A family of adaptive H ∞ controllers with full information for dissipative hamiltonian systems

Abstract

This paper investigates a parameterization method of adaptive H∞ controllers for dissipative Hamiltonian systems with disturbances and unknown parameters. The family of adaptive H∞ controllers with full information is obtained by interconnecting an adaptive H∞ controller with a generalized zero-energy-gradient (ZEG) detectable, free generalized Hamiltonian system. The present parameterization method avoids solving Hamilton-Jacobi-Issacs equations and thus the controllers obtained are easier in operation as compared to some existing ones. Simulations show the effectiveness and feasibility of the adaptive control strategy proposed in this paper.

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

“…This completes the proof. (1) The condition (8) in Theorem is not restrictive, and can be easily satisfied in many systems [15,19]. (2) The condition (9) can be easily satisfied in many systems through controller design.…”

“…From condition (8), we can obtain the γ*, which is the threshold disturbance attenuation level. Let γ ≥ γ* such that condition (8) holds. Then we propose an algorithm to find the tuning parameters' ranges of controller (11) via solving the tuning parameters' ranges of Φ(X 1 , X 2 , ν) in condition (10).…”

“…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.…”