A family of H_∞ controllers for dissipative Hamiltonian systems

Abstract

Using structure properties of dissipative Hamiltonian systems, this paper investigates the parameterization problem of H ∞ controllers for such systems. A family of H ∞ controllers with full information is first obtained by interconnecting an H ∞ controller with a generalized zero-energy-gradient (ZEG) detectable, free generalized Hamiltonian system. Then, a family of H ∞ controllers with partial information is presented in terms of the solution to an inequality only in 2n independent variables (twice as many as the one used to characterize the state feedback) and without imposing an additional cascade condition. Both of the parameterization methods avoid solving Hamilton-Jacobi-Issacs equations (or inequalities), and thus the proposed controllers are relatively simple in form and easy in operation. Numerical experiments show the effectiveness and feasibility of the proposed methods.

Hamiltonian stabilization additional L 2 adaptive control and its application to hydro turbine generating sets

“…Many approaches, such as H ∞ theory [9][10][11][12][13], L 2 disturbance attenuation theory [14][15][16][17][18][19] and other adaptive methods [20][21][22][23], are developed to handle the robustness of the Hamiltonian system. The L 2 method, investigating system robustness directly from model error and parameters disturbance, is the most direct approach.…”

A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

“…It is an efficient way to find the parameterized controller to solve complex control problems. Therefore, controller parameterization is a fundamental problem in control theory and has aroused considerable attention in recent decades [1][2][3][4][5][6][7][8][9]. The controller parameterization problem was first proposed by Doyle [1].…”

Robust Simultaneous Stabilization Control Method for Two Port-Controlled Hamiltonian Systems: Controller Parameterization

“…Yung et al [24] extended the state-space formulas and presented a family of ∞ statefeedback controllers for -dimensional nonlinear system. Xu and Hou [25,26] studied the generalized Hamiltonian system and proposed a family of parameterized controllers in ∞ control and adaptive control. The controllers [21][22][23][24][25][26] are intended to solve the control problem for just one system.…”

“…Xu and Hou [25,26] studied the generalized Hamiltonian system and proposed a family of parameterized controllers in ∞ control and adaptive control. The controllers [21][22][23][24][25][26] are intended to solve the control problem for just one system. There are fewer works for RSS control design of two PCH systems.…”