Global adaptive output feedback stabilization for nonlinear time‐delay systems with unknown measurement sensitivity

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.

This paper addresses the problem of global output feedback stabilization for a class of upper-triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that upper-triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.

In this paper, the output feedback control problem is considered for a class of uncertain nonlinear time-delay systems. The system nonlinearities satisfy linear growth condition on unmeasured states multiplied by unknown growth rate and output polynomial function. With appropriate Lyapunov-Krasovskii functional, a memoryless adaptive output feedback controller is developed to guarantee global stability of the nonlinear time-delay systems. The precise knowledge of the time-delay is not required to be known a priori. Furthermore, only one dynamic gain is designed, which makes the controller easier to implement. A numerical example is used to illustrate the effectiveness of the proposed method.

This paper considers global output feedback stabilization of a class of upper-triangular nonlinear systems with multiple outputs. By coupling a finite-time convergent observer and a saturated homogeneous stabilizer, the global output feedback stabilization can be achieved without the homogeneous growth condition. The proposed techniques are also extended to more general complex nonlinear systems. Various examples, including a ball-and-beam mechanical system and a planar vertical takeoff and landing aircraft, are presented to illustrate the design.

SummaryIn this paper, we investigate the problem of global output feedback stabilization for a class of planar nonlinear systems under a more general growth condition, which encompasses both lower‐order and higher‐order state growths with output‐dependent rates. For more accurate estimation, two new observers with nonlinear gains are constructed to estimate the states on the lower‐order and higher‐order scales, respectively. The estimates produced from the dual‐observer are used delicately in the output feedback control law with both lower‐order and higher‐order modes. The overall stability of the system is guaranteed by rigorously choosing these nonlinear gains in the control law and the dual‐observer.

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.

This article presents a first constructive solution to the global finite-time output feedback stabilization of a large class of lower triangular nonlinear systems under relaxed conditions. The key idea is to introduce a switching strategy in the control design scheme. Unlike the previous literature, the nonlinearities of the systems are assumed to satisfy a general Hölder continuous condition, which include Lipschitz continuous nonlinearities as a special case. Global finite-time stability of the closed-loop observer-controller systems is proved by means of innovative Lyapunov-based analytical techniques. A benchmark practical example of controlling the single-link robotic manipulator coupled to a dc motor is adopted to illustrate the proposed method.

This paper considers the problem of global stabilization by output feedback for a class of uncertain nonholonomic systems. By combining the output feedback domination design and nonsmooth change of coordinates together, we explicitly construct a simple output feedback controller, which can universally stabilize a whole family of uncertain nonholonomic systems. The effectiveness of the proposed approach is illustrated by solving the output feedback stabilization for wheeled mobile robots.

In this brief, the global output-feedback stabilization is addressed for a class of uncertain feedforward nonlinear systems. By integrating a dynamic event-triggered mechanism, a novel observer-based control scheme is established, where a time-varying gain is introduced to cope with large uncertainties and sampling errors in the system. Under this control scheme, the global convergence is ensured for the resulting closed-loop system states. Different from the related results, the system states are intermittently monitored by imposing suspension time after each sampling, so that the inter-event intervals have a uniform positive lower bound, and the Zeno behavior is automatically ruled out. Additionally, an internal dynamic variable is incorporated into the triggering mechanism to further extend the inter-event intervals. Finally, the obtained results are extended to a class of feedforward nonlinear systems with unknown time-varying growth rates. A simulation example is given by applying the proposed scheme to a nonlinear liquid level control (LLC) resonant circuit system.

A NONLINEAR TRANSFORMATION APPROACH TO GLOBAL ADAPTIVE OUTPUT FEEDBACK CONTROL OF 3RD-ORDER UNCERTAIN NONLINEAR SYSTEMS

SummaryIn this paper, we aim at addressing the problem of global output feedback stabilization for a class of uncertain nonlinear systems with quantized input and output. The nonlinear functions of the system are assumed to satisfy high‐order growth condition on the unmeasurable states. Based on the homogeneous domination approach and sector bound approach, a homogeneous quantized controller computed from quantized output is constructed, and a guideline is derived to select the parameters of the quantizers. Further, it is proved that, with the proposed scheme, the closed‐loop system is globally asymptotically stable. Copyright © 2016 John Wiley & Sons, Ltd.

Global stabilization of a class of partially known nonnegative systems

Global output feedback practical tracking for time-delay systems with uncertain polynomial growth rate

The authors design a global adaptive output feedback control for a fifth-order model of induction motors, which guarantees asymptotic tracking of smooth speed references on the basis of speed and stator current measurements, for any initial condition and for any unknown constant value of torque load and rotor resistance. The proposed seventh-order nonlinear compensator generates estimates both for the unknown parameters (torque load and rotor resistance) and for the unmeasured state variables (rotor flux); they converge to the corresponding true values under persistency of excitation which actually holds in typical operating conditions. The control algorithm generates references for the magnetizing flux component and for the torque component of stator current which lead to significant simplification for current-fed motors. Simulations show that the proposed controller is suitable for high dynamic performance applications.