Nonholonomic Systems In Chained Form Research Articles

Global κ-exponential Tracking Control of Nonholonomic Systems in Chained-form by Output Feedback

The output tracking control problem of nonholonomic chained form systems is studied in this paper and global κ-exponential output trackers are presented without persistent excitation or not-converging to zero on reference trajectories. First, a time-varying coordinate transformation is introduced to avoid manipulating exponentially converging signals. Then, with the help of theory of cascaded systems and linear perturbed systems, global κ-exponential output trackers are successfully obtained. A new feature of the proposed controller is that the output tracking control problem of nonholonomic chained form systems is also resolvable without the popular condition of persistent excitation or not converging to zero on reference signals in the previous works. The proposed method is demonstrated and discussed by means of nonholonomic mobile robots and cars with one trailer.

Predictive variable structure control of nonholonomic chained systems

A novel variable structure control strategy for a class of second-order nonlinear systems is presented based on the phase-plane analysis and computing prediction. In this strategy control is switched by online prediction of the trajectory behaviour of the closed-loop system; control switching does not occur continuously, so the chattering that occurs in conventional variable structure control methods can be avoided completely. It is proved that the states of the closed-loop system can be stabilized to the origin exponentially and the trajectory of the closed-loop system does not overshoot in general. As an application, the proposed predictive variable structure control strategy is used to stabilize nonholonomic systems in chained form. An example of a wheeled mobile robot is studied and associated simulation results demonstrate the effectiveness of the proposed control strategy.

Robust Adaptive Control of Nonholonomic Systems with Nonlinear Parameterization

A global-adaptive state feedback control strategy is presented for a class of nonholonomic systems in chained form with strong nonlinear drifts and unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterization nonholonomic system into a linear-like parameterized nonholonomic system. Then, the feedback domination design is applied to design a global adaptive stabilization controller and a switching strategy is developed to eliminate the phenomenon of uncontrollability. The proposed controller can guarantee that all the system states globally converge to the origin, while other signals remain bounded. Simulation example demonstrates the effectiveness and the robust features of the proposed controller.

Smooth time-varying stabilization of driftless systems over communication channels

We address the problem of smooth time-varying stabilization of port-interconnected driftless passive systems. The benchmark that we study is reminiscent of driftless systems interconnected over communication channels and constitutes a generalization of the well-known chained-form nonholonomic systems. Our contribution consists in proposing a smooth time-varying controller that guarantees uniform global asymptotic stability; moreover, a necessary condition is also stated. Both the sufficient and necessary conditions are formulated in terms of the so-called δ -persistency of excitation previously used in set-point control of nonholonomic systems. The proof of sufficiency relies on a recently reported extended Matrosov's theorem which may be regarded as an extension of Krasovskı˘i-La Salle's invariance principle to the case of nonautonomous systems.

Adaptive robust control of nonholonomic systems with stochastic disturbances

This paper deals with nonholonomic systems in chained form with unknown covariance stochastic disturbances. The objective is to design the almost global adaptive asymptotical controllers in probability u0 and u1 for the systems by using discontinuous control. A switching control law u0 is designed to almost globally asymptotically stabilize the state x0 in both the singular x0(t0)=0 case and the non-singular x0(t0)≠0 case. Then the state scaling technique is introduced for the discontinuous feedback into the (x1, x2, ⋯, xn)-subsystem. Thereby, by using backstepping technique the global adaptive asymptotical control law u1 has been presented for (x1, x2, ⋯, xn)-subsystem for both different u0 in non-singular x0(t0)≠0 case and the singular case x0(t0)=0. The control algorithm validity is proved by simulation.

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.

Robust Adaptive Neural Network Control of Uncertain Nonholonomic Systems With Strong Nonlinear Drifts

In this paper, robust adaptive neural network (NN) control is presented to solve the control problem of nonholonomic systems in chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive NN control laws are developed using state scaling and backstepping. Uniform ultimate boundedness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neighborhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. The proposed adaptive NN control is free of control singularity problem. An adaptive control based switching strategy is used to overcome the uncontrollability problem associated with x0 (t0) = 0. The simulation results demonstrate the effectiveness of the proposed controllers.

Robust adaptive control of nonholonomic systems with uncertainties

Robust adaptive control of nonholonomic systems in chained form with linearly parameterized and strongly nonlinear disturbance and drift terms is dicussed. The novelty of the proposed method is a combined use of the state-scaling and the back-stepping procedure.

Constrained Minimum-Time-Oriented Feedback Control for the Stabilization of Nonholonomic Systems in Chained Form

In this paper, a discontinuous state-feedback law is proposed for the stabilization of nonholonomic systems in power form. The feedback law is based on a receding-horizon strategy in which the open-loop optimization problem is a minimum-time steering process. Suboptimal formulations are used explicitly to meet the real-time implementability requirements. Stability is established in a sampled-data context and illustrative simulations are given to show the effectiveness and the real-time implementability of the proposed scheme.

