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In this article, an adaptive switching controller is designed for the stabilization control and the tracking control of nonlinear systems suffering from full state constraints, unknown control directions, and system uncertainties. Featured with changing signs and unbounded increasing magnitudes, a switching control structure is proposed to deal with the unknown control direction problem. In order to explore and finally fix the correct control direction, an adaptive switching rule, a switching function, and a reference function are constructed. An integral Lyapunov function is adopted for the design of the control law, which ensures that full state constraints will not be violated. Using this method, the nonlinear system can be properly controlled without extra estimations or approximations. The boundedness of all the states and the stability of the system are analyzed and guaranteed. Finally, simulations are conducted to validate the proposed method, and the results illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

This article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This article addresses the event‐triggered adaptive consensus control of nonlinear multi‐agent systems with unknown control direction and actuator saturation. A new robust adaptive control algorithm based on an event‐triggered mechanism is designed. The smooth Lipschitz function approximates the saturated nonlinear function, while the Nussbaum function handles unknown control directions and residual terms. The event‐triggered mechanism is designed to determine the time of communication, significantly reducing the communication burden. An additional estimator is utilized to deal with unknown parameters involved in neighbor dynamics and prevent information exchange to consistency errors between connected subsystems. The results show that all the signals of the closed‐loop system are uniformly bounded, and the consensus tracking error converges to a bounded set. Meanwhile, Zeno's behavior is eliminated. Simulation results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an event‐triggered control strategy for stochastic interconnected nonlinear systems with unknown control directions. Firstly, a new lemma is proposed for stochastic nonlinear systems with multiple time‐varying unknown control directions, which guarantees the boundedness of Nussbaum function parameter variables. Different from the existing results, each subsystem is allowed to have multiple time‐varying unknown control directions. Then, by using the backstepping method, a novel controller is proposed based on the relative threshold event‐triggered strategy. The controller not only reduces the communication burden but also eliminates the interference of unknown control directions. Based on Lyapunov stability theory, it is proved that the controller can make all signals in the closed‐loop system be bounded in probability and the system state variables converge to zero in probability. Finally, two simulation examples are presented to certify the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

In this article, an event‐triggered zero‐error adaptive output tracking controller with fixed‐time convergence mode is designed for a kind of uncertain nonlinear systems under full‐state constraints, unknown control coefficients, input dead‐zone, and saturation. The constrainedly practically fixed‐time stability is investigated for the considered high‐order nonlinear system. Then applying the barrier Lyapunov function technology and blending an error transformation into backstepping scheme, the Nussbaum‐gain‐based adaptive fuzzy control is proposed with prescribed performance. The control process consists of two phases, among which the first phase is used to render tracking error into the preset adjustable residual set within a preassigned fixed time at a prescribed decay rate, and the second phase further force the tracking error to converge to zero asymptotically. Additionally, the desired full‐state constraints are not violated in the whole control process. The simulation results are also given to show the effectiveness of the designed control method [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]

In this article, we develop an adaptive global prescribed performance tracking control scheme for nonlinear multiple‐input multiple‐output (MIMO) robotic systems in the presence of unknown control directions and nonparametric uncertainties, in which the proposed solution mainly includes the following steps. Firstly, by constructing a global prescribed performance function, together with a series of transformations, the corresponding control guarantees the position tracking error evolves strictly within the prespecified region for all time, which is independent of initial conditions; Secondly, in order to cope with the problem of multiple unknown control directions, we make use of a symmetric matrix lemma to convert the underlying problem from matrix form to scalar form, so that the Nussbaum‐gain lemma for SISO systems becomes effective for MIMO systems with multiple inputs; In addition, we employ the integrable function to handle the nonparametric uncertainties, enabling the control scheme with the capability to drive the tracking error toward zero asymptotically. The effectiveness of the proposed control is validated via a two‐link rigid robotic manipulator. [ABSTRACT FROM AUTHOR]

