Unknown Growth Rate Research Articles

Asymptotic adaptive output-feedback stabilisation of nonlinear systems with unknown growth rate and sensor uncertainty

For a class of nonlinear systems with sensor uncertainty, the problem of adaptive output feedback stabilisation is investigated in this paper. It is assumed that only the output is available for feedback control, which suffers from sensor uncertainty. At the same time, the nonlinear function in the system model has an unknown growth rate. To solve this problem, a set of state observers is designed to estimate the unknown system states based on the uncertain output, and an adaptive output-feedback control is designed based on this. By using the corollary of Barbalet's Lemma, it is shown that the equilibrium of the closed-loop system is asymptotically stable. Finally, simulation results verify the effectiveness of the control scheme

Global adaptive event-triggered output feedback control for p-normal feedforward nonlinear systems with uncertain output function

This paper concentrates on the global adaptive event-triggered output feedback controller design for a class of p-normal feedforward nonlinear systems with uncertain output function. Due to the existence of unknown growth rate and uncertain output function, the considered uncertain nonlinear systems contain more uncertainties. To overcome this difficulty, a dynamic gain technique is introduced and an elaborate adaptive law of the gain is designed. Then, a completely time-varying event-based strategy is presented, which can effectively eliminate the effects caused by event-triggered errors. Since the presented event-triggered controller is not differentiable, a new analysis manner is developed to prove that the system is Zeno-free. Meanwhile, the closed-loop system(CLS) states are asymptotically convergent with the proposed strategy. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate

Article Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate Manman Yuan 1,2,*, and Wei Qian 1,2,* 1 School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454003, China 2 Henan Key Laboratory of Intelligent Detection and Control of Coal Mine Equipment, Jiaozuo 454003, China * Correspondence: ymmamhappy@163.com; qwei@hpu.edu.cn Received: 4 September 2023 Accepted: 7 November 2023 Published: 26 March 2024 Abstract: In this paper, the problem of adaptive output feedback tracking is considered for a class of nonlinear systems with lower-triangular structures. A novel dynamic gain is introduced to deal with the unknown growth rate. By coupling the dynamic gain with the observer and the controller, an adaptive output tracking controller is developed, which can guarantee that all signals of the closed-loop system are globally bounded. Finally, the effectiveness of the presented control scheme is illustrated by a numerical example.

Cooperative Control for a Class of Stochastic Upper-Triangular Nonlinear Systems With Unknown Growth Rates

Cooperative Control for a Class of Stochastic Upper-Triangular Nonlinear Systems With Unknown Growth Rates

Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate

Article Adaptive Output Feedback Tracking Control for Nonlinear Systems with Unknown Growth Rate Manman Yuan 1,2,*, and Wei Qian 1,2,* 1 School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454003, China 2 Henan Key Laboratory of Intelligent Detection and Control of Coal Mine Equipment, Jiaozuo 454003, China * Correspondence: ymmamhappy@163.com; qwei@hpu.edu.cn Received: 4 September 2023 Accepted: 7 November 2023 Abstract: In this paper, the problem of adaptive output feedback tracking is considered for a class of nonlinear systems with lower-triangular structures. A novel dynamic gain is introduced to deal with the unknown growth rate. By coupling the dynamic gain with the observer and the controller, an adaptive output tracking controller is developed, which can guarantee that all signals of the closed-loop system are globally bounded. Finally, the effectiveness of the presented control scheme is illustrated by a numerical example.

Global output feedback control of feedforward nonlinear time-delay systems with unknown growth rate and unknown measurement sensitivity

Global output feedback control of feedforward nonlinear time-delay systems with unknown growth rate and unknown measurement sensitivity

Adaptive output-feedback control for uncertain nonlinear systems with function control coefficients

This article addresses the global adaptive output-feedback state regulation problem for a class of uncertain nonlinear systems with generalized control coefficients. Remarkably, the system under investigation simultaneously possesses function control coefficients, input matching uncertainty, and unknown growth rate, which is essentially different from the closely related existing literature. Such nonlinearities from function control coefficients and uncertainties from unknown growth rate bring great technical difficulties to controller design. A novel dynamic gain is introduced to deal with the extra system nonlinearities from function control coefficients and unknowns from the growth rate. In addition, the extended state observer is developed to reconstruct the unmeasured states of the system. By integrating the dynamic gain and extended state observer, an adaptive output-feedback controller is designed, which ensures that the states of the system globally converge to zero, and the estimation of the input matching uncertainty converges to its actual value. Two simulation examples are given to demonstrate the effectiveness of the proposed method.

