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In this paper, the issue of event-triggered fixed-time tracking control is investigated for a class of nonlinear systems subject to unknown control directions (UCDs) and asymmetric input saturation. Firstly, to cope with the design challenge imposed by nondifferential saturation nonlinearity in the system, the asymmetric saturation function is approached by introducing a smooth nonlinear function with respect to the control input signal. Secondly, a variable separation technique lemma is developed to remove the restrictive growth conditions that must be fulfilled by the nonlinear functions, and a new practically fixed-time stability lemma with more accurate upper-bound estimate of the settling time is put forward by means of the Beta function. Then, a technical lemma regarding a class of type-B Nussbaum functions (NFs) with unique properties is introduced, which avoids specific NFs-based complex stability analysis. Moreover, in compensation for the sampling error incurred by the event-triggered mechanism under UCDs, an adaptive law is skillfully constructed to co-design the fixed-time control law and the event-triggered mechanism. The results show that the controlled system is practically fixed-time stable (PFxTS), the tracking error can converge to a small neighborhood of the origin in a fixed time, and the saturation constraint is satisfied while reducing the communication burden. Finally, the effectiveness of the practically fixed-time stability criterion and control method developed in this study are verified by two simulation examples. • A novel practically fixed-time stability criterion is proposed, which provides a more accurate estimation of the settling time. • To avoid the restrictive growth assumptions on system nonlinearities, a variable separation technique lemma is developed. • We introduce a technical lemma for a class of type-B Nussbaum functions with unique properties. • An adaptive law is skillfully constructed to co-design the fixed-time control law and the event-triggered mechanism. [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]

We propose a quantization-based distributed consensus tracking design to resolve the unknown control direction problem of uncertain switched nonlinear multiagent systems under a fully quantized environment. All feedback and communication signals for the local control design are quantized and the control coefficient functions and directions of agents are unknown. Differing from the previous literature results, the primary contribution of this work is to present a quantization-based distributed design solution to the unknown control direction problem of asynchronously switched agents in the consensus tracking field. The non-differentiability problem of virtual control laws using quantized feedback signals is addressed by employing the filter-based recursive method and developing the analysis technique of the quantization errors of Nussbaum functions. Quantization effects in local adaptive neural control laws are compensated via the adaptive tuning mechanism using quantized states. The practical stability of the overall closed-loop system is established by the common Lyapunov theory. Illustrative simulations verify the efficacy of the proposed quantization-based consensus tracking approach. [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]