An adaptive approximated inverse control scheme for a class of high-order nonlinear multi-agent systems with unknown control directions is proposed in this paper. The adaptive control problem under the case it is not required to be identical for the unknown control directions is solved by some novel Nussbaum functions and a monotonously increasing sequence, leading our multiple Nussbaum functions reinforce rather than counteract each other. Also, it is introduced in the design and analysis like some integrable auxiliary signals and a novel contradiction argument. Moreover, hysteresis nonlinearity is counteracted by constructing its approximated inverse compensator. With these efforts, stability analysis ensures that all the closed-loop system signals are uniformly bounded, and it is successfully achieved the asymptotic convergence of tracking error to zero, circumventing the obstacle caused by the unknown control directions. Experiment results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive synchronization sliding mode control is proposed for a dual-arm robot against parameter variations, external disturbance, and unknown control directions. The proposed control is designed by using cross-coupling error and sliding mode control to guarantee the position synchronization of the dual-arm manipulator. The control objective of the proposed control is to synchronize the movement of both arms beside the trajectory tracking issue. In order to manage the lumped uncertainties caused by the parameter variations, external disturbance, and unknown control directions, an extended state observer is used in the proposed control. It enhances the stability of the controlled system against uncertainties. Additionally, a Nussbaum gain function is integrated into the control algorithm to deal with the issue of unknown control direction. Lyapunov stability theory is used to demonstrate the stability of the controlled system. Finally, some simulations are implemented in MATLAB Simulink with a dual 3-DOF manipulator system. The results of the proposed control are compared to other controllers to verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper deals with the consensus output tracking problem for multi-agent systems with unknown high-frequency gain signs, in which the subsystems are connected over directed graphs. The subsystems may have different dynamics, as long as the relative degrees are the same. A new type of Nussbaum gain is first presented to tackle adaptive consensus control of network-connected systems without the knowledge of the high-frequency gains. Adaptive laws and internal models are then proposed to handle the uncertainties and unknown parameters. An integral Lyapunov function based on sufficient conditions is finally introduced to tackle the asymmetry of the Laplacian matrix of directed graphs, into which we incorporate the new Nussbaum gain and the adaptive internal model to design the controller. It is apparent that the control scheme and the adaptive laws are fully distributed, which means that only the relative information of the neighbourhood subsystems' outputs is used, and the simulation results validate the effectiveness of the control design, whereby they guarantee the asymptotic convergence of errors to zero as well as the boundedness of the state variables. [ABSTRACT FROM AUTHOR]

This paper concentrates on the study of the adaptive fast finite-time control method for a class of nonlinear time-delay systems with unknown control directions and dead zone. Fuzzy logic systems (FLSs) are employed to handle the problem of uncertain nonlinear terms. The Nussbaum function is utilised to deals with the problem of unknown control directions. Based on the fast finite-time stability theory, a novel adaptive fast finite-time fault tolerant control scheme is proposed under the framework of adaptive backstepping control. Choosing an appropriate Lyapunov-Krasovskii function, it is theoretically proved that the proposed control scheme can not only ensure that the control system is semi-global practical fast finite-time stable but also the tracking error converges to a small neighbourhood of the origin in a fast finite-time. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the finite time stabilization problem for a class of nonlinear systems with unknown control directions and unstructured uncertainties. The unstructured uncertainties indicate that not only the parameters but also the structure of the system nonlinearities are uncertain. A new adaptive control method is proposed for the considered system. Logic‐based switching rule is utilized to tune the controller parameters online to stabilize the system in finite time. Different from the existing adaptive controllers for structured/parametric uncertainties, a new switching barrier Lyapunov method and supervisory functions are introduced to overcome the obstacles caused by unstructured uncertainties and unknown control directions. Both simulations and experiments are conducted on mechatronic systems to verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called "explosion of complexity" in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law. [ABSTRACT FROM AUTHOR]

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In the article, the issues of asymptotic adaptive tracking control for the uncertain nonlinear systems in the presence of actuator faults and unknown control directions are investigated. By using the properties of the Nussbaum function and backstepping technique, the problems resulting from the unknown signs of the nonlinear control functions are circumvented successfully. Moreover, a new adaptive asymptotic tracking control method is presented with the fault-tolerant control framework, which is capable of realising zero-tracking performance. The stability of the controlled system is ensured through fractional Lyapunov stability analysis. Finally, the validity of the raised scheme is verified by a simulation example. [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 investigates the consensus control problem for strict-feedback nonlinear multiagent systems (MASs) under false data injection attacks (FDIAs) and unknown control directions. Different from the existing results, an attack detection mechanism that only uses the information of adjacent agents is designed to judge the occurrence times of the FDIAs, and the negative effects of FDIAs are eliminated by proposing a switching topologies strategy. By introducing the multiple Nussbaum functions, the multiple unknown control directions are addressed, while the effects of these functions enhance each other rather than offset each other. It is shown that the consensus performance and the boundedness of all the signals in the closed-loop systems can be ensured. Finally, the validity of the proposed control scheme is verified through a simulation example. [ABSTRACT FROM AUTHOR]

