High-order Nonholonomic Systems Research Articles

Design of Stabilizing Feedback Controllers for High-Order Nonholonomic Systems

Design of Stabilizing Feedback Controllers for High-Order Nonholonomic Systems

Prescribed-time control of high-order nonholonomic systems in chained form by time-varying feedback

In this paper, the prescribed-time control problem for a class of high-order nonholonomic systems is investigated. With the aid of a novel state transformation, the nonholonomic systems are decoupled. Further, a time-varying high-gain feedback controller is constructed by backstepping. It is shown that the proposed control law can achieve the prescribed-time convergence for high-order nonholonomic systems and the controller is bounded. Numerical examples verify the effectiveness of the method proposed in this paper.

Robust Fixed-Time Consensus Tracking Control of High-Order Multiple Nonholonomic Systems

Convergence rate is an important performance index in consensus control. Yet, most of the existing results can only achieve asymptotic consensus, or finite-time consensus whose settling time is contingent on initial conditions. This paper studies the robust fixed-time consensus tracking control problem for high-order nonholonomic chained-form systems subject to unknown parameters and nonlinear uncertainties. By using the modified power integrator method, we propose a new robust fixed-time consensus tracking algorithm, with which the consensus tracking can be achieved in a fixed time independent of initial conditions even in the presence of uncertainties. An observer-based fixed-time consensus tracking algorithm is also developed as an alternative method to overcome the communication loop problem. Lyapunov analysis shows the fixed-time stability of the closed-loop system. An application to multiple wheeled mobile robots is presented.

Distributed adaptive consensus control for high-order multiple non-holonomic systems

ABSTRACT In this paper, we investigate the consensus problem for high-order multiple non-holonomic systems, in which the leader's reference input signals are unknown to all the followers. Under the assumption that the leader is the root of a spanning tree, by using the backstepping design method, distributed adaptive controllers are constructed recursively. To assure the stability of the overall scheme, projection techniques are employed to modify the uncertain parameters of the desired trajectory. By using algebraic graph theory and Lyapunov theory, it is shown that all closed-loop signals are bounded, and the followers' states converge to the desired reference trajectory asymptotically. Finally, simulation examples are given to show the effectiveness of the proposed control scheme.

A New Approach to Adaptive Stabilization of Stochastic High-Order Nonholonomic Systems

This paper studies the problem of adaptive stabilization for a class of stochastic high-order nonholonomic systems. Under the weaker assumptions, by constructing the appropriate Lyapunov function and combining sign function technique, an adaptive state feedback controller is designed to guarantee global asymptotic stability in probability of the closed-loop system. The effectiveness of the controller is demonstrated by a mechanical system.

Adaptive state feedback stabilization of more general stochastic high‐order nonholonomic systems

SummaryThis paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method.

Output feedback control for a class of high-order nonholonomic systems with complicated nonlinearity and time-varying delay

This paper considers the output feedback control problem for high-order nonholonomic time-delay system. Remarkably, the studied system allows the polynomial time-delay growing conditions. Moreover, the applicable power ranges of nonlinear drift and diffusion terms are further relaxed to be a interval rather than a fix point. By choosing a new Lyapunov–Krasovskii (L–K) functional, and by modifying the adding a power integrator method, a delay-independent output feedback controller is designed such that the system is globally asymptotically stable. A simulation example is given to show the validity of the proposed theory.

State-feedback stabilization for stochastic high-order nonholonomic systems with Markovian switching

This paper investigates the problem of stabilization control design for a class of stochastic high-order nonholonomic systems with Markovian switching. A state feedback controller is obtained by using input-state scaling technique and the generalized Itô formula, and adding a power integrator backstepping approach. The switching strategy is proposed to eliminate the phenomenon of uncontrollability and to guarantee that closed-loop system has a unique solution and the solution of the closed-loop systems is almost surely asymptotically stable. Simulation examples demonstrate the effectiveness of the proposed scheme.

Adaptive state-feedback stabilization of stochastic high-order nonholonomic systems with nonlinear parameterization

This paper investigates the adaptive stabilization of stochastic high-order nonholonomic systems with nonlinear parameterization. An adaptive state feedback controller is designed by using the parameter separation technique and input-state scaling technique, and adding a power integrator backstepping approach. The switching strategy is proposed to eliminate the phenomenon of uncontrollability and to guarantees that the closed-loop system has an almost surely unique solution for any initial state, the equilibrium of interest is globally stable in probability, and the state can almost surely be regulated to the origin. Simulation examples demonstrate the effectiveness of the proposed scheme.

Adaptive finite-time stabilization for a class of uncertain high order nonholonomic systems

In this paper, the adaptive finite-time stabilization problem is investigated for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts and nonlinear parameterization. By skillfully using finite-time stability theorem, parameter separation technique and adding a power integrator method, an adaptive state feedback controller is obtained. To overcome the obstacle that x-subsystem is uncontrollable when the control input u0=0, a novel switching control strategy is given. Based on this, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. Two illustrative examples are also provided to demonstrate the effectiveness of the proposed controller.