In this work, output-feedback control problems for a class of discrete-time non-affine nonlinear systems with unknown control directions and input constraints are considered by using reinforcement learning (RL) method. Two neural networks (NNs) implement the control: 1) a critic NN that estimates a non-quadratic strategic utility function (SUF) and 2) an action NN that generates optimized control input and minimizes the SUF. The implicit function theorem is applied to obtain the optimal control law since the control is appeared in a non-affine form. For the first time, the discrete Nussbaum gain is introduced to overcome the difficulty that the control directions are unknown and a non-quadratic SUF is used to deal with the control constraints in the RL-based control. The theoretical derivation of the uniformly ultimately boundedness of the NN weights and the closed-loop output tracking error is given. And two numerical examples have been supplied to valid the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the fuzzy tracking control problem of nonlinear multi-agent systems with time-varying actuator faults and unknown control directions. The term of time-varying actuator faults is estimated via designing adaptive parameter. For the problem of the unknown control directions, the Nussbaum function is introduced to ensure the controller is unaffected on unknown direction. Moreover, based on algebraic graph theory and Lyapunov stability theory, a new distributed controller is designed to guarantee that the tracking error converges to a small neighborhood near the origin. Finally, simulation examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed consensus control of higher-order nonlinear multi-agent systems under directed graphs. We consider two cases: (i) multi-agents with unknown identical control directions and uncertain dynamics, and (ii) multi-agents with unknown nonidentical control directions and known dynamics. In the first case, a distributed adaptive control protocol is designed based on neural networks (NN) and Nussbaum functions. In the second case, a distributed nonlinear PI control protocol is proposed. It is proved via Lyapunov stability analysis that our developed protocols can ensure the asymptotical convergence of the consensus errors and global uniform boundedness of all the closed-loop signals. Theoretical results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the problem of adaptive fuzzy fault-tolerant control (FTC) is investigated for a class of nonlinear pure-feedback systems with unknown control directions and sensor failures. By utilizing the mean value theorem, the considered nonlinear pure-feedback system is transformed into a strict-feedback structure. The unavailability of state variables caused by sensor faults is dealt with by using parameter separation and regrouping technique. Based on cancelation and decoupled backstepping technique, an adaptive fuzzy fault-tolerant control method is developed. It is proved that the proposed adaptive FTC scheme can guarantee the exponential stabilization of the resulting closed-loop system. Furthermore, all the signals of the system remain semi-global uniformly ultimately bound (SGUUB). The simulation results are provided to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive prescribed performance tracking control problem for a class of nonlinear time-delay systems with actuator fault, input quantization, unknown control directions and disturbances. Neural networks (NNs) are employed to approximate the unknown nonlinear functions and the Nussbaum function is used to deal with the unknown control directions. Then, a novel adaptive prescribed performance controller is designed to reduce the effects of actuator fault, input quantization, NNs approximation errors and disturbances. Compared with the existing results, a new error transformation method is presented, and the knowledge of the quantization parameters and the control directions are unknown in the control design. Furthermore, the proposed control scheme can guarantee the semi-global boundedness of all the closed-loop signals and the prescribed time-varying tracking performance. Finally, simulation results are given to demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed leader-following consensus problem for a class of first-order and second-order Lipschitz nonlinear multi-agent systems with unknown control directions and unknown bounded external disturbances. Moreover, the Lipschitz constant is unknown for controller design and the disturbances are only required to have unknown upper bounds and not necessarily have explicit expression. Some distributed protocols are proposed by using the Nussbaum gain function combing with adaptive control technique. By virtue of algebraic graph theory, Barbalat’s lemma and Lyapunov theory and under the assumption that the interconnection topology is undirected and connected, it is proved that the multi-agent systems can achieve global asymptotic consensus even in the presence of external disturbances. Simulation examples are provided to illustrate the effectiveness of the proposed methods. [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]

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]

This paper addresses an adaptive output-feedback tracking problem of arbitrarily switched pure-feedback nonlinear systems with time-varying output constraints and unknown control directions. In this work, the tracking problem of switched non-affine nonlinear systems with output constraints is transformed into the stabilization problem of switched unconstrained affine systems. The main contribution of this paper is to present a universal formula for constructing an adaptive state-observer-based tracking controller with only two adaptive parameters by using the common Lyapunov function method. These adaptive parameters in the proposed control scheme are derived using the function approximation technique and a priori knowledge of the signs of control gain functions is not required. The theoretical analysis is presented for the Lyapunov stability and the constraint satisfaction of the resulting closed-loop system in the presence of arbitrary switchings. [ABSTRACT FROM AUTHOR]

This paper deals with the cooperative control problem of high-order multi-agent systems with unknown control directions. Adaptive backstepping technology is utilized to handle the difficulties caused by the unknown control direction in every order’s dynamics. By using a conditional inequality related to multiple terms of the Nussbaum-type function at each step, the consensus problem for systems with undirected and connected topology is solved. Then, it is shown that cooperative asymptotic regulation problem can be addressed by the same design procedure. The agents can achieve consensus and converge to the equilibrium asymptotically as well. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. [ABSTRACT FROM AUTHOR]

In this paper, a specified-time neural-adaptive control algorithm is developed to solve the consensus tracking control problem of high-order nonlinear multi-agent systems with full-state constraints, unknown control directions, and actuator faults, which is intrinsically challenging due to the existence of high-order (positive odd integers greater than one) terms. More precisely, a novel specified-time performance function (STPF) is skillfully incorporated into the time-varying high-order log-type barrier Lyapunov function (BLF) to guarantee that the tracking errors remain under time-varying constraints within specified time. To handle the mixed unknown control directions, the hybrid Nussbaum function is innovatively employed in the distributed high-order nonlinear multi-agent scenario. By combining radial basis function neural networks (RBFNNs) with the adding-one-power-integrator technique, an adaptive approximation policy is introduced to derive the neural adaptive controllers. Moreover, actuator faults are also considered in this work. The variable-separable lemma is exploited to extract the fault signals in a "linear-like" manner. Comparative simulations are provided to demonstrate the effectiveness of the designed control framework. [ABSTRACT FROM AUTHOR]