This work discusses the adaptive consensus tracking for first-order and second-order uncertain multi-agent systems (UMASs). The systems allow multiple uncertainties, including unknown control directions, parameterized unknown nonlinearities, and unknown external disturbances. To compensate for these uncertainties, two novel distributed adaptive control protocols with the dynamic compensation based on Nussbaum-type gain are proposed for first-order and second-order UMASs, respectively. Remarkably, the control protocol is devised in a fully distributed fashion, which is not dependent on the global information of communication graph. Then, under undirected connected graph, it is proved that the proposed control protocol can guarantee the boundedness of all signals in the closed-loop system and the achievement of the consensus tracking (CT). Finally, the theoretical results are validated by two simulation examples. [ABSTRACT FROM AUTHOR]

This article devises an adaptive quantized control scheme for full-state constrained Markov jumping nonlinear systems with incomplete transition probabilities and unknown control directions. First, the barrier Lyapunov functions were utilized to achieve full-state constraints on the investigated system, while the Nussbaum function has been adopted to overcome the issue of unknown control directions. Then, by means of command filtered backstepping control technique, an adaptive quantized controller is developed, where an improved error compensation mechanism was established to eliminate the effect of filter error, and a hysteresis quantizer was employed to diminish the transmission rate. Furthermore, it is demonstrated that the designed controller assures that all signals of the closed-loop system are bounded in the mean square sense. Finally, two illustrative examples were provided to validate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This brief proposes a novel tracking control strategy to cope with the asymmetric state constraints for nonstrict-feedback and nonlinear switched stochastic systems with unknown control directions. Firstly, without requiring piecewise Barrier Lyapunov functions (BLFs), the asymmetric constraint restrictions are unfastened well in the recursive idea according to a series of new-style coordinate transformations. Then, a novel error compensation mechanism based on the state constraint conditions is incorporated into the tracking differentiator (TD) technology to tackle the "differential explosion" problem in the backstepping design, and a low-cost adaptive control strategy under single adaptive law is built to simplify the computation, meanwhile, the control objective is achieved. Followed by the rigorous theoretical proof, the applicability is presented by a practical example. • A new tracking controller is presented for switched stochastic systems to manage asymmetric constraints without constructing the A-BLFs. • The restrictive feasibility conditions are circumvented and the prerequisite of knowledge of control gains are relaxed. • New compensation signals with TD method are designed to manage the "differential explosion" and improves the tracking accuracy simultaneously. • The designed low computation controller relaxes the assumption on nonstrict-feedback functions and the calculation burden is thus reduced. [ABSTRACT FROM AUTHOR]

This article studies the issue of command filter-based adaptive fault-tolerant control for a class of nonlinear systems subject to unknown control directions and disturbance. First, the neural network is employed to deal with the nonlinear functions, and the explosion of the complexity problem is handled by the command filter approach. Second, the bound estimation method and the Nussbaum function are utilized to compensate for the influence of the actuator faults and the unknown directions, respectively. Finally, the tracking error signals are guaranteed to converge into bounded compact sets around the origin, and all closed-loop signals are bounded. The effectiveness of the proposed method is illustrated by three simulations. [ABSTRACT FROM AUTHOR]

In this paper, the finite-time adaptive fuzzy control method is proposed for nonlinear nonstrict-feedback multi-agent systems (MASs) with unknown control directions. The Nussbaum function is introduced to compensate the influence of unknown control directions. By combining the finite-time stability criterion, an adaptive fuzzy controller is constructed to ensure that systems reach a steady state in a finite time, and the tracking errors of all output signals converge to a small neighbourhood of the origin. By using the Lyapunov finite-time stability theorem, all signals are proved to be semi-global practically finite-time stable. Finally, the effectiveness of the proposed control method is proved through some results of simulation experiments. [ABSTRACT FROM AUTHOR]

