Modeling and adaptive tracking for stochastic nonholonomic constrained mechanical systems

This paper is devoted to the problem of modeling and trajectory tracking for stochastic nonholonomic dynamic systems in the presence of unknown parameters. Prior to tracking controller design, the rigorous derivation of stochastic nonholonomic dynamic model is given. By reasonably introducing so-called internal state vector, a reduced dynamic model, which is suitable for control design, is proposed. Based on the backstepping technique in vector form, an adaptive tracking controller is then derived, guaranteeing that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters. The efficiency of the controller is demonstrated by a mechanics system: a vertical mobile wheel in random vibration environment

Output Feedback Stabilization for Stochastic Nonholonomic Systems under Arbitrary Switching

The output feedback controllers of stochastic nonholonomic systems under arbitrary switching are discussed. We adopt an observer which can simplify the design process. The designed control laws cause the calculation of the gain parameter to be very convenient since the denominator of virtual controllers does not contain the gain parameter. Finally, an example is given to show the effectiveness of controllers

Adaptive Exponential Stabilization for a Class of Stochastic Nonholonomic Systems

This paper investigates the adaptive stabilization problem for a class of stochastic nonholonomic systems with strong drifts. By using input-state-scaling technique, backstepping recursive approach, and a parameter separation technique, we design an adaptive state feedback controller. Based on the switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the states of closed-loop system are global bounded in probability

Adaptive State-Feedback Stabilization for Stochastic Nonholonomic Mobile Robots with Unknown Parameters

The stabilizing problem of stochastic nonholonomic mobile robots with uncertain parameters is addressed in this paper. The nonholonomic mobile robots with kinematic unknown parameters are extended to the stochastic case. Based on backstepping technique, adaptive state-feedback stabilizing controllers are designed for nonholonomic mobile robots with kinematic unknown parameters whose linear velocity and angular velocity are subject to some stochastic disturbances simultaneously. A switching control strategy for the original system is presented. The proposed controllers that guarantee the states of closed-loop system are asymptotically stabilized at the zero equilibrium point in probability

Global inverse optimal stabilization of stochastic nonholonomic systems

Optimality has not been addressed in existing works on control of (stochastic) nonholonomic systems.This paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize (in probability) nonholonomic systems affine in stochastic disturbances. The design is based on the Lyapunov direct method, the backstepping technique, and the inverse optimal control design. A class of Lyapunov functions, which are not required to be as nonlinearly strong as quadratic or quartic, is proposed for the control design. Thus, these Lyapunov functions can be applied to design of controllers for underactuated (stochastic) mechanical systems, which are usually required Lyapunov functions of a nonlinearly weak form. The proposed control design is illustrated on a kinematic cart, of which wheel velocities are perturbed by stochastic noise