Analysis And Synthesis Of Some Classes Of Constraint Hamilton Systems

Constraint systems are more general system models which can be found in constraint robots, power systems, industrial control et al. So far, a relatively systemic thoery has been founded for linear constraint systems. But for nonlinear constraint systems, because of its singularity and complexity, relative research works are just at starting. The dynamic systems can be devided into holonomic constraint systems and nonholonomic constraint systems.Generalized Hamiltonian systems, an important kind of nonlinear systems, describe a kind of open systems which can have energy dissipation and energy exchange with environment. Because of good structures, clear physical expression and the fact that Lyapunov candidates can be chosen from Hamiltonian functions, generalized Hamiltonian systems have advantages over other plants in many control problems such as stability analysis, stabilization control and H_∞control design.The research on constraint Hamilton systems can make full use of the structural merits of the generalized Hamiltonian systems. In this dissetation, stabilization and robust control of constraint Hamilton systems are investigated and the result are extended into the genneral nonlinear constraint systems. The main contributions of the dissertation are as follows:First, the analysis and synthesis of holonomic constraint Hamilton systems are discussed. Based on the stuctural propoties of Hamilton sys-tems,some criteria for stability analysis and the stabilization controller are obtained. When the systems have exterior disturb, H_∞control is studyed. The results are finally extended into the ordinary nonlinear holonomic constraint systems.Second, the anlysis and synthesis of a new kind of nonholonomic Hamilton systems are investigated. Some preliminary results on the stabilization and simultaneous stability of such systems are obtained.Third, the simultaneous stabilization of Hamilton systems are studyed. Based on the thought of system augmentation, the simultaneous stabilization of two Hamilton systems is investigated. When the systems have exterior disturb, the H_∞controller is designed. Finally, the results are extended to the case of more than two Hamilton systems.The dissertation contains five chapters. Chapter 1 is the introduction. Chapters 2 is the analysis and synthesis of holonomic Hamilton sysmtems. Chapter 3 is concerned with the analysis and synthesis of nonholonomic Hamilton systems. Chapter 4 is simultaneous stabilization of Hamilton systems, which is followed by conclusion in Chapter 5.