In this article, an event‐triggered adaptive control strategy is presented for nonlinear pure‐feedback multi‐agent systems, and the problem of the unknown control gain is also considered. In contrast to most of the existing results, each agent's control item is a power exponential function, and this problem is handled by utilizing the "adding a power integrator" technique. Based on the Nussbaum gain technique, a control scheme is presented to handle the problem concerning unknown control gains. The tracking differentiator is used to eliminate the problem of "explosion of complexity" in the backstepping method. Furthermore, an event‐triggered control strategy is designed to reduce the communication burden and the computational cost. It is proved via the Lyapunov stability method that the consensus tracking errors can converge to a small neighborhood of the origin and all signals of the closed‐loop systems are semi‐globally uniformly ultimately bounded. Finally, some simulation results are proposed to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This study reports adaptive quantized control for a class of uncertain strict‐feedback nonlinear systems with unknown control directions. Combining backstepping technique and Lyapunov stability theory, a systematic analysis method is designed. Based on the disintegration of the hysteresis quantizer, a Nussbaum‐based scheme can be developed to get over the obstacle of the quantized input signal and unknown control directions. Moreover, the number of adaptive laws is small, thereby reducing the computational burden. Then we testify the boundedness of all signals in the closed‐loop system. Besides, the tracking error can converge to an arbitrarily small domain of origin. Finally, a simulation example is provided to verify the feasibility of the control scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of global state-feedback regulation for a class of switched uncertain nonlinear systems with quantised input and unknown control directions under arbitrary switchings. A hysteretic quantiser is introduced to avoid actuator chattering. The powers of all subsystems are positive odd rational numbers and depend on the switching signals. Incorporating Nussbaum-type gain technique into adding a power integrator approach, a new adaptive controller is designed to guarantee that all the signals of the closed-loop system are bounded and the system state is globally asymptotically regulated to zero. An example is given to illustrate the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of output feedback adaptive tracking control for a class of uncertain nonlinear time-delay systems (NTDS) with both uncertain output function and unknown control directions. By introducing a linear state transformation, the original system is transformed into a new system for which output feedback control design becomes feasible. Without the precise information on output function, an input-driven high-gain state observer is presented to estimate the unavailable states of the new system. Moreover, some radial basis function neural networks (RBFNNs) are employed to approximate the lumped unknown nonlinear functions during the procedure of control design. Then, by combining the Lyapunov–Krasovskii functional method, the Nussbaum gain function approach and the backstepping technique, a novel adaptive output feedback control scheme including only one parameter to be updated is developed for such systems. As a result, all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) while the tracking error can remain in a small neighbourhood of zero. Finally, two simulation examples are given to validate the effectiveness and applicability of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with an adaptive neural output-feedback control for a class of stochastic nonlinear systems with unknown control directions and hysteresis input. An output-feedback controller is developed for stochastic nonlinear via using radial basis function neural networks (RBFNNs) and adaptive backstepping method. A state observer is designed to estimate the unmeasurable system state signals. Nussbaum gain technique is employed to deal with the unknown control directions. Simultaneously, the backlash-like hysteresis input control in this paper is considered. An adaptive controller is designed to ensure that the output tracking error converges on a small region of the origin. Finally, the control scheme ensures that all signals in the closed-loop systems are semi-global uniformly ultimately bounded. Results of simulation cases are presented to prove the effectivity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, an integral reinforcement learning-based adaptive neural network (NN) tracking control is developed for the continuous-time (CT) nonlinear system with unknown control directions. The long-term performance index in the CT domain is prescribed. Critic and action NNs are designed to approximate the unavailable long-term performance index and the unknown dynamics, respectively. The reinforcement signal is explicitly embedded in the updated law of the action NN and then the estimated long-term performance index can be minimized. Rigorous theoretical analysis is provided to show that the closed-loop system is stabilized and all closed-loop signals are semiglobally uniformly ultimately bounded. Finally, to demonstrate the control performance, simulation results are provided to verify the tacking control performance of an autonomous underwater vehicle model. [ABSTRACT FROM AUTHOR]

