scholarly journals A Symbolic Computation Approach to Parameterizing Controller for Polynomial Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Cao ◽  
Xiaorong Hou
Keyword(s):  
Nonlinear Systems ◽  
Hamiltonian Systems ◽  
Symbolic Computation ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Internal Stability ◽  
Parameterization Method ◽  
Numerical Example ◽  
Isaacs Equations ◽  
Controller Parameterization

This paper considers controller parameterization method ofH∞control for polynomial Hamiltonian systems (PHSs), which involves internal stability and external disturbance attenuation. The aims of this paper are to design a controller with parameters to insure that the systems areH∞stable and propose an algorithm for solving parameters of the controller with symbolic computation. The proposed parameterization method avoids solving Hamilton-Jacobi-Isaacs equations, and thus the obtained controllers with parameters are relatively simple in form and easy in operation. Simulation with a numerical example shows that the controller is effective as it can optimizeH∞control by adjusting parameters. All these results are expected to be of use in the study ofH∞control for nonlinear systems with perturbations.

scholarly journals Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems

2017 ◽  
Vol 27 (4) ◽  
pp. 505-525
Author(s):  
Zhong Cao ◽  
Xiaorong Hou ◽  
Wenjing Zhao
Keyword(s):  
Hamiltonian Systems ◽  
Symbolic Computation ◽  
Control Design ◽  
Design Approach ◽  
Parametric Uncertainties ◽  
Simultaneous Stabilization ◽  
External Disturbances ◽  
Tuning Parameters ◽  
Parameterization Method ◽  
Controller Parameterization

AbstractThis paper investigates the problem of adaptive robust simultaneous stabilization (ARSS) of two dissipative Hamiltonian systems (DHSs), and proposes a number of results on the controller parameterization design. Firstly, an adaptiveH∞control design approach is presented by using the dissipative Hamiltonian structural for the case that there are both external disturbances and parametric uncertainties in two DHSs. Secondly, an algorithm for solving tuning parameters of the controller is proposed using symbolic computation. The proposed controller parameterization method avoids solving Hamilton-Jacobi-Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Finally, an illustrative example is presented to show that the ARSS controller obtained in this paper works very well.

scholarly journals H∞ Robust T-S Fuzzy Design for Uncertain Nonlinear Systems with State Delays Based on Sliding Mode Control

2010 ◽  
Vol 5 (4) ◽  
pp. 592 ◽  
Author(s):  
Xizheng Zhang ◽  
Yaonan Wang ◽  
Xiaofang Yuan
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Mode Control ◽  
Disturbance Attenuation Level ◽  
Takagi Sugeno

This paper presents the fuzzy design of sliding mode control (SMC) for nonlinear systems with state delay, which can be represented by a Takagi-Sugeno (TS) model with uncertainties. There exist the parameter uncertainties in both the state and input matrices, as well as the unmatched external disturbance. The key feature of this work is the integration of SMC method with H∞ technique such that the robust asymptotically stability with a prescribed disturbance attenuation level γ can be achieved. A sufficient condition for the existence of the desired SMC is obtained by solving a set of linear matrix inequalities (LMIs). The reachability of the specified switching surface is proven. Simulation results show the validity of the proposed method.

scholarly journals Exponential Feedback Passivity of Switched Polynomial Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Huawei Zhu ◽  
Xiaorong Hou
Keyword(s):  
Nonlinear Systems ◽  
External Disturbance ◽  
Robust Stabilization ◽  
Solution Algorithm ◽  
Switched Nonlinear Systems ◽  
Parameter Uncertainties ◽  
Numerical Example

The exponential feedback passivity problem of switched polynomial nonlinear systems is studied. To obtain this aim, a method of parameterization of controller is presented and parameter solution algorithm is described. Then, the addressed method is utilized to solve the robust stabilization for a class of switched polynomial nonlinear systems with parameter uncertainties and external disturbance. This result extends the previous results on exponential feedback passivity from the case of nonlinear systems to switched nonlinear systems. A numerical example is given to demonstrate the effectiveness of the proposed result.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Cao ◽  
Xiaorong Hou
Keyword(s):  
Structural Properties ◽  
Hamiltonian Systems ◽  
Symbolic Computation ◽  
Control Method ◽  
Simultaneous Stabilization ◽  
Robust Controller ◽  
External Disturbances ◽  
Stabilization Control ◽  
Pch System ◽  
Controller Parameterization

This paper investigates robust simultaneous stabilization (RSS) control method for two port-controlled Hamiltonian (PCH) systems and proposes results on the design of simultaneous stabilization controller with parameters for such systems. Firstly, two PCH systems are studied. Using the dissipative Hamiltonian structural properties, the systems are combined to generate an augmented PCH system. When there are external disturbances in the systems, a robust controller with parameters is designed for the systems. Secondly, an algorithm for solving parameters of the controller is proposed with symbolic computation. Finally, an illustrative example is presented to show that the RSS controller obtained in this paper works very well.

Disturbance Attenuating Adaptive Controllers for Parametric Strict Feedback Nonlinear Systems With Output Measurements

1999 ◽  
Vol 121 (1) ◽  
pp. 48-57 ◽  
Author(s):  
I. Egemen Tezcan ◽  
Tamer Bas¸ar
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Robust Adaptive Control ◽  
Disturbance Attenuation ◽  
Parameter Estimates ◽  
Minimum Phase ◽  
Feedback Form ◽  
Output Measurement ◽  
Adaptive Controllers ◽  
Strict Feedback

We present a systematic procedure for designing H∞-optimal adaptive controllers for a class of single-input single-output parametric strict-feedback nonlinear systems that are in the output-feedback form. The uncertain nonlinear system is minimum phase with a known relative degree and known sign of the high-frequency gain. We use soft projection on the parameter estimates to keep them bounded in the absence of persistent excitations. The objective is to obtain disturbance attenuating output-feedback controllers which will track a smooth bounded trajectory and keep all closed-loop signals bounded in the presence of exogenous disturbances. Two recent papers (Pan and Bas¸ar, 1996a; Marino and Tomei, 1995) addressed a similar problem with full state information, using two different approaches, and obtained asymptotically tracking and disturbance-attenuating adaptive controllers. Here, we extend these results to the output measurement case for a class of minimum phase nonlinear systems where the nonlinearities depend only on the measured output. It is shown that arbitrarily small disturbance attenuation levels can be obtained at the expense of increased control effort. The backstepping methodology, cost-to-come function based H∞ -filtering and singular perturbations analysis constitute the framework of our robust adaptive control design scheme.

scholarly journals Internal Stability and L2 Gain of Nonlinear Systems

1993 ◽  
Vol 29 (6) ◽  
pp. 659-667 ◽  
Author(s):  
Junichi IMURA ◽  
Toshiharu SUGIE ◽  
Tsuneo YOSHIKAWA
Keyword(s):  
Nonlinear Systems ◽  
Internal Stability ◽  
L2 Gain
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