Abstract
This paper further investigates the problem of finite-time state feedback stabilization for a class of stochastic nonholonomic systems in chained form. Compared with the existing literature, the stochastic nonholonomic systems under investigation have more uncertainties, such as thex0-subsystem contains stochastic disturbance. This renders the existing finite-time control methods highly difficult to the control problem of the systems or even inapplicable. In this paper, by extending adding a power integrator design method to a stochastic system and by skillfully constructingC2Lyapunov function, a novel switching control strategy is proposed, which renders that the states of closed-loop system are almost surely regulated to zero in a finite time. A simulation example is provided to demonstrate the effectiveness of the theoretical results.
Highlights
The nonholonomic systems, which can be used to model many frequently met mechanical systems, such as wheeled mobile robot, knife edge and rolling disk, have been an active research field over the past decades
We give two lemmas where the first one provides sufficient conditions to ensure the existence of pathwise unique strong solution to system (1), and the other one has been used to determine the finite-time stability of stochastic nonlinear systems
Motivated by the statement in [18, 23] that many nonholonomic mechanical systems, such as wheeled mobile robot, subject to stochastic disturbances, can be transformed to a kind of stochastic nonholonomic systems in the so-called chained form, this paper considers the following class of stochastic nonholonomic systems in chained form: dx0 = d0 (t) u0dt + f0 (t, x0) dt + g0T (t, x0) dw, dxi = di (t) xi+1u0dt + fi (t, x0, x) dt + giT (t, x0, x) dw, i = 1, . . . , n − 1, (8)
Summary
The nonholonomic systems, which can be used to model many frequently met mechanical systems, such as wheeled mobile robot, knife edge and rolling disk, have been an active research field over the past decades. In [20], a novel switching finite-time control strategy was proposed to nonholonomic systems in a chained form with uncertain parameters and perturbed terms by the use of time rescaling and Lyapunov based method. Later this result was essentially extended under weaker constraints on drift terms in [21]. This paper continues the investigation in [23] and addresses the finitetime stabilizing control design for stochastic nonholonomic systems with more uncertainties than those in [16,17,18, 23], which cannot be handled by general existing methods.
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