Controllability of periodic linear systems, the Poincaré sphere, and quasi-affine systems
Copyright policy )Controllability of periodic linear systems, the Poincaré sphere, and quasi-affine systems
AbstractFor periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here, a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere, one obtains a compactification of the state space allowing us to describe the behavior “near infinity” of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior.
- State University of Maringa Brazil
- Institut für Mathematik Universität Augsburg Germany
- Augsburg College United States
- Universität Augsburg Germany
- Institut für Mathematik Germany
Controllability, Floquet theory, Artificial intelligence, Control (management), Mathematical analysis, Bounded function, Engineering, quasi-affine control system, periodic linear control system, Optimization and Control, Linear system, control set, Control theory (sociology), FOS: Mathematics, Compactification (mathematics), Poincaré conjecture, ddc:510, Discontinuous Systems, Linear subspace, Bifurcations in Planar Polynomial Systems, Pure mathematics, Statistical and Nonlinear Physics, Applied mathematics, Affine transformation, Computer science, Affine space, 93B05, 34H05, Physics and Astronomy, Linear systems in control theory, Control and Systems Engineering, Limit Cycles, Optimization and Control (math.OC), Physical Sciences, Analysis and Control of Distributed Parameter Systems, Characterization of Chaotic Quantum Dynamics and Structures, Geometry and Topology, Control/observation systems governed by ordinary differential equations, Mathematics, Control problems involving ordinary differential equations
Controllability, Floquet theory, Artificial intelligence, Control (management), Mathematical analysis, Bounded function, Engineering, quasi-affine control system, periodic linear control system, Optimization and Control, Linear system, control set, Control theory (sociology), FOS: Mathematics, Compactification (mathematics), Poincaré conjecture, ddc:510, Discontinuous Systems, Linear subspace, Bifurcations in Planar Polynomial Systems, Pure mathematics, Statistical and Nonlinear Physics, Applied mathematics, Affine transformation, Computer science, Affine space, 93B05, 34H05, Physics and Astronomy, Linear systems in control theory, Control and Systems Engineering, Limit Cycles, Optimization and Control (math.OC), Physical Sciences, Analysis and Control of Distributed Parameter Systems, Characterization of Chaotic Quantum Dynamics and Structures, Geometry and Topology, Control/observation systems governed by ordinary differential equations, Mathematics, Control problems involving ordinary differential equations
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