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ABSTRACT In this article, we propose a new strategy for prescribed‐time stabilization of uncertain nonlinear systems via continuous adaptive output feedback. Notably, the systems allow non‐parameterized unknown nonlinearities and particularly permit unknown control directions for the first time. The two ingredients lead to the stabilization rather intractable and appeal to new methods and analysis routes. Following a conversion idea, we transform the system in finite‐time horizon into a new system with strong time‐variants in infinite‐time horizon. Integrated with a capable dynamic high gain and an unbounded time‐varying gain, a new concise observer which owns control‐free and tractable error dynamics is worked out for the new system. We particularly exploit a new set of time‐varying scalings, to devise a weakly time‐varying entire system whose boundedness amounts to the wanted prescribed‐time convergence. From the entire system, the adaptive controller design is conducted. The high gain, which is endowed with tailored dynamics, is integrated with (sufficiently smooth) pseudosign and pseudo‐dead‐zone functions to largely simplify the design and analysis. [ABSTRACT FROM AUTHOR]

This article is devoted to the event‐triggered practical tracking control for a class of high‐order nonlinear systems with serious uncertainties. Remarkably, the serious uncertainties are greatly reflected from the unknown control directions and input powers which give rise to essential obstacles in control design and hence lead to incapability of the traditional control methods on this topic. To solve the control problem, a novel switching event‐triggered control scheme is proposed by a skillful incorporation of logic‐based switching mechanism into the event‐triggered one. Specifically, two pivotal events are smartly chosen to give the event‐triggered mechanism for the determination of the sampling times. In particular, one of the events is used to give the switching varying mechanism, by which the controller parameters are respectively switched in two groups of sequences which are carefully chosen for the compensation of serious uncertainties. Under the proposed switching event‐triggered mechanism, a state‐feedback controller is designed which guarantees that all the signals of the closed‐loop system are bounded while system output practically tracks the reference signal, along with a finite number of switching of controller parameters as well as the exclusion of the Zeno phenomenon. Finally, simulation examples are provided to validate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive consensus with limited information for a class of uncertain nonlinear multi-agent systems (MASs). The limited information, meaning the incomplete information transmitted between agents, stems from nonzero-kernel weight matrices of communication networks, which deserves concerns owing to its practical interest such as in privacy preserving and information compression. Apart from the limited/incomplete information, the paper considers nonlinear MASs with large uncertainties (without known upper bounds). This is essentially different from the existing results of linear systems and poses challenges for the design and analysis of adaptive consensus. As for fully distributed protocol design, dynamic high gains are introduced to compensate for the system uncertainties and for the unavailable global graph information. In closed-loop consensus analysis, a new Lyapunov function is constructed by utilising weight and incidence matrices instead of Laplacian matrix. It turns out that the designed protocol can guarantee the boundedness of closed-loop MASs signals and the convergent consensus. Two numerical examples are given to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

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]

The paper considers adaptive event‐triggered control for nonlinear systems with time‐varying parameter uncertainties. The time‐varying uncertainties do not need to be differentiable, but their variation amplitudes are required to be known. Such uncertainties appear not only in the system nonlinearities but also as the control coefficient. We pursue a tight design scheme by combining tuning functions and the congelation of variables method, thereby avoiding the overuse of dominations and obtaining a less conservative controller. In view of the essence of the control problem, we don't design a continuous controller first and then search for a complex and suitable event‐triggering mechanism, as emulation methods done in the literature. In contrast, we adopt a simple event‐triggering mechanism with the relative threshold, while seeking a complex and appropriate adaptive controller which contains the new adaptive treatment for execution error due to the unknown time‐varying control coefficient. Note that there are three parameter dynamic compensators in the adaptive controller, and one is specialized to the execution error, which is not required in the continuous feedback context. It is shown that with the proposed adaptive event‐triggered controller, all the closed‐loop signals are bounded, the system state converges to zero, and no Zeno behavior occurs. A comparative simulation is provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: Rapid convergence that can be prescribed by a user is appealing for many applications with high requirements. This stimulates finite‐time stabilization with arbitrarily prescribed settling‐time and so‐called prescribed‐time stabilization. But their continuous realizations had to restrict uncertainties and/or to bear truncated run of controllers. This paper, for nonlinear systems with large uncertainties, realizes not only the convergence within the prescribed time, but also the non‐truncated run. First, by lending finite‐time stabilization to prescribed‐time stabilization and integrating dynamic compensation, an adaptive controller with time‐varying components is devised such that the system state reaches the origin at a finite time less than the prescribed time, while exhibiting local asymptotic stability (of the origin). Then by monitoring the finite time online, the time‐varying components of the adaptive controller are frozen as their values at the finite time. The asymptotic stability guarantees the frozen adaptive controller can make the system state remain at the origin for all future time. But the above finite time could not be detected in practice, due to ubiquitous disturbances. We thus modified the detection to ensure that the system state enters a vicinity of the origin before the prescribed time and stays there afterwards under some conditions on uncertainties and disturbances. Two simulation examples illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper typically concerns more efficient event‐triggered implementation, and specifically establishes an adaptive event‐triggered framework to achieve global stabilization for a class of uncertain nonlinear systems while reducing both sensor‐to‐controller and controller‐to‐actuator communication (rather than only one‐side communication). First, a novel switching event‐triggering mechanism is proposed to determine when to transmit information and adjust parameters. Particularly, with the switching varying mechanism incorporated, not only large uncertainties (whose bounds are unknown) but also inherent nonlinearities can be effectively dealt with. Then, a linear simple controller, rather than a complicated nonlinear one as in the related literature, is designed based on the switching event‐triggering mechanism. It turns out that the closed‐loop system states converge to zero while no infinitely fast sampling/execution or infinite switchings occur. Notably, just owing to the linearity of controller function, the controller signal is kept from entering the event‐triggering mechanism, which enables the sensor‐to‐controller event‐triggered communication. Besides, by strengthening the switching varying mechanism, an explicit pre‐evaluation is derived for the lower bound of inter‐execution intervals, in order to ensure moderate communication rates for reliable implementation of the event‐triggered controller. [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]