Summary: This article solves the leaderless consensus problem of a class of uncertain nonlinear multiagent systems with unknown control directions and unknown system parameters. Without using the Nussbaum function approach, a novel control scheme is proposed by means of the switching mechanism. The control algorithm guarantees that consensus errors converge to the origin asymptotically, and the amplitude of the control signals is much smaller compared with those using Nussbaum functions. The simulation results illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of adaptive fuzzy finite‐time consensus tracking control for multiple Euler‐Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite‐time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function‐based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm. [ABSTRACT FROM AUTHOR]

This study introduces an improved multiple model adaptive control (MMAC) algorithm for a class of nonlinear discrete-time systems. The controller consists of a linear direct adaptive controller, a neural network-based nonlinear direct adaptive controller and a switching mechanism. The assumption of the nonlinear term is relaxed by incorporating a parameter estimator with an augmented error. The control direction of the system is not required to be known by employing a linear direct adaptive controller with the discrete Nussbaum gain and future output predictions. The stability of the closed-loop systems applying the proposed MMAC method is proved and the improved transient performance of the system is illustrated by the simulation results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of adaptive control for strict-feedback nonlinear systems with input delay and unknown control directions. The Nussbaum function is utilised to deal with the unknown control directions and a novel compensation system is introduced to handle the time-varying input delay. By using neural network(NN) approximation and backstepping approaches, an adaptive NN controller is designed which can guarantee the semi-global boundedness of all the signals in the closed-loop system. Two simulation examples are also given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the tracking control problem for a class of multiple‐input–multiple‐output systems with unmatched disturbances and the unknown additive and multiplicative nonlinearities. The objective is to provide a low‐complexity control solution in the sense that (i) approximating structures are not involved, despite unknown nonlinearities and (ii) iterative calculations of command derivatives are avoided in the backstepping design. A robust adaptive control strategy is proposed to fulfill the task. In the control design, a new‐type adaptive law is first developed to update Nussbaum gains to handle control direction uncertainties, while ensuring Nussbaum gains bounded. Then, the potential robustness of error constraint techniques is exploited to counteract the effects of unknown nonlinearities and disturbances and achieve predefined transient and steady‐state tracking performance. Finally, simulation results are given to illustrate the above theoretical findings. [ABSTRACT FROM AUTHOR]

Existing adaptive control algorithms at best guarantee that the tracking error is a l2 sequence. This paper presents globally stable adaptive control algorithms for linear discrete-time systems providing l1 tracking performance. Two algorithms with different degree of complexity are proposed, one for the case of known control directions, and a separate algorithm for the case of unknown control directions. It is demonstrated that in both cases the tracking error is l1 sequence, while the input and output signals are uniformly bounded. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed adaptive leader-following consensus control for high-order nonlinear multi-agent systems with a time-varying reference trajectory under directed topology, subjected to mismatched unknown parameters and unknown control directions. By introducing local estimators for the bounds of the reference trajectory and a filter for each agent, a new backstepping-based smooth distributed adaptive control protocol is proposed. Meanwhile, a Nussbaum-type function is applied to address the consensus control with unknown control directions. It is shown that global uniform boundedness of all the closed-loop signals and asymptotic output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme. [ABSTRACT FROM AUTHOR]

Summary: The problem of global stabilization by nonsmooth state feedback is investigated for a family of time‐delay nonlinear systems with unknown control direction. Using the idea of the Nussbaum function from universal control, we present a delay‐free, nonsmooth dynamic state feedback strategy to achieve asymptotic state regulation with boundedness of the closed‐loop system. The proposed control scheme allows one to design a set of Lyapunov‐Krasovskii functionals and nonsmooth dynamic compensators simultaneously, by the technique of adding a power integrator. It is shown that while the effects of unknown control direction can be mitigated by the Nussbaum‐type gains, the strong nonlinearity with time delay can be effectively dealt with by nonsmooth state feedback controllers whose gains are updated dynamically. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates an adaptive state feedback control problem for a class of single‐input and single‐output nonlinear systems with strict‐feedback form. A novel adaptive control strategy is developed for nonlinear systems with unmodeled dynamics, unknown control directions, dynamic disturbances and unknown dead zone. To stabilize this category of systems, a dynamic signal is introduced to dominate the unmodeled dynamics. Nussbaum gain technique is used to overcome the unknown control directions problem. Nonlinear damping terms are framed to counteract the dynamic disturbances, and the assistant signal is constructed to compensate the influence of symmetric dead zone. The adaptive control approach ensures all signals in the closed‐loop system to be bounded. Finally, a numerical example is used to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, robust adaptive control of a class of strict-feedback nonlinear systems with unknown control directions is investigated. A novel Nussbaum-type function is developed and a key theorem is drawn which involves quantifying the addition of multiple Nussbaum functions with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of system output are proved. A simulation example is given to illustrate the effectiveness of the proposed control scheme. [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]

