Research On Robust Controller Parameterization For Dissipative Hamiltonian Systems

Dissipative Hamiltonian systems are a kind of dynamical systems, which exists extensively, and an important tool for controller design of general nonlinear systems. In the controller design of nonlinear systems, controller parameterization is an effective method for researching multi-objective control of systems. Normal controller parameterization methods are achieved through solving Hamilton-Jacobi-Isaacs(HJI) inequalities(or equations). This dissertation proposes a method avoiding to solve HJI inequalities(or equations), and studies robust controller parameterization problems for three types of dissipative Hamiltonian systems, which are single dissipative Hamiltonian system, a set of dissipative Hamiltonian systems and switched dissipative Hamiltonian systems.The main contributions of this dissertation are listed as follows:(1) The definition of polynomial with parameters and structuring of the polynomial with parameters method are proposed in this dissertation firstly. Then, the criteria of a non-negative polynomial with parameters and the algorithm of solving parameters’ ranges(SPR) are proposed for the first time. The algorithm SPR utilizes cylindrical algebraic decomposition(CAD) algorithm ofsymbolic computation to find parameters’ ranges. Finally, two examples show that the algorithm SPR is effective. The algorithm SPRis widely used for controller parameterization in the remained of this dissertation.(2) Robust H? control shows its superiority and widespread applicationin the system control areas. A controller parameterization method proposed and a family of robust H? controller with parameters designed for dissipative Hamiltonian systems in this dissertation. These controllers have strong 2L disturbance attenuation for system, and the system can converge to the equilibrium point quickly, when the disturbance disappears. The parameters’ ranges of controllers can be obtained by using the algorithm SPR. Within the ranges of parameters, the controllers can optimize the robustness of system. We present a family of adaptive H? controller with parameters for the system with external disturbances and internalperturbation. The controllers have strong robustness of system. The methodsof controller parameterization avoid solving HJI inequalities(or equations) by using the good structure of dissipative Hamiltonian systems. The obtained controllers have simple structure and are easy to implement. The numerical experiments and simulations show that controllers obtained in this dissertation have strong robustness of system and can optimize the robustness of system by adjusting parameters’ values.(3)Robust simultaneous stabilization control is an important researching topic for multiple systems. We propose the robust simultaneous stabilization controller parameterization design method for a set of dissipative Hamiltonian systems first time. Robust controller design method for two dissipative Hamiltonian systems has been proposed firstly. We design a family of robust H? controller with parameters under external disturbance and a family of adaptive H? controller with parameters under external disturbance and internalperturbation, respectively. Then, we consider the robust simultaneous stabilization control problem for a set of dissipative Hamiltonian systems and design the H?controllers with parameters in above two cases, respectively. These controllers have strong robustness of systems and can optimize the robustness by adjusting parameters’ values.(4) We propose the problems of robust controller and robust adaptive controller for switched dissipative Hamiltonian systems in this dissertation first time. A family of robust H? controllers with parameters and a family of adaptive H? controllers with parameters are designed by using multiple Hamiltonian function method. The controllers have strong robustness of systems under arbitrary switched law and can optimize the robustness by adjusting parameters values under fixed switched law.(5) We give an engineering example that is twodegrees of freedom active suspension vehicle model. By usingthe method of robustcontroller parameterization for dissipative Hamiltonian system, a family of controllers with parameters for activesuspension system obtained. The obtained controllers havestrong robustness of system in ride comfort and other aspects and can optimize the robustness by adjusting parameters values.The results of this dissertation enrich the researching of dissipative Hamiltonian systems. The methods of controller parameterization provide a theoretical basis for optimization of robust control. We can obtain the optimal solution for controller within parameters’ ranges. When the robustness of systems has been satisfied, the controller can satisfy the other complex control performance by adjusting parameters’ values. The methods of controller parameterizationgive some new methods and thoughts for stability studies and controller design for nonlinear control systems.