Global regulation of large‐scale nonlinear systems via decentralized output‐feedback switching control

AbstractThis article concentrates on the global regulation problem for a class of large‐scale nonlinear systems with unknown growth rate and unknown external disturbances. In contrast to closely related works, the highlight of this article is that a novel decentralized output‐feedback switching control method is proposed for the first time to offset the serious uncertainties. By integrating logic‐based switching technique and gain scaling technique, this method can instantly adjust the controller parameters (that is, the scaling gain can be tuned online in a piecewise constant manner), and thus has strong adaptive capability as well as disturbance tolerance. Moreover, the decentralized output‐feedback switching controller designed by such the method has a concise linear‐like form and low complexity. It is shown that the objective of global regulation is finally achieved after a finite number of switching moments. Finally, two examples, including an engineering feedback control system design example, are given to verify the effectiveness of the proposed control method.

Global regulation of feedforward nonlinear systems with unknown time-varying control coefficients and growth rate

In this paper, we consider a regulation problem for a class of feedforward nonlinear systems with unknown control coefficients and unknown growth rate. More specifically, the unknown control coefficients are assumed to be time-varying and belong to ranges with unknown upper and lower bounds. Due to the described control coefficients with uncertain feedfoward nonlinearities, our considered system is the natural extension of the related existing results. In solving our control problem, a new adaptive controller is derived by constructing a Lyapunov function in backstepping-like procedure and utilizing appropriate parameters based on the gain scaling technique and Nussbaum function. The uniquely designed exponents of a dynamic gain overcome the difficulties caused from the unknown sign and unknown ranges of the control coefficients and uncertain nonlinearities and thus play a key role in system regulation. We give the rigorous system analysis and simulation results of the numerical example to certify our control method.

Global Stabilization for Uncertain Nonlinear Time-Delay Systems With Saturated Input

In this article, global stabilization for a class of nonlinear uncertain time-delay systems with saturated input is considered. The saturated input is handled by a new auxiliary system with dynamic gain and the linear growth condition with unknown growth rates is removed. A novel adaptive observer-controller coupling design framework is put forward, under which the closed-loop system is globally bounded. Finally, a simulation shows that the proposed technique is effective.

Dynamic event‐triggered control for a class of p‐normal nonlinear time‐delay systems via output feedback

ABSTRACTIn this article, the event‐triggered (ET) output feedback control problem is discussed for a class of ‐normal nonlinear time‐delay systems. Different from the related existing literature, the linear growth condition is relaxed to the homogeneous one and the growth rate is unknown. In the case of unknown time‐varying delays and control coefficients, nonsmooth control law and some extra redundant terms will be encountered in the design of ET controller, which would bring substantial challenges to the achievement of global convergence. To cope with unknown growth rate and time‐varying delays, two dynamic gains and an appropriate Lyapunov–Krasovskii functional (LKF) are introduced. Then, a new dynamic ET mechanism is given, in which the triggering threshold can be tuned dynamically. It is proved that all the signals of the closed‐loop system (CLS) are bounded. Corresponding examples are given to indicate the validity of the developed theoretical results.

Distributed consensus control of nonlinear multi‐agent systems with sensor uncertainty

AbstractThis article focuses on the distributed consensus control problem for nonlinear multi‐agent systems subject to sensor uncertainty. To be specific, we study nonlinear multi‐agent systems of lower or upper triangular structure with unknown growth rate and sensor uncertainty. A new time‐varying gain approach is proposed to construct observers as well as distributed output‐feedback controllers. By selecting suitable design parameters, the leader‐follower consensus of nonlinear multi‐agent systems is achieved. Different from the existing results, a time‐varying function in a logarithmic form is introduced to deal with unknown growth rate. Moreover, a monotonically increasing time‐varying function is constructed to cope with uncertain sensor sensitivity. Two simulation examples are provided to demonstrate the effectiveness of the proposed distributed consensus control algorithms.

Adaptive Output Feedback Control for Stochastic Uncertain Nonlinear Time-Delay Systems

In this brief, the adaptive output feedback control problem for stochastic nonlinear time-delay systems with various uncertainties is considered. The unknown output function needs neither to be differentiable, that is, its derivative is limited to known/unknown upper and lower bounds, nor to guarantee its Lipschitz continuity. Besides, the upper bound on the derivative of time-varying delay and the growth rates of the nonlinear functions are proved to be not necessary. An adaptive output feedback control scheme is designed, in which a dynamic gain is embedded in the observer to dominate the time-varying delay and unknown growth rates, and a constant gain is embedded in the controller to dominate the unknown output function. It is proved that all signals of the closed-loop system are globally bounded almost surely and the bounds are ensured to be tuned by design parameters. Finally, a simulation is presented to show the validity of the control scheme.

