Nonlinear Impulsive and Hybrid Dynamical Systems

Nonlinear dynamical systems;Control;Large scale systems;Vector Lyapunov functions;Nonnegative systems;Biological and physiological systems;System thermodynamics;Automated anesthesia;Stability;Impulsive and hybrid dynamical systems

Nersesov, Sergey G ; Aerospace Engineering

University:Georgia Institute of Technology

Department:Aerospace Engineering

关键词: Nonlinear dynamical systems;    Control;    Large scale systems;    Vector Lyapunov functions;    Nonnegative systems;    Biological and physiological systems;    System thermodynamics;    Automated anesthesia;    Stability;    Impulsive and hybrid dynamical systems;   

Others  :  https://smartech.gatech.edu/bitstream/1853/7147/1/Nersesov_Sergey_G_200508_PhD.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

Modern complex dynamical systems typically possess amultiechelon hierarchical hybrid structure characterized bycontinuous-time dynamics at the lower-level units and logicaldecision-making units at the higher-level of hierarchy. Hybriddynamical systems involve an interacting countable collection ofdynamical systems defined on subregions of the partitioned statespace. Thus, in addition to traditional control systems, hybridcontrol systems involve supervising controllers which serve tocoordinate the (sometimes competing) actions of the lower-levelcontrollers. A subclass of hybrid dynamical systems are impulsivedynamical systems which consist of three elements, namely, acontinuous-time differential equation, a difference equation, anda criterion for determining when the states of the system are tobe reset. One of the main topics of this dissertation is thedevelopment of stability analysis and control design for impulsivedynamical systems. Specifically, we generalize Poincare'stheorem to dynamical systems possessing left-continuous flows toaddress the stability of limit cycles and periodic orbits ofleft-continuous, hybrid, and impulsive dynamical systems. Fornonlinear impulsive dynamical systems, we present partialstability results, that is, stability with respect to part of thesystem's state. Furthermore, we develop adaptive control frameworkfor general class of impulsive systems as well as energy-basedcontrol framework for hybrid port-controlled Hamiltonian systems.Extensions of stability theory for impulsive dynamical systemswith respect to the nonnegative orthant of the state space arealso addressed in this dissertation. Furthermore, we designoptimal output feedback controllers for set-point regulation oflinear nonnegative dynamical systems. Another main topic that hasbeen addressed in this research is the stability analysis oflarge-scale dynamical systems. Specifically, we extend the theoryof vector Lyapunov functions by constructing a generalizedcomparison system whose vector field can be a function of thecomparison system states as well as the nonlinear dynamical systemstates. Furthermore, we present a generalized convergence resultwhich, in the case of a scalar comparison system, specializes tothe classical Krasovskii-LaSalle invariant set theorem. Moreover,we develop vector dissipativity theory for large-scale dynamicalsystems based on vector storage functions and vector supply rates.Finally, using a large-scale dynamical systems perspective, wedevelop a system-theoretic foundation for thermodynamics.Specifically, using compartmental dynamical system energy flowmodels, we place the universal energy conservation, energyequipartition, temperature equipartition, and entropynonconservation laws of thermodynamics on a system-theoreticbasis.