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]

Whether or not system performance can be prescribed by users is one core issue for almost all control problems, of course for multi‐agent control systems. But it could pose stern constraints on or exceptions to systems and control methods. How can one guarantee the prescribed performance while covering much more systems? It deserves deep study and particularly entails the integration/reformation of the related techniques. In the paper, we are concerned with the leaderless consensus with a prescribed convergence rate, aiming at n$$ n $$‐dimensional multi‐agent systems typically with unknown heterogeneous nonlinearities under a directed graph. In view of the essence of the problem, we resort to a powerful time‐varying high‐gain method, that is, funnel control. Specifically, to suppress unknown system nonlinearities and guarantee the prescribed performance, funnel gains are devised by utilizing the relative states and a time‐varying design function. Integrating them as well as a series of intermediate variables, a distributed consensus protocol is obtained without involving any global graph information. Remark that besides being used to construct funnel gains, the time‐varying design function is also introduced as a part of the protocol, substantially enhancing the control effect and playing a key role in forcing the relative states to ultimately converge to zero. It is shown that under the proposed protocol, the desired consensus is achieved with a prescribed convergence rate. A simulation example is given to illustrate the effectiveness of the theoretical result. [ABSTRACT FROM AUTHOR]

Communication network could suffer uncertainties originating from link faults and network attacks. This situation, in multi-agent systems, can be featured by unknown weights of network topology. To impair the influence of the uncertain topology, typical compensation should be taken into account in distributed protocols to the workability of multi-agent systems. This paper, in the context of uncertain topology, addresses finite-time leader-following consensus for second-order uncertain nonlinear multi-agent systems. In addition to uncertainties in topology, the systems also allow unknown control coefficients, which together with the unknown weights renders the realisation of finite-time leader-following consensus nontrivial. Specifically, a fully distributed protocol based on distributed finite-time observer is designed via integrating the adaptive compensation scheme. Notably, in the designed protocol, dynamic high gains are introduced for the compensations of the network uncertainties and agents uncertainties. It turns out that the designed fully distributed protocol guarantees the global finite-time leader-following consensus. Simulation examples are provided to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Event-triggered control, as networked systems are popular, is increasingly appreciated. Such control could arouse essential saving of communication/computation and would lay the groundwork for networked (control) systems. However, due to the discontinuity and hybrid nature of event-triggered control, the exclusion of Zeno phenomenon is the premise of its workability. Aiming to circumvent the Zeno behaviour more explicitly, we attach a dynamic dwell time to triggering mechanism and propose a new adaptive event-triggered control scheme for uncertain nonlinear systems. Specifically, a set of dynamic gains are first introduced to compensate for large uncertainties and nonlinearities, and the indispensability of a set of gains rather than a gain is elaborated on. Then, from a dynamic-gain-dependent monitoring rule, the positive dwell time is generated so that the Zeno phenomenon can be excluded automatically. In particular, the rule enables system behaviour to be always monitored by evaluating the sampling errors of gains. Based on this, we construct an adaptive controller with linear structure, which allows the execution error can be estimated explicitly, and in turn suppressed by the gains. It is shown that, with the proposed event-triggered control, all the closed-loop system signals are bounded and the system state ultimately converges to zero. Notably, the designed triggering mechanism could save more resources in theory since the event detection and gains monitoring are performed alternately. The effectiveness and superiority of the proposed scheme is illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

