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Summary: This article investigates global finite‐time stabilization with prescribed output convergence for uncertain nonlinear systems. It is possible to achieve finite‐time stabilization via continuous adaptive feedback for the systems, but the transient performance could not be prescribed for such feedback. Although funnel control is capable of tackling serious uncertainties and ensuring prescribed performance (such as convergence rate and overshoot), it alone cannot achieve (global) finite‐time stabilization. To this end, we present an integrated controller to achieve the desirable stabilization, retaining the respective advantages of the above two schemes and circumventing their own disadvantages. Specifically, based on the funnel control scheme with suitable design parameters, the system output converges from any initial value to an arbitrarily adjustable region with the prescribed convergence rate before a pregiven time instant, while the system states keep bounded. The adaptive controller, in conjunction with a time‐dependent function, ensures that the system output and states converge to zero in finite time, and particularly the system output with prescribed convergence rate evolves within the prespecified envelope. The effectiveness of the proposed scheme is illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

Stabilisation via adaptive feedback is investigated for an ODE system cascaded by coupled parabolic equations. The remarkable characteristic of the system is the presence of serious uncertainties since no known or bounded intervals are needed for the unknown parameters. Besides, strong coupling exists in the PDE subsystem which brings essential difference compared with those of the related literature. For this, a passive identifier is skillfully constructed firstly, and in turn adaptive laws are given to compensate the serious parametric unknowns. Then, by constructing a backstepping transformation and its inverse one, the identifier joint with the original system is transformed into a new system. From the new system, an adaptive state-feedback controller is designed which ensures that all the states of the closed-loop system are bounded and particularly those of the original system converge to zero. Finally, a numerical example is provided to validate the proposed algorithm. [ABSTRACT FROM AUTHOR]

Adaptive stabilisation is investigated for a class of uncertain coupled parabolic equations in this paper. The presence of unknown coefficients can reduce the rigorousness of system modelling and enlarge the scope of the systems, whereas it could give rise to essential difficulties to control problems. Mainly due to the latter, certain new initiative, such as uncertainty compensation, should be considered to solve the stabilisation problem. For this, by infinite-dimensional backstepping method combining with adaptive compensation technique, an adaptive control scheme is proposed. Then, an adaptive state-feedback controller is constructed which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A numerical example is provided to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the problem of global adaptive stabilization by output-feedback for a class of uncertain nonlinear systems with unknown growth rate and unknown output function. By constructing a suitable Lyapunov function, a new systematic design scheme is proposed to derive an adaptive output-feedback controller with appropriate design parameters based on a dynamic high-gain, under which the system states can be globally regulated to zero. Because the proposed method uses the adaptive technique rather than the time-varying one, it does not require a priori known information about either the growth rate or the upper and lower bounds of the derivative of the unknown output function. This makes the investigated system substantially different from the existing results and also highlights the main contributions of the paper. A practical example is presented to show the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract This paper is devoted to the global stabilization and practical tracking for a class of uncertain nonlinear systems. The presence of unknown powers and serious parameter unknowns makes the systems in question essentially different from those in the related works. By skillfully combining adaptive technique and adding a power integrator, two novel adaptive state-feedback controllers are successfully designed to achieve global stabilization and practical tracking, respectively. Remarkably, the typical feature of the two controllers lies in the introduction of the adaptive dynamic and the terms of lower and higher powers (with respect to the unknown system powers), which makes the controller powerful enough to compensate the serious parameter unknowns and the unknown powers of the system. Finally, simulation examples are provided to illustrate the effectiveness of the designed controllers. [ABSTRACT FROM AUTHOR]