Adaptive stabilization of uncertain nonholonomic systems by state and output feedback

In this paper, adaptive state feedback and output feedback control strategies are presented for a class of nonholonomic systems in chained form with drift nonlinearity and parametric uncertainties. Both control laws are developed using state scaling and backstepping techniques. In particular, novel adaptive switching is proposed to overcome the uncontrollablity problem associated with x 0( t 0)=0. Observer-based output feedback design is developed when only partial system states are measurable, and a filtered observer rather than the traditional linear observer is used to handle the technical problem due to the presence of unavailable states in the regressor matrix. The proposed control strategies can steer the system globally converge to the origin, while the estimated parameters maintain bounded.

Global stabilization and asymptotic tracking for a class of nonlinear systems by means of time‐varying feedback

AbstractA simple backstepping design scheme is proposed and sufficient conditions for non‐uniform in time global stabilization for parameterized systems by means of time‐varying feedback are established. Our methodology is applicable to a special class of systems that in general cannot be stabilized by static feedback and includes non‐holonomic systems in chained form. For this class of systems the main results on feedback stabilization enable us to derive sufficient conditions for the solvability of the tracking problem. Copyright © 2003 John Wiley & Sons, Ltd.

Non-uniform in time stabilization for linear systems and tracking control for non-holonomic systems in chained form

The paper contains certain results concerning non-uniform in time stabilization for linear time-varying systems by means of a linear time-varying feedback controller. These results enable us to present an explicit solution for the state feedback tracking control problem of non-holonomic systems in chained form under weaker hypotheses than those imposed in earlier existing works.

Adaptive Stabilization of Uncertain Nonholonomic Systems by Output Feedback

In this paper, output feedback control is presented for a class of nonholonomic systems in chained form with drift nonlinearities and parametric uncertainties. The stabilizing control laws are developed for these systems based on the adaptive backstepping technique with tuning functions. Since only partial system states are measurable, an observer-based output feedback design procedure is developed. To facilitate the output feedback controller design, a filtered adaptive observer is constructed to handle the technical problem due to the presence of unavailable states in the regressor matrix. The simulation results demonstrate the global convergence of the proposed controller in the paper when the systems are subjected to uncertain disturbances.

On the reachability of quantized control systems

In this paper, we study control systems whose input sets are quantized, i.e., finite or regularly distributed on a mesh. We specifically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report results on the reachable set of linear quantized systems, and on a particular but interesting class of nonlinear systems, i.e., nonholonomic chained-form systems. For such systems, we provide a complete characterization of the reachable set, and, in case the set is discrete, a computable method to completely and succinctly describe its structure. Implications and open problems in the analysis and synthesis of quantized control systems are addressed.

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.

Adaptive tracking control for nonholonomic systems with unknown parameters

An adaptive control method for a special chained form system with drift terms and unknown parameters is discussed. Tracking controllers have been considered to be effective for solving the problem of the stability of nonholonomic control systems. Since a tracking control system can be transformed to the special chained form system, a tracking controller using the backstepping method is proposed for the nonholonomic chained form system. The asymptotic stability of the system is guaranteed by using Lyapunov's direct method and using adaptive control method, an adaptive controller is proposed for the nonholonomic system with unknown parameters. The ability of the proposed controller is illustrated by simulations. Furthermore, based on a nonholonomic mobile robot, a typical example of nonholonomic system, we demonstrate the efficiency of the proposed method.

STABILIZATION OF NONHOLONOMIC SYSTEMS USING HOMOGENEOUS FINITE-TIME CONTROL TECHNIQUE

This research focuses on the problem of finite-time stabilization of chained-form nonholonomic systems using discontinuous homogeneous feedback and introduces the discontinuous homogeneous (with dilation) controller. The proposed controller has no singular point, stabilizes the system in finite-time, and is not complicated. Moreover, we demonstrate an exponentially stable controller.

Stabilization of second-order nonholonomic systems in canonical chained form

Stabilization of a class of second-order nonholonomic systems in canonical chained form is investigated in this paper. First, the models of two typical second-order nonholonomic systems, namely, a three-link planar manipulator with the third joint unactuated, and a kinematic redundant manipulator with all joints free and driven by forces/torques imposing on the end-effector, are presented and converted to second-order chained form by transformations of coordinate and input. A discontinuous control law is then proposed to stabilize all states of the system to the desired equilibrium point exponentially. Computer simulation is given to show the effectiveness of the proposed controller.

Robust Output-Feedback Tracker Design for Nonholonomic Systems

This paper presents new results for the global output-feedback tracking of nonholonomic systems in chained form. The tracking controllers are obtained on the basis of a recursive technique and a full exploitation of the system structure. Sufficient conditions on the reference paths are given to attain global exponential tracking. When disturbances occur in the dynamic extension of a nonholonomic chained system, it is shown how to modify the controller design procedure to yield robust tracking control laws. The proposed method is demonstrated and discussed by means of a benchmark nonholonomic knife-edge mechanical system.

Control design for chained-form systems with bounded inputs

Discontinuous, time-invariant controllers have been recently proposed in the literature as an alternative method to stabilize nonholonomic systems. These control laws are not continuous at the origin and although they provide exponential rates of convergence, they may use significant amount of control effort, especially if the initial conditions are close to an equilibrium manifold. We seek to remedy this situation by constructing bounded controllers (with exponential convergence rates) for nonholonomic systems in chained form.