Robust stability of uncertain piecewise-linear systems: LMI approach

Benabdallah, Amel; Hammami, Mohamed; Kallel, Jalel

doi:10.1007/s11071-010-9795-2

Cited by 13 publications

(5 citation statements)

References 15 publications

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“…Combining existing research results [27,28], the model of the electro-hydraulic composite valve position control system during the valve position opening process is obtained as follows:…”

Section: Offshore Gas Pipeline Valve Transportationmentioning

confidence: 99%

Design of Constructive Controller of Nonlinear System Based on Polynomial Function Growth Condition and Its Application in Deep Subsea Energy Mining and Production Control System

Guo

Zhou

Tian

et al. 2021

Advances in Civil Engineering

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This paper mainly studies the output feedback control problem of the stochastic nonlinear system based on loose growth conditions and applies the research results to the valve control system of underwater oil and gas pipelines, which can improve the speed and stability of the equipment system. First, the concept of randomness is introduced to study the actual tracking control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general polynomial function growth conditions, and propose a combination of static and dynamic output feedback practices. The design of the tracking controller makes all the states of the system meet boundedness and ensures that the tracking error of the system converges to a small neighborhood of zero. Second, the system is extended to the parameter-uncertain system, and the output feedback tracking controller with complete dynamic gain is constructed by proving the boundedness of the system state and gain. Further, the time-delay factor is introduced, and the nonlinear term of the system satisfies the more relaxed power growth condition, combined with the inverse method to cleverly construct a set of Lyapunov functions and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Stability. Finally, through the ocean library in the Simulation X simulation software, the controller design results are imported into the underwater electro-hydraulic actuator model to verify the effectiveness of the controller design.

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“…Combining existing research results [27,28], the model of the electro-hydraulic composite valve position control system during the valve position opening process is obtained as follows:…”

Section: Offshore Gas Pipeline Valve Transportationmentioning

confidence: 99%

Design of Constructive Controller of Nonlinear System Based on Polynomial Function Growth Condition and Its Application in Deep Subsea Energy Mining and Production Control System

Guo

Zhou

Tian

et al. 2021

Advances in Civil Engineering

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show abstract

“…A robust control method provides more flexibility, Taking an autonomous vehicle as an example [5,6], the weight change of the passengers or cargo in the vehicle will cause the controlled system to change. Such common problems pose challenges to the design of the controller, so the designed controller must have sufficient robustness to continuously control the vehicle over the course of these changes [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Backstepping Control Strategy of an Autonomous Underwater Vehicle Based on Probability Gain

2022

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In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system’s output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system’s control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot’s actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design.

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“…When the state variable is finitely changed, the state variable has a finite increase as a nonlinear function of the independent variable and the rate of growth satisfies certain constraints. As the most basic linear growth condition, this growth condition has been used by quite a lot of research results as the basic assumption for the controller design [5,6]. For later researchers, there is a very challenging task for nonlinear term constraints, which further weaken the constraints on nonlinear terms.…”

Section: Introductionmentioning

confidence: 99%

“…In the case that the input and output are measurable and the state variables are unmeasurable, the design of the system has a very practical value. In [5,6], the state feedback and output feedback control problems of nonlinear systems with unmeasurable states are studied, and the constraints of nonlinear terms are gradually relaxed.…”

Section: Introductionmentioning

confidence: 99%

Bounded Analysis and Practical Tracking Control of Complex Stochastic Nonlinear Systems with Unknown Control Coefficients

Guo

Fang

2020

Complexity

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This paper mainly focuses on the output practical tracking controller design for a class of complex stochastic nonlinear systems with unknown control coefficients. In the existing research results, most of the complex systems are controlled in a certain direction, which leads to the disconnection between theoretical results and practical applications. The authors introduce unknown control coefficients, and the values of the upper and lower bounds of the control coefficients are generalized by constants to allow arbitrary values to be arbitrarily large or arbitrarily small. In the control design program, the design problem of the controller is transformed into a parameter construction problem by introducing appropriate coordinate transformation. Moreover, we construct an output feedback practical tracking controller based on the dynamic and static phase combined by Ito stochastic differential theory and selection of appropriate design parameters, ensuring that the system tracking error can be made arbitrarily small after some large enough time. Finally, a simulation example is provided to illustrate the efficiency of the theoretical results.

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Robust stability of uncertain piecewise-linear systems: LMI approach

Cited by 13 publications

References 15 publications

Design of Constructive Controller of Nonlinear System Based on Polynomial Function Growth Condition and Its Application in Deep Subsea Energy Mining and Production Control System

Design of Constructive Controller of Nonlinear System Based on Polynomial Function Growth Condition and Its Application in Deep Subsea Energy Mining and Production Control System

Backstepping Control Strategy of an Autonomous Underwater Vehicle Based on Probability Gain

Bounded Analysis and Practical Tracking Control of Complex Stochastic Nonlinear Systems with Unknown Control Coefficients

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