Multiple uncertainties/noises, frequently exist in a plant, usually require multiple compensation techniques, which renders feedback controllers highly dynamic and nonlinear. This motivates us to search for a compact design scheme of compensation to reduce the complexity of controllers. In this paper, global output-feedback stabilisation is investigated for a class of uncertain nonlinear systems with unknown unmeasured states-dependent growth and input matching uncertainty. To solve the problem, a compact scheme is proposed to design a global adaptive output-feedback controller, which combines the technique of dynamic gain and extended state observer together. Particularly, only one dynamic gain, rather than two dynamic gains, is introduced to deal with the unknown polynomial-of-output growth rate, which makes our controller to have lower dynamics than those in the related works. Moreover, the input matching uncertainty is asymptotically estimated by the extended state observer, and thus its effect is well counteracted. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non-zero set-point regulation demonstrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the global adaptive state feedback controller design for a class of feedforward nonlinear systems with completely unknown control direction and unknown growth rate. Since the control direction, i.e., the sign of the control coefficient, is unknown, the control problem becomes much more challenging, to which a Nussbaum-type function is exploited. Moreover, the systems heavily depend on the unmeasured states with unknown growth rate, and hence a dynamic gain, rather than a constant one, is adopted to compensate the large system unknowns. For control design, a suitable state transformation is first introduced for the original system. Then, the state feedback controller is proposed based on an appropriate Nussbaum-type function and a dynamic high gain. It is shown that the state of the original system converges to zero, while the other states of the closed-loop system are globally bounded. Finally, a simulation example is provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Finite-time control owns the advantages of precision and rapidness, preferred by many applications with high performance requirements. Its realization calls for subtle treatments, e.g., the Lyapunov method with low-order terms and homogeneity with negative degree. However, the methods available for finite-time control are based on some basic exclusions and essential restrictions to system uncertainties and nonlinearities. This paper addresses for the first time unknown control coefficients without any known bound, and meanwhile extends system nonlinearities, within the framework of continuous adaptive feedback. The success is typically due to several sets of disparate powers in control design and analysis. Specifically, the nonidentical power-type parameters are introduced in high-gain dynamics, instead of an identical one in the literature, to ensure the stabilizing terms have lower powers than the terms containing uncertainties, enabling finite-time convergence. Thus an adaptive finite-time controller is achieved. New integral-type functions are exploited to make up the important Lyapunov function, which are equipped with different powers to make possible the anticipated performance analysis. The effectiveness of the proposed controller is demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

To date, most schemes of adaptive stabilization are confined to convergence, and cannot specify the convergence rate. As such, the possibility of excessively slow convergence could not be ruled out, which undermines the application scope of adaptive schemes. Such imperfection is mainly due to the limited capability of compensation/learning mechanisms which lack the ingredients affording specific convergence rate. For stronger applicability, more comprehensive compensation/learning mechanisms need to be exploited, inevitably aggravating control synthesis and analysis. This paper aims to enhance adaptive control in terms of convergence rate, and particularly, seeks exponential regulation via adaptive output feedback for stochastic nonlinear systems allowing large uncertainties coupling to unmeasurable states and dynamic uncertainties. To this end, a refined adaptive output-feedback scheme is established in the stochastic framework, though no non-stochastic counterpart exists. Critically, a novel dynamic high gain is introduced in a universal manner, with its updating law delicately incorporating the gain-dependent time-varying information in exponential form. The dynamic gain would not only become sufficiently large to capture the large uncertainties, but also render the desired convergence with the rate online regulated to match the dynamic uncertainties. In this way, an adaptive output-feedback controller based on dynamic-gain observer is designed, which guarantees the system and observer states to almost surely converge to zero at an exponential rate. The stochastic framework complicates the validity verification of the established scheme, entailing subtle martingale-based analysis. Correspondingly, a distinctive analysis pattern is developed for the resulting closed-loop system, to attain expected stochastic convergence and boundedness. [ABSTRACT FROM AUTHOR]

