Guaranteeing Uniform Ultimate Boundedness for Uncertain Systems Free of Matching Condition

2018 ◽  
Vol 26 (6) ◽  
pp. 3479-3493 ◽  
Author(s):  
Jinquan Xu ◽  
Yutao Du ◽  
Ye-Hwa Chen ◽  
Hong Guo ◽  
Xiaofeng Ding
Robotica ◽  
2014 ◽  
Vol 33 (1) ◽  
pp. 87-105 ◽  
Author(s):  
Khoshnam Shojaei

SUMMARYMany research works on the control of nonholonomic wheeled mobile robots (WMRs) do not consider the actuator saturation problem and the absence of velocity sensors in practice. The actuator saturation deteriorates the tracking performance of the controller, and the use of velocity sensors increases the cost and weight of WMR systems. This paper simultaneously addresses these problems by designing a saturated output feedback controller for uncertain nonholonomic WMRs. First, a second-order input–output model of nonholonomic WMRs is developed by defining a suitable set of output equations. Then a saturated adaptive robust tracking controller is proposed without velocity measurements. For this purpose, a nonlinear saturated observer is used to estimate robot velocities. The risk of actuator saturation is effectively reduced by utilizing saturation functions in the design of the observer–controller scheme. Semi-global uniform ultimate boundedness of error signals is guarantied by the Lyapunov stability analyses. Finally, simulation results are provided to show the effectiveness of the proposed controller. Compared with one recent work of the author, a comparative study is also presented to illustrate that the proposed saturated controller is more effective when WMR actuators are subjected to saturation.


1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock

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.


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