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首页> 外文期刊>Circuits, systems, and signal processing >Robust Nonlinear H_∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach
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Robust Nonlinear H_∞ State Feedback Control of Polynomial Discrete-Time Systems: An Integrator Approach

机译：多项式离散系统的鲁棒非线性H_∞状态反馈控制：积分器方法

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摘要

This paper investigates the problem of designing a nonlinear H_∞ state feedback controller for polynomial discrete-time systems with norm-bounded uncertainties. In general, the problem of designing a controller for polynomial discrete-time systems is difficult, because it is a nonconvex problem. More precisely, in general, its Lyapunov function and control input are not jointly convex. Hence, it cannot be solved by semidefinite programming. In this paper, a novel approach is proposed, where an integrator is incorporated into the controller structure. In doing so, a convex formulation of the controller design problem can be rendered in a less conservative way than the available approaches. Furthermore, we establish the interconnection between robust H_∞ control of polynomial discrete-time systems with norm-bounded uncertainties and H_∞ control of scaled polynomial discrete-time systems. This establishment allows us to convert the robust H_∞ control problems to H_∞ control problems. Then, based on the sum of squares (SOS) approach, sufficient conditions for the existence of a nonlinear H_∞ state feedback controller are given in terms of solvability of polynomial matrix inequalities (PMIs), which can be solved by the recently developed SOS solvers. A tunnel diode circuit is used to demonstrate the validity of this integrator approach.
机译：本文研究了为具有范数界不确定性的多项式离散时间系统设计非线性H_∞状态反馈控制器的问题。通常，为多项式离散时间系统设计控制器的问题很困难，因为它是一个非凸问题。更准确地说，通常，其Lyapunov功能和控制输入不是共同凸的。因此，它不能通过半定编程解决。在本文中，提出了一种新颖的方法，其中将积分器整合到控制器结构中。这样做，可以以比可用方法更不保守的方式来呈现控制器设计问题的凸形式。此外，我们建立了具有范数有界不确定性的多项式离散时间系统的鲁棒H_∞控制与标度多项式离散时间系统的H_∞控制之间的互连。这种建立允许我们将鲁棒的H_∞控制问题转换为H_∞控制问题。然后，基于平方和（SOS）方法，根据多项式矩阵不等式（PMI）的可解性，给出了存在非线性H_∞状态反馈控制器的充分条件，可以通过最近开发的SOS求解器来解决。隧道二极管电路用于证明这种积分器方法的有效性。

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  • 来源
    《Circuits, systems, and signal processing》 |2014年第2期|331-346|共16页
  • 作者

    Shakir Saat; Sing Kiong Nguang; Chih-Min Lin; Zahriladha Zakaria;

  • 作者单位

    Faculty of Electronics and Computer Engineering, Universiti Teknikal Malaysia Melaka,Hang Tuah Jaya, 76100 Durian Tunggal, Malacca, Malaysia;

    Department of Electrical and Computer Engineering. The University ot Auckland, Private Bag 92019, Auckland City, New Zealand;

    Department of Electrical Engineering, Yuan Ze University, No. 135, Far-Eastern Road, Chung-Li, Tao-Yuan, Taiwan, Republic of China;

    Faculty of Electronics and Computer Engineering, Universiti Teknikal Malaysia Melaka,Hang Tuah Jaya, 76100 Durian Tunggal, Malacca, Malaysia;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Robust controller design; Polynomial discrete-time systems; Integrator method; Norm-bounded uncertainty;

    机译：坚固的控制器设计;多项式离散时间系统;积分法受范数约束的不确定性;

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