Adaptive output feedback control of large-scale nonlinear time-delay systems with uncertain output equations

For a class of large-scale nonlinear time-delay systems with uncertain output equations, the problem of global state asymptotic regulation is addressed by output feedback. The class of systems under consideration are subject to feedforward growth conditions with unknown growth rate and time delays in inputs and outputs. To deal with the system uncertainties and the unknown delays, a novel low-gain observer with adaptive gain is firstly proposed; next, an adaptive output feedback delay-free controller is constructed by combining Lyapunov-Krasovskii functional with backstepping algorithm. Compared with the existing results, the controllers proposed are capable of handling both the uncertain output functions and the unknown time delays in inputs and outputs. With the help of dynamic scaling technique, it is shown that the closed-loop states converge asymptotically to zero, while the adaptive gain is bounded globally. Finally, the effectiveness of our control schemes are illustrated by three examples.

Adaptive output feedback control for a class of switched stochastic nonlinear systems via an event-triggered strategy

This article addresses the adaptive event-triggered output-feedback control issue for a class of switched stochastic nonlinear systems (SSNSs) under arbitrary switchings. To cope with the unknown growth rate, two dynamic gains are introduced. Different from most existing event-triggered strategies, the developed dynamic event-triggered strategy can be dynamically adjusted, which is delicately designed by exploiting two dynamic gains and a decaying function. Then, a new event-triggered output-feedback controller (ETOFC) is established, which can guarantee that all states of the closed-loop system converge to the origin almost surely (a.s.). Finally, two examples are given to verify the effectiveness of the presented control scheme.

Global decentralized control for uncertain large-scale feedforward nonlinear time-delay systems via output feedback

Abstract In this paper, the problem of global decentralized output feedback control is addressed for a class of large-scale nonlinear systems with zero dynamics and unknown time-varying delay. System disturbance nonlinearities are subject to feedforward growth restrictions with unknown growth rate. In the spirit of dynamic scaling change technique, a novel pair of time-varying-gain observer and controller is proposed. Compared with the existing results, the controller proposed is capable of handling the difficulties caused by the zero-dynamics, the uncertainties and the unknown time-varying delay. With the help of the Razumikhin theorem, it is shown that the closed-loop states asymptotically converge to zero. Finally, the effectiveness of the proposed control scheme is illustrated by a numerical example.

Correction to: Regulation of a Class of Nonlinear Systems with Unknown Growth Rate Under Uncertain Measurement Sensitivity

Correction to: Regulation of a Class of Nonlinear Systems with Unknown Growth Rate Under Uncertain Measurement Sensitivity

Regulation of a Class of Nonlinear Systems with Unknown Growth Rate Under Uncertain Measurement Sensitivity

Regulation of a Class of Nonlinear Systems with Unknown Growth Rate Under Uncertain Measurement Sensitivity

Adaptive output feedback control for a class of uncertain stochastic nonlinear systems

This article concentrates on the output feedback controller design for a class of stochastic nonlinear systems with unknown homogeneous growth rates. First, a full-order observer is proposed coupling with a dynamic gain so as to obtain system state estimates. Then, an adaptive output feedback controller is put forward by the homogeneity theory and adding a power integrator technique. Combined with the stochastic Barbalat’s lemma, the signals of the closed-loop system are demonstrated to be bounded and all the system states are proved to converge to the origin in probability. Besides, the results are also expanded to the controller design of upper-triangular stochastic nonlinear system. Two simulation results indicate usefulness of the designed control algorithm.

Dynamic event-triggered output feedback control for a class of nonlinear systems with time-varying delays

This note studies the problem of dynamic event-triggered output feedback control for a class of nonlinear systems under homogeneous growth condition with unknown growth rate and time delays. Firstly, in order to deal with unknown growth rate and time-varying state delays, a double-gain dynamic scheme is introduced and a suitable Lyapunov–Krasovskii functional is selected. Secondly, a dynamic event-triggered strategy is proposed by introducing the dynamic gain to the event-triggered condition, which makes the triggering threshold be tuned dynamically. Compared with some existing works related to event-triggered strategy, the proposed strategy is more flexible for saving communication resources. Subsequently, a new output feedback control law is developed in the context of event-triggered mechanism to guarantee the boundedness of system signals while the system states globally enter a compact set around the origin. Finally, two examples are given to show the feasibility and merit of the presented scheme.