Abstract: The output feedback regulation problem is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics and unknown control direction. The system output together with the complete unmeasured state components appears in the system uncertainties. A systematic output feedback control scheme is presented with the help of a dynamic observer, whose gain comes from an off-line time-varying Riccati matrix differential equation. The proposed scheme can be applied to the analysis of the speed tracking control of a fan. The simulation results demonstrate the validity of the presented algorithm. [Copyright &y& Elsevier]

This work studies logic-based distributed switching control for nonlinear agents in power-chained form, where logic-based (switching) control arises from the online estimation of the control directions assumed to be unknown for all agents. Compared to the state-of-the-art logic-based mechanisms, the challenge of power-chained dynamics is that in general asymptotic tracking cannot be obtained, even for a single agent. To address this challenge, a new logic-based mechanism is proposed, which is orchestrated by a dynamic boundary function. The boundary function is decreasing in-between switching instants and monotonically increasing at the switching instants, depending on the jumps of an appropriately designed Lyapunov-like function. To remove chattering (i.e. two or more switching instants occurring consecutively with zero dwell time), a dynamic threshold is proposed, based on selecting the maximum values of the Lyapunov-like function before and after switching. [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]

This paper considers global finite-time stabilization with arbitrarily prescribed settling-time for nonlinear systems with unknown control directions and other serious uncertainties. In view of the challenge of the problem and the scarcity of available methods, several motivating facts are offered by elaborating examples and counterexamples. The facts disclose the potential obstructions in pursuing continuous controllers and force us to resort to powerful discontinuous feedbacks. By combining the method of adding a power integrator, homogeneous approach and desingularization technique, a state-feedback controller with design parameters is first proposed. Then a switching logic is proposed to tune the parameters online, wherein two types of switching sequences are involved to suppress serious uncertainties and to guarantee arbitrarily prescribed settling-time, respectively. Also, fixed-time stabilization is considered as a special case, aiming at the trade-off between arbitrary rapidness and high control cost. Two examples are provided to demonstrate the effectiveness of the proposed strategy. [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]

This paper studies the problem of adaptive fault tolerant control for a class of switched nonlinear systems with unknown control directions. Through a coordinate transformation, an equivalent system is constructed to eliminate the adverse effects of the unknown control coefficients. Then combining with fuzzy approximation and backstepping design principle, an adaptive fault tolerant control scheme is proposed. Further, by constructing common Lyapunov functions, it is proved that closed-loop system is bounded and the tracking error remains in a neighborhood of the origin. The given simulation example demonstrates the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper considers the global output-feedback stabilization for a class of uncertain strict-feedback nonlinear systems. Besides the unavailability of system state, the nonlinear systems allow unknown control directions and non-parametric uncertainties, which are both arguably the most severe structural uncertainties. Even so, a refined stabilization objective with prescribed convergence rate is pursued in this paper. To solve the control problem, a new output-feedback scheme is established by introducing delicate time-varying gains and utilizing a filtered transformation, where the time-varying gains are pivotal for counteracting the structural uncertainties and guaranteeing the prescribed performance. By forcing certain system signals to evolve within a pre-specified funnel, the designed output-feedback controller can guarantee the system state to converge to zero with prescribed rate. Moreover, unlike the common backstepping design for strict-feedback systems, the established scheme can effectively prevent the computation complexity for controller construction from extremely increasing with system dimension. [ABSTRACT FROM AUTHOR]

This paper addresses the leaderless consensus control problem for higher-order nonlinear multi-agent systems with completely unknown non-identical control directions. In contrast to the existing consensus results, we propose a distributed consensus algorithm using only local information available to the individual agent under a general directed graph. Nussbaum-type functions are used to deal with the unknown control directions, and novel auxiliary variables including the estimate of the consensus value are defined and employed in designing the control algorithm to avoid the appearance of multiple Nussbaum-type function terms in the stability analysis. The uncertain dynamics of each agent is approximated by the function approximation technique, and the unknown disturbance and the approximation error are suppressed by introducing an adaptive robust term. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that under the proposed distributed algorithm, the boundedness of all the closed-loop signals and asymptotic consensus can be achieved. Simulation results on pendulum plants are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]