Analysis And Synthesis Of Hamiltonian Systems With Time Delay And Saturation

Recent years witnessed the full-grown development of nonlinear systems control theory,one of the research hotspots in control theory.Especially with the introduction of differential geometry methodology,the nonlinear control systems theory has been made great progress.However,the research outcome is still insufficient on the more common issues of time-delay and saturation of nonlinear control systems.As well known,the phenomena of time delay and saturation constraint are often encountered in many practical control systems and one of the main reasons resulting in instability and poor performances of the associated control systems.However,the complexity of the system itself leads to the increasing difficult in controlling this kind of nonlinear systems.It is until present that many a fundamental problem has not been settled down and the corresponding outcome is scare as well.Meanwhile,port-controlled Hamiltonian systems,as an important class of nonlinear systems,owing to its clear structure and physical meaning,and that Hamiltonion function is considered as the total energy of the systems,demonstrates salient superiority in stability analysis and control design.In recent years,the viewpoint and methodology of Hamiltonion systems have drawn increasing attention in the field of nonlinear control systems.This thesis mainly studies the issues of stability and control design of Hamiltonian systems with time-delay and saturation.As follows are the main research contents.1.The stability of Hamiltonian systems is discussed.In full utilization of the dissipative structural properties of the Hamiltonian systems,and by using the technique of Lyapunov-Krasovskii functional,from two angles of delay-independent and delay-dependent,several sufficient stability conditions are proposed for two classes of Hamiltonian systems(including constant delay and time-varying delays).The robust stability is considered for a class of time-delay Hamiltonian systems which possesses time-invariant uncertainties belonging to some convex bounded polytypic domain.Besides, based on the proposed results,the stability of a class of nonlinear time-delay systems is also studied by Hamiltonian realization.Some examples are given to support the theoretical results.2.The L₂-disturbance attenuation for a class of time-delay Hamiltonian systems is considered.Aγ-dissipative inequality is established by using a proper control law and a storage function.Then based on the Lyapunov-Krasovskii stability theorem,a sufficient condition is proposed for the asymptotically stable of the closed-loop system. Finally,the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain is investigated and an L₂ disturbance attenuation control law is proposed as well.Simulations further inspects and verifies the correctness and practicability of the results.3.The stabilization problem for a port-controlled Hamiltonian system subject to actuator saturation and input additive external disturbances is investigated.The results are developed from two aspects:finite gain output stabilization and finite gain input stabilization.Conditions are identified under which a static output feedback law would achieve asymptotic stabilization.Under some additional growth conditions on the nonlinear functions involved in the system,the same feedback law would also achieve finite gain L₂ stabilization.In establishing these results,an estimate of the finite gain is also obtained.The illustrative examples verify the effectiveness of the proposed theories.4.The stabilization of a class of Hamiltonian systems with state time-delay and input saturation is addressed.Based on the special structure and dissipative property of the Hamiltonian systems,by using the Lyapunov-Krasovskii functional theory,the sufficient conditions are derived to guarantee the systems as well as the resulted closedloop systems for the system under output feedback to be asymptotically stable when input saturation effectively occurs.These conditions are composed of linear matrix inequalities and can directly be solved and verified through MATLAB/LMI toolbox, easy and simple.Numerical examples are presented to illustrate the effectiveness of the obtained results.5.The finite gain stabilization problem of the generator power systems subject to actuator saturation and external disturbances is investigated.Applying the analysis results of the Hamiltonian control systems subject to saturation,the finite gain stabilization of the single-machine infinite bus systems with excitation saturating and both excitation and steam valve saturating are discussed,respectively.First of all, based on the Hamiltonian energy theory,the power system model is transformed into a port-controlled Hamiltonian system model.Then a static output feedback controller is considered for the obtained Hamiltonian systems.Under some growth conditions, it is shown that the asymptotic stabilization,as well as the finite gain stabilization of the closed-loop system can be achieved,which solves the stabilization of the corresponding power systems.Simulation shows the effectiveness of the stabilizing method proposed.Innovations of the thesis mainly include the following three aspects:●It is first studied stability and controller design of time-delay Hamiltonian systems. Making the most of the special structure and dissipative property of the Hamiltonian systems,some stability and feedback stabilization criterion are derived for several kinds of time delay Hamiltonian systems,respectively;●It is first studied stability and finite gain stabilization of Hamiltonian systems with input saturation.Making the most of the special structure and dissipative property of the Hamiltonian systems,the sufficient conditions on finite gain output stabilization and finite gain input stabilization are proposed for the systems,respectively. Estimates of the finite gain are also obtained;●It is first studied the Hamiltonian systems under the double influences of time delay and saturation.Making the most of the special structure and dissipative property of the Hamiltonian systems,the sufficient conditions of stability and stabilization under an output feedback law are presented.