Some results on disturbance attenuation for Hamiltonian systems via direct discrete-time design

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.

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Sampled-Data Optimal Design and Robust Stabilization

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2897721 ◽

1992 ◽

Vol 114 (4) ◽

pp. 538-543 ◽

Cited By ~ 3

Author(s):

Tongwen Chen ◽

Bruce A. Francis

Keyword(s):

Time Delay ◽

Discrete Time ◽

Robust Stabilization ◽

Disturbance Attenuation ◽

Delay Systems ◽

Time Delay Systems ◽

Sampled Data ◽

Design Problems ◽

Data Control ◽

Time Problem

This paper considers sampled-data control of time-delay systems. First we show that under a certain nonpathological sampling condition, a sampled-data system is internally stable in continuous time if and only if the corresponding discretized system is stable in discrete time. Based on this, we then study two sampled-data design problems for (unstable) time-delay systems: ℋ2-optimal disturbance attenuation and robust stabilization. In both cases, the sampled-data problem can be recast via operator methods as exactly a discrete-time problem and hence be solved using known techniques.

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Observer-based output feedback stabilisation and ℒ2-disturbance attenuation of uncertain Hamiltonian systems with input and output delays

International Journal of Systems Science ◽

10.1080/00207721.2019.1671532 ◽

2019 ◽

Vol 50 (14) ◽

pp. 2565-2578

Author(s):

Weiwei Sun ◽

Xinyu Lv ◽

Kaili Wang ◽

Liping Wang

Keyword(s):

Hamiltonian Systems ◽

Output Feedback ◽

Disturbance Attenuation ◽

Input And Output ◽

Feedback Stabilisation

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Discrete-time backstepping control with nonlinear adaptive disturbance attenuation for the inverted-pendulum system

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219867775 ◽

2019 ◽

pp. 014233121986777

Author(s):

Fatih Adıgüzel ◽

Yaprak Yalçın

Keyword(s):

Discrete Time ◽

Feedback Linearization ◽

Inverted Pendulum ◽

Backstepping Control ◽

Disturbance Attenuation ◽

Pendulum System ◽

Inverted Pendulum System ◽

Partial Feedback Linearization ◽

Partial Feedback ◽

Backstepping Controller

A discrete-time backstepping controller with an active disturbance attenuation property for the Inverted-Pendulum system is constructed in this paper. The main purpose of this study is to show that Immersion and Invariance (I & I) approach can be used to design a nonlinear observer for disturbance estimation and demonstrate its effectiveness considering a nonlinear system with an unstable equilibrium point, namely Inverted-Pendulum system, by utilizing the estimated values in backstepping control design. All designs are directly performed in discrete-time domain to obtain directly implementable observer and controller in discrete processors with superior performance compared to emulators. The Inverted-Pendulum system is not in strict feedback form therefore backstepping procedure cannot be directly applied. In order to enable backstepping construction, firstly a partial feedback linearization is performed and afterwards a novel discrete-time coordinate transformation is proposed. Prior to the construction of partial feedback linearizing and backstepping controller, a nonlinear disturbance estimator design is proposed with Immersion and Invariance approach. The estimated disturbance values used in the partial feedback linearization and construction of the backstepping controller. The global asymptotic stability of the estimator and local asymptotic stability of overall closed loop system are proved in the sense of Lyapunov. Performance of proposed direct discrete-time backstepping control with discrete I & I observer is compared with a backstepping sliding mode controller with another nonlinear disturbance observer (NDO) by simulations.

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H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

10.1115/dscc2011-5935 ◽

2011 ◽

Cited By ~ 1

Author(s):

Xin Wang ◽

Edwin E. Yaz ◽

Susan C. Schneider ◽

Yvonne I. Yaz

Keyword(s):

Riccati Equation ◽

Discrete Time ◽

Steady State Solution ◽

State Feedback Control ◽

Disturbance Attenuation ◽

Performance Criteria ◽

Linear Matrix ◽

Time Step ◽

Control Approach ◽

The Difference

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

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