Finite-time partial stability, stabilization, semistabilization, and optimal feedback control

Dynamic programming;Hamilton-Jacobi-Bellman;Optimal control;Finite-time stability;Partial-state stability;Partial-state finite-time stability;Stabilization;Feedback control;State-feedback control;Singular control

L'afflitto, Andrea ; Haddad, WassimM. Aerospace Engineering Prasad, J. V. R. Dieci, Luca Feron, Eric M. Holzinger, Marcus J. ; Haddad, WassimM.

University:Georgia Institute of Technology

Department:Aerospace Engineering

关键词: Dynamic programming;    Hamilton-Jacobi-Bellman;    Optimal control;    Finite-time stability;    Partial-state stability;    Partial-state finite-time stability;    Stabilization;    Feedback control;    State-feedback control;    Singular control;   

Others  :  https://smartech.gatech.edu/bitstream/1853/53573/1/LAFFLITTO-DISSERTATION-2015.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Asymptotic stability is a key notion of system stability for controlled dynamical systems as it guarantees that the system trajectories are bounded in aneighborhood of a given isolated equilibrium point and converge to this equilibrium over the infinite horizon. In some applications, however, asymptotic stability is not the appropriate notion of stability. For example, for systems with a continuum of equilibria, every neighborhood of an equilibrium contains another equilibrium and a nonisolated equilibrium cannot be asymptotically stable. Alternatively, in stabilization of spacecraft dynamics via gimballed gyroscopes, it is desirable to find state- and output-feedback control laws that guarantee partial-state stability of the closed-loop system, that is, stability with respect to part of the system state. Furthermore, we may additionally require finite-time stability of the closed-loop system, that is, convergence of the system's trajectories to a Lyapunov stable equilibrium in finite time.The Hamilton-Jacobi-Bellman optimal control framework provides necessary and sufficient conditions for the existence of state-feedback controllers that minimize a given performance measure and guarantee asymptotic stability of the closed-loop system. In this research, we provide extensions of the Hamilton-Jacobi-Bellman optimal control theory to develop state-feedback control laws that minimize nonlinear-nonquadratic performance criteria and guarantee semistability, partial-state stability, finite-time stability, and finite-time partial state stability of the closed-loop system.