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Brockett's Second Example:A FAS Approach Treatment

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Journal of Systems Science & Complexity 2023年第5期36卷 1789-1808页

作者： duan Guang-ren Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern University of Science and TechnologyShenzhen 518055China Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China

In this paper,several equivalent forms of the well-known Brockett's second example system are firstly *** stabilization of the system is then treated in the fully actuated system approach.A simple continuous time-invariant sub-stabilizing controller is designed,and the corresponding region of attraction is *** a result,all trajectories of the system starting from the characterized region of attraction are driven exponentially to the *** the region of attraction is very large,the designed sub-stabilizing controller can be directly useful in many practical *** cases where the initial values are indeed needed to be chosen out of the region of attraction,extremely simple pre-controllers can be designed,which drive the system trajectories into the designed region of attraction.A simulation of the designed control system is carried out to show the effect of the proposed approach.

关键词： Brockett integrator continuous time-invariant controllers fully actuated system approach region of attraction sub-stabilization

Stabilization via Fully Actuated System Approach:A Case Study

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Journal of Systems Science & Complexity 2022年第3期35卷 731-747页

作者： duan Guang-ren Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055China Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China

In this note,a benchmark example system which is not stabilizable by a smooth state feedback controller is considered with the fully actuated system(FAS)*** is shown that a smooth controller exists which drives the trajectories starting from a large domain in the initial value space to the origin *** a result brings about a generalization of Lyapunov asymptotical stability,which is termed as global exponential *** region of attraction is allowed to be an unbounded open set of the initial values with closure containing the *** sub-stability result may be viewed to be superior to some local stability results in the Lyapunov sense because the region of attraction is much larger than any finite ball containing the origin and meanwhile the feasible trajectories are always driven to the origin *** on this sub-stabilization result,globally asymptotically stabilizing controllers for the system can be provided in two general ways,one is through combination with existing globally stabilizing controllers,and the other is by using a pre-controller to first move an initial point which is not within the region of attraction into the region of attraction.

关键词： Feedback stabilization fully actuated system approach nonlinear systems region of attraction singularity sets

Brockett’s First Example: An FAS Approach Treatment

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Journal of Systems Science & Complexity 2022年第2期35卷 441-456页

In this note,the well-known Brockett’s first example system is treated with the fully actuated system(FAS)***,it is shown that the system can be exponentially substabilized by a smooth controller in the sense that,except those starting from initial values on the z0-axis of the initial value space,all trajectories of the designed system as well as the control signals decay to zero ***,global stabilization is realized through a way of enabling the trajectories starting from initial values on the z0-axis also to go to the *** idea is to firstly move an initial point on the z0-axis away from the axis using a pre-controller,and then to take over by the designed exponentially sub-stabilizing controller.

关键词： Exponential sub-stabilization feedback stabilization fully actuated system approach region of attraction singularity sets

A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

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Science China(Information Sciences) 2024年第2期67卷 118-143页

作者： Guang-ren duan Center for Control Theory and Guidance Technology Harbin Institute of Technology Center for Control Science and Technology Southern University of Science and Technology

In this paper, a type of general nonholonomic systems is proposed, which contains both the Brockett’s two example systems, and their extended n-dimensional chained forms, as special cases. For the stabilization of such systems, a stabilizing controller is proposed based on the fully actuated system(FAS)approach, which is discontinuous at the origin but time-invariant when the open-loop system is time-invariant,and drives the feasible trajectories of the system to the origin exponentially. Furthermore, the proposed FAS approach is also extended to the sub-normal system case and the time-delay system case.