Finite-time Stabilization of High-order Nonholonomic Systems with More General Nonlinear Drifts

This paper addresses the finite-time stabilization problem for a class of more general high-order nonholonomic systems with more general nonlinear drifts., the upper bound of which involves not only state variables x1; · · · ;xi but also xi+1. By using finite-time Lyapunov stability theorem and adding a power integrator technique, a recursive controller design procedure is developed. Based on switching strategy to overcome the uncontrollability problem associated with x0(0) = 0, the uncertain closed-loop system is regulated to zero in a finite time. An illustrative example is provided to demonstrate the effectiveness of the proposed controller.

The integral variational principles for embedded variation identity of high-order nonholonomic constrained systems

In this article, from the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems, three kinds of dynamics for high-order nonholonomic constrained systems are obtained, including the vakonomic dynamical model, Lagrange-d'Alembert model and a new one if utilizing respectively three kinds of conditional variation to them. And the integral variational principles for embedded variation identity of high-order nonholonomic constrained systems is also fitted for the general nonholonomic systems when the constrained equation is reduced to a first-order one. Then, the vakonomic dynamic, Chetaev dynamics and a new model of general nonholonomic systems can also be obtained. Finally, two illustrated examples are used to verify the validity of the theory.

Adaptive Sliding Mode Control of Uncertain High-Order Nonholonomic Systems with Unknown Control Coefficients

This paper investigates the global stabilization problem for a class of high-order nonholonomic systems with unknown control coefficients and uncertain nonlinearities. An adaptive sliding mode control (SMC) law based on a constructive manipulation is proposed by adding a power integrator technique. A switching control strategy is employed in the control scheme to overcome the uncontrollability problem associated with the nonholonomic systems. The designed sliding mode controller could guarantee the attractiveness of the sliding surfaceS=0and achieve the asymptotical convergence of the state as well as the boundedness of the estimated parameters. A simulation example is provided to demonstrate the effectiveness of the proposed scheme.

Adaptive stabilization of a class of high-order uncertain nonholonomic systems with unknown control coefficients

SUMMARY This paper is concerned with the globally stabilizing control design for a class of high-order nonholonomic systems. Compared with the existing literature, the high-order nonholonomic systems under investigations have more uncertainties and unknowns, such as neither lower nor upper bound is known for each control coefficient of the systems. This renders the existing control methods highly difficult to the control problems of the systems or even inapplicable. In this paper, by defining two new unknown parameters whose dynamic updating laws are properly chosen and also by using the discontinuous coordinates transformation and the method of adding a power integrator, a new design approach is given to the adaptive stabilizing controllers for the systems. A numerical simulation is provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

This paper investigates the problem of adaptive stabilization control design for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts, including unmodeled dynamics, and dynamics modeled with unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterized system into a linear-like parameterized system. Then, by the use of input-state scaling technique and adding a power integrator backstepping approach, an adaptive state feedback controller is obtained. The adaptive control based switching strategy is proposed to eliminate the phenomenon of uncontrollability. Global asymptotic regulation of the closed-loop system states and the boundedness of other signals are guaranteed. Simulation examples demonstrate the effectiveness of the proposed scheme.

Controller design of high order nonholonomic system with nonlinear drifts

A controller design is proposed for a class of high order nonholonomic systems with nonlinear drifts. The purpose is to ensure a solution for the closed-loop system regulated to zero. Adding a power integrator backstepping technique and the switching control strategy are employed to design the controller. The state scaling is applied to the recursive manipulation. The simulation example demonstrates the effectiveness and robust features of the proposed method.

入力を陽に含む座標変換による1generator高階非ホロノミックシステムの制御

入力を陽に含む座標変換による1generator高階非ホロノミックシステムの制御

Adaptive regulation of high order nonholonomic systems

The problem of adaptive regulation of a class of high-order parametric nonholonomic systems in chained-form was discussed. Using adding a power integrator technique and state scaling with discontinuous projection technique, a discontinuous adaptive dynamic controller was constructed. The controller guarantees the estimated value of unknown parameter is in the prescribed extent.

Backsteppingアプローチによる高次Chained formの制御

Backsteppingアプローチによる高次Chained formの制御

Control of high-order nonholonomic systems in power chained form using discontinuous feedback

Addresses the problems of almost-asymptotic stabilization and global asymptotic regulation (GAR) for a class of high-order nonholonomic systems in power-chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state-feedback control law (or a switching controller) can be recursively constructed, using the so-called "adding a power integrator" technique of C. Qian et al. (2001). We also illustrate how the results can be extend to multi-input systems in power-chained form. Simulation examples are provided to demonstrate the effectiveness of the proposed controllers.