Deterministic Controllers for a Class of Mismatched Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Sandeep
Keyword(s):  
Dynamical Systems ◽  
Uniform Boundedness ◽  
Sufficient Condition ◽  
Ultimate Boundedness ◽  
Matching Conditions ◽  
Uncertain Dynamical Systems ◽  
Uniform Ultimate Boundedness

In this paper a class of nonlinear uncertain dynamical systems, which do not satisfy the matching conditions, is considered. This class of mismatched systems is more general than one considered earlier. A sufficient condition, in terms of a critical mismatch threshold, is given, which ensures uniform boundedness and uniform ultimate boundedness. The theory is illustrated by an example of controlled aircraft take-off under windshear conditions.

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

A Novel Robust Control of Uncertain Furuta Pendulum Based on a General Lyapunov Function

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Xinrong Zhang ◽  
Ruiying Zhao ◽  
Jie Ma ◽  
Chul-Hee Lee
Keyword(s):  
Robust Control ◽  
Lyapunov Function ◽  
Control Design ◽  
Uniform Boundedness ◽  
Fast Time ◽  
Ultimate Boundedness ◽  
Pendulum System ◽  
System A ◽  
Uniform Ultimate Boundedness ◽  
Nonlinear Pendulum

AbstractA novel robust approach for the obedience control of Furuta pendulum with uncertainty is proposed. The uncertainty considered in this paper is (possibly fast) time-varying and bounded, which may exist in any stage of the pendulum subsystem. By the Lagrangian formulation of the nonlinear pendulum system, a robust control, based on a general Lyapunov function, is designed to render the Furuta pendulum a position obedience. As a consequence of the Lyapunov approach, the control design is not restricted to linearize the pendulum system. The system performance under the proposed control is guaranteed as uniform boundedness and uniform ultimate boundedness. The salient features of this new control are demonstrated both analytically and numerically. The experiment is conducted in the Furuta pendulum system to prove the validity and effectiveness of the control design.

scholarly journals Robust control design for home pension service mobile robots with passive and servo constraints

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042095221
Author(s):  
Yating Zhao ◽  
Xiaolong Chen ◽  
Han Zhao
Keyword(s):  
Robust Control ◽  
Mobile Robots ◽  
Control Design ◽  
Uniform Boundedness ◽  
Control Force ◽  
Dynamics Modeling ◽  
Ultimate Boundedness ◽  
Uniform Ultimate Boundedness ◽  
Robust Control Design ◽  
Servo Constraints

This paper presents a novel robust control design for a class of home pension service mobile robots (HPSMRs) with non-holonomic passive constraints, based on the Udwadia-Kalaba theory and Udwadia control. The approach has two portions: dynamics modeling and robust control design. The Udwadia-Kalaba theory is employed to deal with the non-holonomic passive constraints. The frame of the Udwadia control is employed to design the robust control to tracking the servo constraints. The designed approach is easy to implement because the analytical solution of the control force can explicitly be obtained even if the non-holonomic passive constraints exists. The uniform boundedness and uniform ultimate boundedness are demonstrated by the theoretical analysis. The effectiveness of the proposed approach is verified through the numerical simulation by a HPSMR.

scholarly journals Stability, boundedness and existence of unique periodic solutions to a class of fourth order functional differential equations

2021 ◽  
Vol 40 (2) ◽  
pp. 271-303
Author(s):  
Adeleke Timothy Ademola
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Ultimate Boundedness ◽  
Uniform Asymptotic Stability ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Theoretical Results

In this paper a novel class of fourth order functional differential equations is discussed. By reducing the fourth order functional differential equation to system of first order, a suitable complete Lyapunov functional is constructed and employed to obtain sufficient conditions that guarantee existence of a unique periodic solution, asymptotic and uniform asymptotic stability of the zero solutions, uniform boundedness and uniform ultimate boundedness of solutions. The obtained results are new and include many prominent results in literature. Finally, two examples are given to show the feasibility and reliability of the theoretical results.

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