This paper is concerned with event-triggered bounded consensus tracking for a class of second-order nonlinear multi-agent systems with uncertainties (MASs). Remarkably, the considered MASs allow multiple uncertainties, including unknown control coefficients, parameterized unknown nonlinearities, uncertain external disturbances, and the leader's control input being unknown. In this context, a new estimate-based adaptive control protocol with a triggering mechanism is proposed. We rule out Zeno behavior by testifying that the lower bound on the interval between two consecutive events is positive. It is shown that under the designed protocol, all signals caused by the closed-loop systems are bounded globally uniformly and tracking errors ultimately converge to a bounded set. The effectiveness of the devised control protocol is demonstrated through a simulation example. [ABSTRACT FROM AUTHOR]

The paper is concerned with the global adaptive stabilisation via output feedback for a class of uncertain planar nonlinear systems. Remarkably, the unknowns in the systems are rather serious: the control coefficients are unknown constants which do not belong to any known interval, and the growth of the systems heavily depends on the unmeasured states and has the rate of unknown polynomial of output. First, a delicate state transformation is introduced to collect the unknown control coefficients, and subsequently, a suitable state observer is successfully designed with two different dynamic gains. Then, an adaptive output feedback controller is proposed by flexibly combining the universal control idea and the backstepping technique. Meanwhile, an appropriate estimation law is constructed to overcome the negative effect caused by the unknown control coefficients. It is shown that, with the appropriate choice of the design parameters, all the states of the resulting closed-loop system are globally bounded, and furthermore, the states of the original system converge to zero. [ABSTRACT FROM PUBLISHER]

This study considers the global adaptive control design for a class of high‐order uncertain non‐linear systems. Different from the existing results, the systems under investigation have serious unknowns which cannot be bounded by any known constants, and particularly have double control input channels, that is, the scalar control input directly affects two one‐dimensional subsystems. Inspired by the author's recent results, by skillfully combing the method of adding a power integrator and some adaptive techniques, an adaptive controller is successfully constructed which can guarantee the asymptotical convergence of the system states for any given initial conditions. A simulation example is given to demonstrate the validity of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stabilization of a class of uncertain reaction–diffusion equations with dynamic boundary condition. Remarkably, the dynamics of boundary condition at control end are considered while unknown parameters are contained in both the intra-domain and the dynamic boundary. This greatly relaxes the restrictions on boundary dynamics and system uncertainties of the related literature where dynamic boundary condition is neglected or considered but unknown parameters are only contained in the dynamic boundary or even completely excluded from the whole system. To solve the control problem, a novel control framework is established by infinite-dimensional backstepping method combining with adaptive compensation technique based on passive identifier. Then, an adaptive state-feedback controller is explicitly constructed which guarantees that all the states of the resulting closed-loop system are bounded while those of the original system converge to zero. A simulation example is provided to validate the effectiveness of the proposed theoretical results. • The restrictions of the existing literature imposed on boundary dynamics and system uncertainties are greatly relaxed since a dynamic boundary condition at control end is considered while unknown parameters are allowed in both the intra-domain and the dynamic boundary in the paper. • A novel passive identifier is designed, combining which with the infinite-dimensional backstepping method, a novel control framework is established that can compensate both the boundary dynamics and system uncertainties, and in turn to stabilize the system under investigation. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization of an uncertain wave equation which describes the vibration dynamics of a flexible string. All the system parameters are unknown while the disturbance with unknown bound and period is allowed which lead to more serious uncertainties than the related literature, and hence result into the incapability of the traditional schemes. To solve the control problem, a novel condition-based adaptive control framework is developed in the paper. Specifically, as preparation for the adaptive control design, a state-feedback controller is first designed under the assumption that all the system parameters are known. Then, an adaptive controller, together with two continuous adaptive laws and a condition-based updating mechanism for the online tuning of the controller parameters, is proposed for the original uncertain system. Finally, it is proven that the updating of controller parameters under the proposed condition-based updating mechanism stops at a finite time instant, then the proposed controller guarantees the stability of the resulting closed-loop system. The proposed theoretical results are validated by a simulation example. [ABSTRACT FROM AUTHOR]