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This paper aims at adaptive event-triggered output-feedback stabilisation in the presence of intractable non-parametric uncertainties. Typically, double-side (i.e. sensor-to-controller and controller-to-actuator) event-triggered communication is pursued for efficient resource utilisation, unlike in related works only reducing single-side communication. This renders more constrained information transmitted via network, challenging the co-design of the compensation and event-triggering mechanisms. By incorporating a switching-varying mechanism, a distinctive adaptive event-triggered output-feedback scheme is established based on a switching filter reconstructing the unmeasurable states. Crucially, a convergence-preserving event-triggering mechanism is proposed with the adaptiveness for uncertainty compensation, by suitably exploiting the switching-varying gain. As such, a desired event-triggered output-feedback control is designed with linearity (with respect to the system output and the filter states) rendered for the controller signal. Just owing to the linearity, the controller signal is subtly kept from entering the event-triggering mechanism, so as to match the double-side event-triggered architecture. Furthermore, it is achieved that the system and filter states converge to zero while a positive minimum inter-execution time is ensured. [ABSTRACT FROM AUTHOR]

This paper addresses global output-feedback stabilisation in the context of unknown control directions and intrinsic unmeasurable-states-dependent growth, and focuses on rectifying the substantial deficiencies in the related works and developing a new adaptive output-feedback controller essentially reducing conservativeness. First, a varying parameter which takes value 1 or − 1 , instead of in an unbounded countable set, is specialised to capture the unknown control direction and accordingly a supervisory mechanism is delicately constructed to decide when to switch the parameter from 1 to − 1 or from − 1 to 1. A dynamic high gain, rather than a switching one, is appointed to compensate the serious system uncertainties. Then, the wanted controller is constructed, for which the design functions and design parameters are recursively generated by backstepping method (instead of analytically defined owing to the unknown control coefficients). Based on the designations and supervisory mechanism, it turns out that no Zeno phenomenon occurs, and global boundedness and convergence (to zero) hold, both for the resulting closed-loop system. An example is given to show the effectiveness and the advantage of the proposed scheme. [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]

This paper is devoted to the output-feedback stabilisation for a class of wave equations. Remarkably, only one boundary measurement corrupted by disturbance is available for feedback, and the boundary condition at the control end is dynamic, rather than static. This renders the control problem more challenging than those in the related literature, largely because certain reconstruction and compensation mechanisms respectively for the state and disturbance are necessary but difficult to integrate with the control design for dynamic boundary condition. For this, a powerful adaptive output-feedback stabilising scheme is proposed. Specifically, a delicate observer is constructed for the state in the space domain, with which a dynamic estimate for the disturbance is incorporated. Then, a desired output-feedback controller is designed by backstepping method, which renders the states of the original system and observer to converge to zero, while the estimate of the unknown disturbance converges to its true value. [ABSTRACT FROM AUTHOR]

This paper addresses the global stabilisation via adaptive event-triggered output-feedback for a class of uncertain nonlinear systems. Remarkably, the systems under investigation simultaneously allow large uncertainties and linearly unmeasured states dependent growth for the first time in the event-triggered framework, for which a dynamic high gain and an observer based on the high gain are introduced. By integrating compensation and time-varying strategies, an adaptive event-triggered output-feedback controller is established. Particularly, a new event-triggering mechanism is introduced, in which the time-varying threshold (strictly positive and gradually decaying) is key to ensure the validity of the event-triggered controller and achieve the convergence. A simulation example is given to illustrate the effectiveness of the proposed approach. [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]

This paper is devoted to the global output-feedback stabilisation for a class of nonlinear systems with inherent nonlinearities and coarse disturbance. Remarkably, the disturbance may be non-periodic, non-differentiable and/or of unknown magnitude, and hence some critical requirements on the disturbance in the existing related literature are successfully removed. Recognising that the strategies of disturbance compensation, such as internal model principle, sliding mode control method, learning method and active disturbance rejection control method, are quite hard or even impossible to apply, a time-varying design scheme is developed in the paper. Moreover, the serious unknowns and time-variations reflected in the growth rate of the system are also dealt with by the proposed scheme. By designing a time-varying output-feedback controller, all the signals of the resulting closed-loop system are globally bounded, and the original system state and the observer state ultimately converge to zero. [ABSTRACT FROM AUTHOR]

