Robust Stabilization Of Hamiltonian Systems With Input Delay

In practical controlled systems, there usually emerge parameter uncertainties and delays,which include electrical networks and engineering systems, and communication systems, etc.These delays and uncertain parameters often result in poor performance and even instability of many systems. In recent years, the study of uncertain nonlinear systems with input delay has aroused wide concern of experts and scholars. It is the problem faced by studying robust control of that how to design controller to make the system to keep it’s stability with input delay and parameter uncertainties.There also emerge delays and uncertainties produced by various factors in Port Hamiltonian systems. Port-Hamiltonian systems have extensive practical background which is a class of nonlinear controlled systems. Some practical systems, which include mechanical systems, and electromagnetic systems, etc, can be expressed as Port-Hamiltonian system form.The Hamilton function in a Port-Hamiltonian system represents generalized energy, and can be used as a good candidate of Lyapunov function. If Hamilton function in a Hamiltonian system is assumed that it is not positive definite or has not a minimum point, it can not be a Lyapunov function. To make full use of Hamiltonian system’s structural characteristics,energy shaping is needed for Hamiltonian systems to design a desired Hamilton function which satisfies Lyapunov condition. If the state can not be measured, a state observer is needed to study the system’s stability. In this paper, from two aspects that the perspective of energy-shaping and whether the state can be measured or not, the problems of robust control design of a class of uncertain Port-Hamiltonian systems with input delay are investigated.This paper’s mainly content is as follows:1) Stabilization of input delayed Hamiltonian systems.For input delayed Hamiltonian systems, controllers are designed and several su?cient conditions are obtained by proposing the definition of Casimir-Like function and using energy-shaping approach. A numerical example is presented to illustrate the correctness of the proposed results.2) Robust stabilization of uncertain Hamiltonian systems with input delay.Using Casimir-Like function and energy-shaping approach, this part considers robust stabilization of uncertain Hamiltonian systems with input delay by designing adaptive controllers. Several numerical examples are proposed to demonstrate the results obtained at the end of this part.3) Observer-based robust stabilization of uncertain Hamiltonian systems with input delay.For the case that the state can not be measured, a robust adaptive observer is designed,such that the closed-loop system is robustly asymptotically stable for all admissible parametric uncertainties. Two numerical examples are presented to show the correctness and e?ectiveness of the results obtained at last.