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Journal Article•DOI•

Stabilization of uncertain chained form systems within finite settling time

Yiguang Hong, Jiankui Wang, Zairong Xi
12 Sep 2005-IEEE Transactions on Automatic Control (IEEE)-Vol. 50, Iss: 9, pp 1379-1384
TL;DR: A novel switching control strategy with help of homogeneity, time-rescaling, and Lyapunov-based method is proposed to design a nonsmooth state feedback law such that the controlled chained form system is both LyAPunov stable and finite-time convergent within any given settling time.
Abstract: This note considers finite time stabilization of uncertain chained form systems. The objective is to design a nonsmooth state feedback law such that the controlled chained form system is both Lyapunov stable and finite-time convergent within any given settling time. We propose a novel switching control strategy with help of homogeneity, time-rescaling, and Lyapunov-based method. Also, the simulation results show the effectiveness of the proposed control design approach.
Citations
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Journal Article•DOI•
Finite/Fixed-Time Stabilization for Nonlinear Interconnected Systems With Dead-Zone Input

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Changchun Hua1, Yafeng Li1, Xinping Guan2•
Yanshan University1, Shanghai Jiao Tong University2
01 May 2017-IEEE Transactions on Automatic Control
TL;DR: Based on the recursive method, a new decentralized finite-time controller is designed such that all the state variables reach zero in finite time and the reaching time only depends the control design parameters.
Abstract: The decentralized control problem is considered for a class of nonlinear time-varying interconnected systems. Each subsystem is with the dead-zone input and unmodeled dynamics. The interconnections are bounded by time-varying nonlinear functions, which relaxes the commonly used linear condition or time-invariant condition. Based on the recursive method, we design a new decentralized finite-time controller such that all the state variables reach zero in finite time. The reaching time is based on the design parameters and initial value of system state. Furthermore, the fixed time stability conditions are given and the constructed controller can guarantee the fixed-time stabilization of the system, in which the reaching time only depends the control design parameters. Finally, simulation results are presented to illustrate the effectiveness of proposed method.

170 citations

Cites background from "Stabilization of uncertain chained ..."

  • ...The work [4] studied the finite-time stabilization for lower-triangular nonlinear systems, while [8] considered the finite-time stabilization problem for the uncertain chained form systems....

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Journal Article•DOI•
Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer

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Haibo Du1, Guanghui Wen2, Xinghuo Yu2, Shihua Li2, Michael Z. Q. Chen3 •
Hefei University of Technology1, Southeast University2, University of Hong Kong3
01 Dec 2015-Automatica
TL;DR: The consensus tracking problem of multiple nonholonomic high-order chained-form systems is considered and a finite-time observer-based distributed control strategy is proposed.

152 citations

Journal Article•DOI•
Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots

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Haibo Du1, Guanghui Wen2, Yingying Cheng1, Yigang He1, Ruting Jia3 •
Hefei University of Technology1, Southeast University2, California State University3
01 Dec 2017-IEEE Transactions on Neural Networks
TL;DR: A finite-time cooperative controller is explicitly constructed which guarantees that the states consensus is achieved in a finite time to solve the consensus problem of multiple nonholonomic mobile robots.
Abstract: The consensus problem of multiple nonholonomic mobile robots in the form of high-order chained structure is considered in this paper. Based on the model features and the finite-time control technique, a finite-time cooperative controller is explicitly constructed which guarantees that the states consensus is achieved in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

142 citations

Cites methods from "Stabilization of uncertain chained ..."

  • ...Inspired by [45], we first divide the considered systems into two subsystems a high-order case and a low-order case....

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  • ...To this end, we will employ the switching control scheme proposed in [45], that is...

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  • ...Based on the finite-time control technique, the work [45] considered the finite-time stabilization problem for single chained form nonholonomic system....

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Journal Article•DOI•
Adaptive output feedback control of stochastic nonholonomic systems with nonlinear parameterization

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Hui Wang1, Hui Wang2, Hui Wang3, Quanxin Zhu2, Quanxin Zhu3 •
Nanjing University of Information Science and Technology1, Hunan Normal University2, Nanjing Normal University3
01 Dec 2018-Automatica
TL;DR: An adaptive control method is utilized, together with a parameter separation technique, to construct an adaptive output feedback controller to regulate the whole systems of nonlinearly parameterized stochastic nonholonomic systems.

84 citations

Journal Article•DOI•
Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation

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Hua Chen1•
Hohai University1
08 Oct 2014-International Journal of Control Automation and Systems
TL;DR: In this paper, the robust stabilization problem is addressed for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation, and a continuous, time varying, saturated controller is presented for the kinematic system of the robots.
Abstract: In this paper, the robust stabilization problem is addressed for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation Firstly, a continuous, time varying, saturated controller is presented for the kinematic system of the robots Secondly, for the dynamic feedback system, a special derivable, saturated kinematic controller with slope restrictions is selected as a virtual control law that can be tracked by the real generalized velocity in a finite time, furthermore, the dynamic input signals are continuous and saturated at any time The systematic strategy combines the theory of finite-time stability with the virtual-controller-tracked method Finally, the simulation results show the effectiveness of the proposed controller design approach

72 citations

Cites background from "Stabilization of uncertain chained ..."