关键词： nonholonomic systems feedback stabilization exponential convergence sub-fully actuated systems time-delay systems

A FAS approach for stabilization of generalized chained forms: part 2. Continuous control laws

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Science China(Information Sciences) 2024年第3期67卷 114-135页

作者： Guang-ren duan Center for Control Theory and Guidance Technology Harbin Institute of Technology Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern University of Science and Technology

In this paper, continuous time-varying stabilizing controllers for the type of general nonholonomic systems proposed and treated in part 1 are designed using the fully actuated system(FAS) approach. The key step is to differentiate the first scalar equation, and by control of the obtained second-order scalar system, a proportional plus integral feedback form for the first control variable is obtained. With the solution to this designed second-order scalar system, the rest equations in the nonholonomic system form an independent time-varying subsystem which is then handled by the FAS approach. The overall designed controller contains an almost arbitrarily chosen design parameter, and is proven to guarantee the uniformly and globally exponential stability of the closed-loop system. The proposed approach is simple and effective,and is demonstrated with a practical example of ship control.

关键词： nonholonomic systems feedback stabilization fully actuated systems Lyapunov stability continuous controllers

Fully Actuated System Approach for Linear Systems Control:A Frequency-Domain Solution

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Journal of Systems Science & Complexity 2022年第6期35卷 2046-2061页

作者： duan Guang-ren ZHOU Bin The Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055China The Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China

This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system *** method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD *** continuous-time and discrete-time linear systems are *** numerical examples are worked out to illustrate the effectiveness of the proposed approaches.

关键词： Column reduced factorization first-order linear state-space systems high-order fully actuated systems polynomial matrix description right coprime

High-Order Fully Actuated System Models for Strict-Feedback Systems With Increasing Dimensions

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IEEE/CAA Journal of Automatica Sinica 2024年第12期11卷 2451-2462页

作者： Xiang Xu Guang-ren duan Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern University of Science and Technology the School of System Design and Intelligent Manufacturing Southern University of Science and Technology

This paper mainly addresses control problems of strict-feedback systems(SFSs) with increasing dimensions. Compared with the commonly-considered SFSs where the subsystems have the same dimension, we aim to handle more complex cases,i.e., the subsystems in the considered SFSs are assumed to have increasing dimensions. By transforming the systems into highorder fully-actuated system(HOFAS) models, the stabilizing controllers can be directly given. Besides first-order SFSs, secondorder and high-order SFSs are also considered.

关键词： Increasing dimensions high-order fully-actuated system nonlinear systems strict-feedback systems

On the Role of Zeros in the Pole Assignment of Scalar High-Order Fully Actuated Linear Systems

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Journal of Systems Science & Complexity 2022年第2期35卷 535-542页

作者： ZHOU Bin duan Guang-ren Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055China

It is well known that for a linear system in state space form,controllability is equivalent to arbitrary pole assignment by state *** brief points out that for a scalar high-order fully actuated linear system,the pole assignment problem is solvable if and only if the desired pole set of the closed-loop system should not include the zero set of the open-loop system if the implementation issue of the controller is taken into account,that is,controllability cannot guarantee arbitrary pole assignment by state feedback.

关键词： High-order fully actuated systems pole assignment state feedback zeros

Fully Actuated System Approach for 6DOF Spacecraft Control Based on Extended State Observer

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Journal of Systems Science & Complexity 2022年第2期35卷 604-622页

作者： ZHAO Qin duan Guang-ren Center for Control Science and Technology Southern University of Science and TechnologyShenzhen 518055China Center for Control Theory and Guidance Technology Harbin Institute of TechnologyHarbin 150001China

This paper deals with the problem of position and attitude tracking control for a rigid spacecraft.A fully actuated system(FAS)model for the six degree-of-freedom(6DOF)spacecraft motion is derived first from the state-space model by variable *** the uncertainties from external disturbance,unknown motion information,and uncertain inertia properties,an extended state observer(ESO)is designed to estimate the total ***,a tracking controller based on FAS approach is designed,and this makes the closed-loop system a constant linear one with an arbitrarily assignable *** solution to the parameter matrices of the observer and controller is given *** is proved via the Lyapunov stability theory that the observer errors and tracking errors both converge into the neighborhood of the ***,numerical simulation demonstrates the effectiveness of the proposed controller.

关键词： Constant linear closed-loop system extended state observer fully actuated system approach relative position and attitude control