and to have a parameter-dependent Uncontrollable Mode, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and in their verifications, all arithmetic calculations are performed separately on each subsystem. In addition, these conditions also reveal influences on NDS controllability from subsystem input–output relations, subsystem Uncontrollable Modes, and subsystem interconnection topology. Based on these observations, the problem of selecting the minimal number of subsystem interconnection links is studied under the requirement of constructing a structurally controllable NDS. A heuristic method is derived with some provable approximation bounds and a low computational complexity.