Among system uncertainties, unknown control direction is a rather essential one, whose compensation should entail the so-called Nussbaum function. Recently, strategies based on multiple Nussbaum functions (MNFs) have been proposed to make possible continuous adaptive control for the systems with nonidentical unknown control directions, such as large-scale systems and multi-agent systems, which cannot be addressed by a single Nussbaum function. But the existing stability theorems required: MNFs have explicit expressions; MNFs are all odd or all even. This paper aims to overcome the limitations of the theorems. We first delineate MNFs by two aspects of basic properties, replacing their explicit expressions as in the literature. Specifically, MNFs have the bivariate-product form, where one variate delineates frequent changes of signs and persistent intensity of MNFs, and the other delineates the rapid growth of MNFs. Such a delineation can capture the essence of MNFs and cover as many MNFs as possible. Based on the delineated MNFs, we present two stability theorems overcoming the aforementioned limitations. Notably, the two theorems do not require MNFs to have explicit expressions. Specifically, Theorem 1 allows nonmonotonic dynamic variables of MNFs while requiring MNFs to be odd, avoiding too large gains and excessive control cost. Theorem 4 does not require all MNFs to be odd while requiring dynamic variables of MNFs to be monotonic, giving users more freedom in selecting MNFs. The two stability theorems are applied to a large-scale system and a nonlinear system with parameterized uncertainties, both with nonidentical unknown control directions, to avoid monotonicity of dynamic gains and overparameterization, respectively, in control design. [ABSTRACT FROM AUTHOR]

This paper researches the fixed-time leader-following consensus problem for nonlinear multi-agent systems (MASs) affected by unknown disturbances under the jointly connected graph. In order to achieve control goal, this paper designs a fixed-time consensus protocol, which can offset the unknown disturbances and the nonlinear item under the jointly connected graph, simultaneously. In this paper, the states of multiple followers can converge to the state of the leader within a fixed time regardless of the initial conditions rather than just converging to a small neighborhood near the leader state. Finally, a simulation example is given to illustrate the theoretical result. [ABSTRACT FROM AUTHOR]

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]

This article is devoted to the global output‐feedback stabilization of nonlinear systems with unknown control directions and unmeasured states dependent growth whose rate is an unknown arbitrary function of output. In view of limited capability of continuous feedback in compensating system uncertainties and nonlinearities, a novel switching adaptive scheme is proposed. The scheme involves a logic‐based switching mechanism, based on which, a proper controller is selected (from a family of candidate controllers) to act on the system during its execution interval. The main differences between the proposed scheme and those in the related works are as follows. First, the set of candidate controllers is determined online, rather than specified in advance, which provides foundations for compensating arbitrary function‐of‐output growth rate. Second, an iterative function composed of system memory signals is introduced into the switching mechanism, aiming to evaluate the differences between the system states and observe states. Finally, when switching stops, only by introducing an extra transformation and adopting elaborate analysis, can the boundedness of the closed‐loop system signals be obtained, rather than those in the related works where the boundedness can be naturally established once switching stops. The constructed switching adaptive controller guarantees that all the signals of the resulting closed‐loop system are bounded and ultimately converge to zero. [ABSTRACT FROM AUTHOR]

This article is devoted to explore the periodic event-triggered stabilization for continuous-time stochastic systems, and to develop analysis tools/methods for stochastic periodic event-triggered control. Notably, without real-time monitoring of system behavior as in the scenario with continuous event evaluation, it is critical to delicately estimate and govern the execution/sampling error to achieve the desired system performance. This, under stochastic effects, would be substantially challenging, since the behavior of the stochastic system is hard to predict and is disparate between trials even with the same initial conditions. In this article, a framework of global stabilization via periodic event-triggered output-feedback is established: 1) a criterion condition based on the ISS-Lyapunov function is presented for the feasibility of the desired event-triggered stabilization; 2) both the asymptotic stabilization and exponential stabilization are achieved for the systems, with delicately specifying the periodic event-triggering mechanism; and 3) the involved analysis, without applying the well-known Lyapunov theorems, can serve as a pattern from estimating sampling and execution errors to assess the closed-loop stability for stochastic periodic event-triggered control. Moreover, based on the established framework, we contribute the stabilizing controller design via periodic event-triggered output-feedback for a class of stochastic nonlinear systems. [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]