In this paper, we propose a decentralized adaptive control scheme for a class of interconnected strict-feedback nonlinear systems without a priori knowledge of subsystems' control directions. To address this problem, a novel Nussbaum-type function is proposed and a key theorem is drawn which involves quantifying the interconnections of multiple Nussbaum-type functions of the subsystems with different control directions in a single inequality. Global stability of the closed-loop system and asymptotic stabilization of subsystems' output are proved and a simulation example is given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The problem of adaptive control is studied for a class of nonlinearly parameterised systems with quantised input signal and unknown control directions. The homogeneous domination approach and the Nussbaum-type gain method are applied to design an adaptive state-feedback controller. A hysteretic type of quantiser is incorporated to reduce actuator chattering. The proposed controller can ensure that all signals of the nonlinear system are globally bounded, and that the system state asymptotically converges to zero. Two numerical examples are presented to demonstrate the effectiveness and potential of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper considers the output feedback adaptive controller design problem for a class of discrete-time nonlinear systems in output feedback form with unknown control directions and preceded by unknown hysteresis. The problem of lacking in a-priori knowledge on the control directions and unknown hysteresis are solved by using the discrete Nussbaum gain and Prandtl–Ishlinskii model, respectively. The system is transformed into the form of a nonlinear auto regressive moving average (NARMA) model to construct an output feedback control. To overcome the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead-zone technique are constructed on the basis of the NARMA model. The proposed control algorithm guarantees that all the signals in the controlled system are bound and the output tracking error is made to be neighbourhood around zero, ultimately. Finally, simulations are performed on a nonlinear system to show the effectiveness of the proposed method [ABSTRACT FROM PUBLISHER]

An adaptive iterative learning control method is proposed for a class of nonlinear strict-feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. Ann-step ahead predictor approach is employed to estimate the future states in the control design. Discrete Nussbaum gain method is utilised to deal with the lack ofa prioriknowledge of control directions. The proposed control algorithm guarantees the boundedness of all the signals in the controlled system. The tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions. The effectiveness of the proposed control scheme is verified through numerical simulation. [ABSTRACT FROM AUTHOR]

• A resilient decentralized observer-based control scheme is proposed for nonlinear interconnected systems to realize the bounded tracking result under DOS attacks. • An adaptive control architecture with only one parameter updated is developed to deal with the unknown control directions under DoS attacks. • The relationship between the maximum sampling interval and the tolerable attack intensity is quantified. • The proposed control synthesis scheme only needs to calculate LMIs offline and leads to less computational complexity. This paper investigates the problem of resilient decentralized control for nonlinear interconnected systems with unknown control directions under denial-of-service (DoS) attacks. For each subsystem, a novel switched sampled-data observer and an adaptive control architecture are respectively proposed to deal with the unavailable correction term in the existing results. Then a resilient decentralized adaptive controller is developed by employing the backstepping technique to reduce the negative influences of the system uncertainties and DoS attacks. By using average dwell time (ADT) and piecewise Lyapunov stability theories, one can ensure that the closed-loop system is semiglobally uniformly ultimately bounded (SUUB), while the output reference signal of each subsystem is tracked bounded. Furthermore, this scheme has a better utilization of computing and communication resources. Finally, the proposed scheme is verified by a power network system simulation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, output feedback adaptive control is investigated for a class of nonlinear systems in output-feedback form with unknown control gains. To construct output feedback control, the system is transformed into the form of the NARMA (nonlinear-auto-regressive-moving-average) model, based on which future output prediction is carried out. With employment of the predicted future output, a constructive output feedback adaptive control is given with the discrete Nussbaum gain exploited to overcome the difficulty due to unknown control directions. Under the global Lipschitz condition of the system functions, the boundedness of all the closed-loop signals and asymptotical output tracking are achieved by the proposed control. Simulation results are presented to show the effectiveness of the proposed approach. [Copyright &y& Elsevier]