Abstract
This paper presents an adaptive control strategy for a class of nonholonomic systems in chained form with virtual control coefficients, nonlinear uncertainties, and unknown time delays. State scaling technique and backstepping recursive approach are applied to design a nonlinear state feedback controller, which can guarantee the stabilization of the closed-loop systems. The simulation results are provided to show the effectiveness of the proposed method.
Highlights
In the last few decades, considerable efforts have been devoted to the research of nonholonomic system, which is a particular class of nonlinear systems and widespread in real world, such as mobile robots, car-like vehicle, underactuated satellites, and knife-edge
It is well known that the control of nonholonomic systems is extremely challenging, largely due to the impossibility of asymptotically stabilizing nonholonomic systems via smooth time-invariant state feedback, a well-recognized fact pointed out in [1, 2]
We introduce a new class of chained nonholonomic systems with unknown virtual control coefficients, uncertain nonlinearities, and unknown time delays and study the problem of adaptive state feedback stabilization
Summary
In the last few decades, considerable efforts have been devoted to the research of nonholonomic system, which is a particular class of nonlinear systems and widespread in real world, such as mobile robots, car-like vehicle, underactuated satellites, and knife-edge. It is well known that the control of nonholonomic systems is extremely challenging, largely due to the impossibility of asymptotically stabilizing nonholonomic systems via smooth time-invariant state feedback, a well-recognized fact pointed out in [1, 2]. Some new adaptive control strategies have been proposed to stabilize the nonholonomic systems. In [19, 20, 25], the problem of stabilization is studied for delayed nonholonomic systems; the virtual control coefficients and unknown parameter vector are not considered. We introduce a new class of chained nonholonomic systems with unknown virtual control coefficients, uncertain nonlinearities, and unknown time delays and study the problem of adaptive state feedback stabilization. The switching control strategy for the first subsystem is employed to achieve the asymptotic stabilization
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