  • ...In addition, as an example in [19], Jiang has derived a robust state-feedback controller to drive the states of (2) to the origin with exponential convergence, and in [21], Hong et al....

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  • ...[21] proposed a finite time stabilizer for nonholonomic chained system, Ma et al....

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References
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Journal Article•DOI•
Continuous finite-time stabilization of the translational and rotational double integrators

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Sanjay P. Bhat1, Dennis S. Bernstein2•
Indian Institutes of Technology1, University of Michigan2
01 May 1998-IEEE Transactions on Automatic Control
TL;DR: A class of bounded continuous time-invariant finite-time stabilizing feedback laws is given for the double integrator because Lyapunov theory is used to prove finite- time convergence.
Abstract: A class of bounded continuous time-invariant finite-time stabilizing feedback laws is given for the double integrator. Lyapunov theory is used to prove finite-time convergence. For the rotational double integrator, these controllers are modified to obtain finite-time-stabilizing feedback that avoid "unwinding".

1,389 citations

"Stabilization of uncertain chained ..." refers background in this paper

  • ...The following result can be found in [2]....

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  • ...To date, finite-time stabilizing control has been studied and several explicitly-constructed continuous (but nonsmooth) finite-time controllers for some nonlinear systems (with single input) have been obtained in the references such as [2], [6], and [7]....

    [...]

  • ...On the other hand, nonsmooth finite time control, which makes the controlled system reach the target in a finite time, provides fast response and high tracking precision, and moreover, shows disturbance-rejection properties because of its nonsmoothness [2]....

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Journal Article•DOI•
Control and stabilization of nonholonomic dynamic systems

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Anthony M. Bloch1, Mahmut Reyhanoglu2, N.H. McClamroch2•
Ohio State University1, University of Michigan2
01 Nov 1992-IEEE Transactions on Automatic Control
TL;DR: In this article, a class of inherently nonlinear control problems arising directly from physical assumptions about constraints on the motion of a mechanical system is identified and a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested.
Abstract: A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested. >

857 citations

"Stabilization of uncertain chained ..." refers background in this paper

  • ...INTRODUCTION The last several decades have witnessed the increasing interest in the control of nonholonomic systems (see, for example, [3], [4], and [8]–[12])....

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Journal Article•DOI•
Exponential stabilization of nonholonomic chained systems

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O.J. Sordalen1, Olav Egeland1•
Norwegian Institute of Technology1
01 Jan 1995-IEEE Transactions on Automatic Control
TL;DR: This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form, which are controllable but not asymptotically stabilizable by a smooth static-state feedback control law.
Abstract: This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form. These systems are controllable but not asymptotically stabilizable by a smooth static-state feedback control law. In addition, exponential stability cannot be obtained with a smooth, time-varying feedback control law. Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth, time-varying feedback control law. The control law depends, in addition to the state and time, on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the analysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is presented. Simulation results are also shown. >

591 citations

"Stabilization of uncertain chained ..." refers background in this paper

  • ...In recent years, important steps in feedback design have been made for the exponential regulation of chained form systems [10], [11], [1], [8]....

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Journal Article•DOI•
Finite-time stabilization and stabilizability of a class of controllable systems

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Yiguang Hong1, Yiguang Hong2•
Chinese Academy of Sciences1, Duke University2
23 Jul 2002-Systems & Control Letters
TL;DR: In this paper, finite-time control problem of a class of controllable systems is considered and explicit formulae are proposed for the finite time stabilization of a chain of power-integrators, and discussions about a generalized class of nonlinear systems are given.

577 citations

"Stabilization of uncertain chained ..." refers background or methods in this paper

  • ...To solve the finite time stabilization problemwith (8) holding for any t 0, here we can extend the design idea given in [6] to this uncertain time-varying system (9)....

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  • ...To date, finite-time stabilizing control has been studied and several explicitly-constructed continuous (but nonsmooth) finite-time controllers for some nonlinear systems (with single input) have been obtained in the references such as [2], [6], and [7]....

    [...]

Journal Article•DOI•
Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

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Robert T. M'Closkey1, Richard M. Murray2•
University of California, Los Angeles1, California Institute of Technology2
01 May 1997-IEEE Transactions on Automatic Control
TL;DR: This paper provides a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers, and can be extended to a large class of systems with torque inputs.
Abstract: This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.

420 citations

"Stabilization of uncertain chained ..." refers background in this paper

  • ...In recent years, important steps in feedback design have been made for the exponential regulation of chained form systems [10], [11], [1], [8]....

    [...]

Related Papers (5)
Discontinuous control of nonholonomic systems

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Alessandro Astolfi
Finite-Time Stability of Continuous Autonomous Systems

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01 Feb 2000-Siam Journal on Control and Optimization
Sanjay P. Bhat, Dennis S. Bernstein
Asymptotic stability and feedback stabilization

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01 Jan 1983
Roger W. Brockett
Nonholonomic motion planning: steering using sinusoids

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01 May 1993-IEEE Transactions on Automatic Control
Richard M. Murray, S. Shankar Sastry
Finite-time stabilization and stabilizability of a class of controllable systems

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