Summary: The paper is devoted to the asymptotic output consensus for a class of uncertain nonlinear multi‐agent systems. The disturbance that the system suffered is said to be "atypical" since, unlike the related literature, it is unnecessarily continuously differentiable (e.g., sawtooth wave), and even permitted to be discontinuous (e.g., square wave), despite requiring it to be of unknown integer multiples of certain period. Typically, the multi‐agent systems admit more than one ingredient causing heterogeneities: (i) No identical requirement is made on the system nonlinearities and input directions (the unknown signs of the input coefficients). (ii) The orders of agent dynamics can be different (the dynamics are first‐order, second‐order, or even high‐order). Nevertheless, in the context, we still pursue the asymptotic output consensus, and unlike some related literature, instead of seeking a time‐varying strategy which means the introduction of infinitely large gains, we combine a refined switching strategy with continuous adaptive one together to propose a new consensus protocol. It turns out that under the proposed protocol, all the agent outputs reach a common value while all the closed‐loop signals are bounded. Simulation examples are given to demonstrate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

Summary: This article is devoted to global adaptive stabilization for a class of uncertain nonlinear systems. Notably, the systems under investigation admit unknown control directions and unknown input powers, and particularly the latter, which are a new type of system uncertainties, largely challenge the feasibility of continuous feedbacks. This spurs us to pursue a switching adaptive feedback which is actual a discontinuous one with high feedback capability. To solve the control problem, a parameterized controller in a specified form is first introduced, which can globally stabilize the system once the design parameter involved belongs to a certain set. However, the controller cannot directly be implemented since the set depends heavily on the unknown input powers. To make the parameterized controller implementable, a new switching strategy is delicately proposed, which can instantly update the parameters of the controller to compensate the serious system uncertainties. It turns out that the parameterized controller with switching updating mechanism guarantees that all the signals of the closed‐loop system are globally bounded and ultimately converge to zero. Simulation examples demonstrate the effectiveness of the proposed design scheme. [ABSTRACT FROM AUTHOR]

Summary: This article is devoted to the global practical tracking for a class of uncertain nonlinear systems. Notably, the input powers of the system are unknown and not required to be upper bounded by known constants. This means the presence of new type of serious uncertainties, which makes the problem under investigation largely challenging and urges us to develop a new powerful adaptive control scheme, particularly the compensation strategy to overcome the negative influence caused by the uncertainties. For this, a dual high‐gain‐based adaptive control design scheme is proposed, in which a dynamic high gain and a high gain function are jointly introduced to compensate the serious system uncertainties. Under the designed controller, all the signals of the resulting closed‐loop system are bounded and furthermore the tracking error remains any prescribed small after a finite time. [ABSTRACT FROM AUTHOR]

This paper considers the global stabilization for a class of uncertain nonlinear systems with unknown powers, unknown control directions, and unknown nonlinearities. Mainly due to the presence of the unknown powers which have not known upper bound, no existing methods are applicable to the control problem to be solved. In this paper, to compensate the serious system uncertainties and particularly to overcome the major obstruction from unknown powers, we appeal to the mechanism of switching adaptive feedback. By flexibly combining the domination and the method of adding a power integrator, we propose a new adaptive controller design, whose design parameters are tuned online based on a switching logic. The designed controller will become operative as long as finite switchings happen and will not lead to Zeno phenomenon, and can guarantee the global boundedness as well as ultimate convergence of the resulting closed-loop system. Two numerical examples are given to demonstrate the effectiveness of the developed design scheme. [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]

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]

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]

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]

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]

LaSalle theorems, sometimes called as invariance-like theorems, have witnessed abundant applications as powerful tools of analysing system convergence. However, these theorems have twofold limitations: On the one hand, the uniformity of convergence with respect to initial state values cannot be offered, which indicates that the possibility of excessively slow convergence could not be ruled out for a given bounded set of initial state values. On the other hand, unbounded time-variations are not allowed in the systems, and meanwhile, the boundedness of all the states are required even if one merely concerns the convergence of partial states, precluding many scenarios with the unboundedness (e.g., induced by stochastic noise) for some states defined on the whole time horizon. Towards the limitations of LaSalle theorems, this paper seeks to further develop convergence theorems in the stochastic framework. First, a Lyapunov-like function based theorem on the convergence owning the uniformity with respect to initial state values is presented for Itô-type stochastic systems, with the infinitesimal of Lyapunov-like functions exploited more delicately than those in stochastic LaSalle theorems. Based on this, a framework of adaptive stabilization with the uniformity of convergence is established for uncertain stochastic nonlinear systems. In particular, the performance specifications involved are impossible to achieve by applying LaSalle theorems as in the related results. Second, an enlarged convergence theorem is established with Lyapunov-like conditions moderately relaxed, which allows the unboundedness for partial states defined on the whole time horizon and has potential applications in the presence of unbounded time-variations. What is notable, the enlarged convergence theorem is nontrivial to verify, which compels us to propose an extended Barbălat lemma with the conventional requirement of uniform continuity relaxed in the stochastic framework. [ABSTRACT FROM AUTHOR]