In this paper, finite-time consensus tracking is investigated via time-varying feedback for uncertain nonlinear multi-agent systems (NMASs). The presence of inherent uncertainties and disturbances in the NMASs highlights the main novelty : (1) The inherent uncertainties imply that more serious unknowns and time-variations are allowed in the nonlineartities and the control coefficients of the NMASs. (2) The inherent disturbances mean that the upper bound of the disturbances is unknown. To compensate the inherent uncertainties and disturbances, time-varying protocols are proposed by integrating time-varying technique and sliding mode method. Based on the proposed protocols, the finite-time leader-following consensus and finite-time containment are achieved under directed graph. Finally, the validation of the proposed protocols is verified by two examples. [ABSTRACT FROM AUTHOR]

This paper considers the global output-feedback stabilisation for power integrator systems with unknown control direction. The presence of uncontrollable and unobservable linearisation renders the strategy based on Nussbaum function rather difficult (even impossible) to compensate the unknown control direction. In this paper, to dominate the inherent nonlinearities and unknowns, a powerful switching strategy is proposed by combining an output-feedback scheme and a switching mechanism. First, a special case with known control direction is considered to provide a basic structure and selection rules of design parameters for the expected controller, and then, the essential case with unknown control direction is investigated to build a suitable switching logic to online tune the design parameters. The proposed switching-type output-feedback controller guarantees that all the system signals are globally bounded and ultimately converge to zero. A numerical example is given to illustrate the effectiveness of the proposed methods. [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]

Adaptive stabilisation is investigated for ordinary differential equation systems via distributed effect of uncertain diffusion-dominated actuator dynamics. The presence of the unknowns/uncertainties and the distributed effect makes the system under investigation more general and representative than those of the related literature, and moreover yields the ineffectiveness of the existing methods on this topic. By constructing an invertible spatial and time-varying state transformation, the original closed-loop system is first changed into a target system, from which the design of parameter updating law and the analysis of the closed-loop system performance become more convenient. Then, by Lyapunov method and adaptive compensation technique, an adaptive stabilising controller is successfully constructed, which guarantees that the original system states converge to zero while other closed-loop system states are bounded. A simulation example is provided to validate the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the adaptive output-feedback stabilisation for a class of hybrid partial differential equation (PDE)–ordinary differential equation (ODE) systems with uncertain input disturbances. Remarkably, in this paper, only two boundary measurements of the considered system are available for feedback. Moreover, the unknown parameters involved in the system are allowed to belong to an unknown interval. These two aspects make the considered system essentially different from those in the closely related literature. Inspired by the existing results, an observer is first introduced to estimate the unmeasured states of the original system. Then, by adaptive technique and backstepping method, an adaptive output-feedback controller is successfully constructed, which guarantees that the entire closed-loop system is asymptotically stable, and moreover, the parameter estimates converge to their own real values ultimately. Besides, by the semigroup approach, the well-posedness of the entire closed-loop system is achieved. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses the global adaptive stabilisation via switching and learning strategies for a class of uncertain nonlinear systems. Remarkably, the systems in question simultaneously have unknown control directions, unknown input disturbance and unknown growth rate, which makes the problem in question challenging to solve and essentially different from those in the existing literature. To solve the problem, an adaptive scheme via switching and learning is proposed by skilfully integrating the techniques of backstepping design, adaptive learning and adaptive switching. One key point in the design scheme is the introduction of the learning mechanism, in order to compensate the unknown input disturbance, and the other one is the design of the switching mechanism, through tuning the design parameters online to deal with the unknown control directions, unknown bound and period of input disturbance and unknown growth rate. The designed controller guarantees that all the signals of the resulting closed-loop systems are bounded, and furthermore, the closed-loop system states globally converge to zero. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global practical tracking via adaptive output feedback for a class of uncertain nonlinear systems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinearities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high gain is the multiplication of two dynamic gains: one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical example demonstrates the effectiveness of the proposed method. [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]

The adaptive stabilisation is investigated for a class of coupled partial differential equation–ordinary differential equation systems with parametric uncertainties. The presence of the uncertainties makes the systems under investigation essentially different from those in the existing literature, and moreover it results in the incapability of the existing methods. Motivated by the related works, an infinite-dimensional backstepping transformation is first introduced to transform the original system into a pivotal target system, which makes the control design and performance analysis much convenient. Then, by utilising Lyapunov method and some adaptive techniques, an adaptive stabilising controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A simulation example is provided to validate the proposed method. [ABSTRACT FROM PUBLISHER]

This paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems. Comparing with the existing relevant literature, the systems under investigation allow more serious unknowns/uncertainties. More importantly, by remarkably reducing the dimension of dynamic compensator for system unknowns (fromnto 2) and considerably diminishing the overparametrisation in the existing literature, this paper proposes an improved design scheme for adaptive state-feedback controllers. It is turned out that, with the designed controller in loop, all the closed-loop system states are globally bounded and the original system states converge to the origin, both in the sense of probability one. A simulation example is also given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]