Abstract
This paper investigates the problem of finite‐time stabilization for a class of stochastic nonholonomic systems in chained form. By using stochastic finite‐time stability theorem and the method of adding a power integrator, a recursive controller design procedure in the stochastic setting is developed. Based on switching strategy to overcome the uncontrollability problem associated with x0(0) = 0, global stochastic finite‐time regulation of the closed‐loop system states is achieved. The proposed scheme can be applied to the finite‐time control of nonholonomic mobile robot subject to stochastic disturbances. The simulation results demonstrate the validity of the presented algorithm.
Highlights
The nonholonomic systems, which can model many classes of mechanical systems such as mobile robots and wheeled vehicles, have attracted intensive attention over the past decades
We focus our attention on the following class of stochastic nonholonomic systems: dx[0] d0 t u0dt, dxi di t xi 1u0dt giT x0, x i dw, i 1, . . . , n − 1, 3.1 dxn dn t u1dt gnT x0, x n dw, where x0 ∈ R and x x1, . . . , xn T ∈ Rn are system states, u0 ∈ R and u1 ∈ R are control inputs, respectively; x i x1, . . . , xi T, x n x; di, i 1, . . . , n represent the possible modeling error, refered to as disturbed virtual control coefficients; gi : R × Ri → Rm, i
Under Assumptions 3.2 and 3.3, if the proposed control design procedure together with the above switching control strategy is applied to system 3.1, for any initial conditions in the state space x0, x ∈ Rn 1, the closed-loop system is globally finite-time regulated at origin in probability
Summary
The nonholonomic systems, which can model many classes of mechanical systems such as mobile robots and wheeled vehicles, have attracted intensive attention over the past decades. In order to overcome this obstruction, several approaches have been proposed for the problem, such as discontinuous time-invariant stabilization 2, 3 , smooth time-varying stabilization 4–6 , and hybrid stabilization 7 Using these valid approaches, many fruitful results have been developed 8–15. The problem of finite-time stabilization for nonlinear systems has been studied and numerous theoretical control design methods were presented and developed for various types of nonlinear systems over the last years 23–27. The finite-time controller design for stochastic nonholonomic systems in this paper should solve the following questions. Inspired by the works 25, 28 , we generalize adding a power integrator design method to a stochastic system and based on stochastic finite-time stability theorem, by skillfully constructing C2 Lyapunov functions, a state feedback controller is successfully achieved to guarantee that the closed-loop system states are globally regulated to zero within a given settling time almost surely.
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