This paper addresses the global stabilization via adaptive output-feedback for a class of uncertain nonlinear systems. Remarkably, the systems under investigation are with multiple uncertainties: unknown control directions, unknown growth rates and unknown input bias, and can be used to describe more physical plants. Multiple uncertainties, which usually cannot be compensated by a sole compensation technique, may give rise to big technical difficulty for controller design. To overcome such difficulty and to achieve the global stabilization, a new adaptive output-feedback scheme is proposed in this paper, by flexibly combining Nussbaum-type function, tuning function technique and extended state observer. It is shown that, under the designed controller, the system states globally converge to zero. A simulation example on non-zero set-point regulation is given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

System nonlinearities, immeasurableness, and uncertainties (especially their coupling/coexistence) have constantly challenged the control design, which requires the controller to be powerful enough to counteract the resulting negative effects. In this paper, a global adaptive output-feedback controller is designed for uncertain nonlinear systems. The proposed controller is of switching type, in which the design parameters are online adjusted on the basis of a switching logic in a recursive manner. This makes the controller powerful enough to compensate the system unknowns and dominate the system nonlinearities and therefore be applicable to a rather wide range of systems. Remarkably, our strategy allows the coexistence of an unknown control direction and unmeasured state--dependent growth but which are substantially excluded in the related literature.An example of the single-link robot arm systemis provided to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Summary: This paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper. [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]

Abstract: This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the leader-following consensus for a class of uncertain nonlinear multi-agent systems (NMASs) with rather coarse input disturbances, unknown control coefficients and unknown Lipschitz rate. The essential unknowns render the existing compensation strategies inapplicable and motivate us to explore a new one. First, a time-varying strategy is developed to compensate the essential unknowns, where a suitable design function of time is introduced so that the unknowns can be overtaken by the design function as time increases. Then, distributed time-varying consensus protocols are designed and the leader-following consensus is achieved. When essential time-variations exist, the designed consensus protocols are still valid if the involved design function of time is replaced by a new one. Two examples are given to illustrate the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

This paper considers the global stabilization via time-varying output-feedback for a class of high-order uncertain nonlinear systems with rather weak assumptions. Essentially different from the existing literature, the systems under investigation simultaneously have more serious nonlinearities, unknowns, immeasurableness, and time-variations, which are indicated from the unknown time-varying control coefficients and the higher-order and lower-order unmeasured states dependent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time-varying design scheme is proposed by combining time-varying approach, certainty equivalence principle and homogeneous domination approach. One key point in the design scheme is the selection of the design functions of time, in order to compensate/capture the serious unknowns and serious time-variations, and another one is the design of a time-varying observer to rebuild the unmeasured system states. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed-loop system globally bounded and ultimately converge to zero. Copyright © 2016 John Wiley & Sons, Ltd. [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]

In this paper, we investigate global-exponential stabilisation of a class of nonlinear networked control systems. The network-induced delays are assumed to be random and significantly smaller than the sampling period. First, sufficient conditions are presented to ensure global-exponential stability for a class of hybrid systems with time delay. Then, the networked control systems are modelled as the hybrid systems with time delay. By the techniques of adding a power integrator and a recursive argument, a sampled-data state feedback control law is presented. Sufficient conditions are given to ensure global-exponential stability of the closed-loop system by constructing a Lyapunov–Krasovskii function. Finally, a numerical example is presented to show the validity of the new methods. [ABSTRACT FROM AUTHOR]

This paper investigates the global output-feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced-order observer is introduced to reconstruct the unmeasured system states before a smooth output-feedback controller is designed using the backstepping method, which guarantees that the closed-loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output-feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach. [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 investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. Detailedly, based on a time-varying observer and transformation, an output-feedback controller is designed by skillfully combining adaptive technique, time-varying technique and well-known backstepping method. It is shown that, with the appropriate choice of the design parameters/functions, all the signals of the closed-loop system are bounded, and furthermore, the original system states globally converge to zero. It is worth mentioning that, the heavy nonlinearities are compensated by an updating law, while the serious unknowns and time-variations are compensated by a time-varying function. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant. [ABSTRACT FROM AUTHOR]