Regulating Constraint Obedience for Fuzzy Mechanical Systems Based on $\beta$-Measure and a General Lyapunov Function

Yang, Guolai; Zhao, Han; Sun, Qinqin; Chen, Ye‐Hwa

doi:10.1109/tfuzz.2016.2633366

Cited by 27 publications

(18 citation statements)

References 24 publications

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“…And then, a performance index, incorporating fuzzy and deterministic performance, was designed to solve the optimal design of the proposed control. The effectiveness of the joint utilization of UKFE and various control methods, such as optimal control, fuzzy control, etc., was also verified in [17]- [21].…”

Section: Introductionmentioning

confidence: 61%

Adaptive Robust Constraint Following Control for Omnidirectional Mobile Robot: An Indirect Approach

et al. 2021

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The tracking performance of mobile robot is often affected by uncertainties from the deviation of initial conditions, external disturbances and varying loads, etc. An Udwadia-Kalaba based adaptive robust control is proposed for the trajectory tracking of an omnidirectional mobile robot in the presence of uncertainties. The proposed control includes nominal control part based on Udwadia-Kalaba theory and adaptive robust control part. The desired trajectory is considered as a virtual servo constraint applied to the robot system and converted into the second order standard form. So that the analytical form of constraint force could be obtained via Udwadia-Kalaba Fundamental Equation (UKFE). The system will precisely obey the given constraint (i.e., the desired trajectory) under the obtained constraint force in ideal cases. No auxiliary variables are required and it is effective whether the constraints are holonomic or nonholonomic. The designed adaptive law is in leakage type and the adaptive parameters are adjusted according to the performance of the system in order to compensate for the effect caused by uncertainty in the system. No extra information of uncertainty is needed except for the existence of uncertainty bound. Comparing with PID control, it can be found that the proposed control has better performance and can realize higher precision trajectory tracking control.

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Section: Introductionmentioning

confidence: 61%

Adaptive Robust Constraint Following Control for Omnidirectional Mobile Robot: An Indirect Approach

et al. 2021

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“…It is obvious that the problem formulated above is with triple objectives and triple design parameters, and the uncertainty considered is not necessary fuzzy. This shows the advantage of the Stackelberg game theory over the past methods in related studies (such as [1][2][3][4]), which merely handle optimal design problem with single objective, single design parameter and fuzzy uncertainty.…”

Section: Statement Of Optimal Design Problemmentioning

confidence: 94%

“…When more specifics of the system characteristics and tasks are used in the design, it is generally anticipated that the control is in more coherence with the said framework. As an outstanding representative of system-task-specific control, a creative approach of constraintfollowing control is explored by Chen et al [1][2][3][4][5][6][7], which guides the design of control strategy in this paper.…”

Section: Introductionmentioning

confidence: 99%

Optimal Parameter Selection for Constraint-Following Control for Mechanical Systems Based on Stackelberg Game

Sun

Yang

Chen

et al. 2021

Preprint

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This paper proposes an optimal parameter design of control scheme for mechanical systems by adopting the Stackelberg game theory. The goal of the control is to drive the mechanical system to follow the prescribed constraints. The system uncertainty is (possibly fast) time-varying and bounded. A β-measure is defined to gauge the performance. A robust control is proposed to render the β-measure uniformly ultimately bounded. This control scheme is based on feasible design parameters (i.e., parameters within prescribed range), whose choice may not be unique. For optimal (unique) parameter selection, a Stackelberg game is formulated. By taking the control design parameters as the players, for each player, a cost function is built with the consideration of the performance cost, the time cost and the control cost. To follow, the Stackelberg strategy is then carried out via backward induction, which results in the choice of the optimal parameters.

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“…3–5 The second study takes advantage of the characteristics of problems specific to mechanical systems, with the help from the strategy of control theory. 6–9…”

Section: Introductionmentioning

confidence: 99%

“…[3][4][5] The second study takes advantage of the characteristics of problems specific to mechanical systems, with the help from the strategy of control theory. [6][7][8][9] Chen et al [10][11][12][13][14][15][16][17][18] have made some pioneering efforts on servo-constraint control with the methodology of approximate constraint following. In their studies, an equality constraint, which may be holonomic or nonholonomic, is considered to represent desired system performance and desired trajectory.…”

Section: Introductionmentioning

confidence: 99%

Adaptive robust control for tank stability: A constraint-following approach

Sun

Yang

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article addresses a control problem for tank stability based on constraint following. The objective is to design a control to drive the tank stability control system to follow a pre-specified stability constraint approximately: with the consideration of (possibly) time-varying uncertainty (including system modeling error and road excitation), if the barrel deviates from the target angle, drive it to be arbitrarily close to the target angle; and if the barrel points to the target angle, drive it to stay there. This is formulated as a problem of approximate constraint-following control. First, as the model-based control design object, the dynamic equation of the tank stability control system with the system modeling error and the road excitation is obtained. Second, as the control objective, the stability constraint is formulated. Third, as the control strategy, an adaptive robust control is proposed for approximate constraint following. Fourth, as the control object, a virtual prototype model of tank driving on bumpy road is established with multi-body dynamics software RecurDyn. Finally, real-time servo control and target observation of the tank stability system are performed by co-simulation. It shows that the constraint-following error converges quickly to [Formula: see text] in 1.5 s. By this, the tank stability control system can be always stable even if the tank is driving and disturbed with frequent road excitation.

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Regulating Constraint Obedience for Fuzzy Mechanical Systems Based on $\beta$-Measure and a General Lyapunov Function

Cited by 27 publications

References 24 publications

Adaptive Robust Constraint Following Control for Omnidirectional Mobile Robot: An Indirect Approach

Adaptive Robust Constraint Following Control for Omnidirectional Mobile Robot: An Indirect Approach

Optimal Parameter Selection for Constraint-Following Control for Mechanical Systems Based on Stackelberg Game

Adaptive robust control for tank stability: A constraint-following approach

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