This research focuses on the distributed formation issue of a class of uncertain nonlinear multiagent systems. Specifically, the objective system suffers from unknown nonlinear dynamics, external disturbances and parameter uncertainties. With the aid of adaptive technique, an ideal fully distributed event-triggered formation reference signal without requiring any knowledge of global information is first designed. Then an RBF neural network (NN) is employed to approximate the nonlinear dynamics. On the basis of the work above, an adaptive NN-based robust event-triggered controller is further delicately constructed, which can guarantee that the formation goal is achieved. A distinct feature of this robust controller, compared to related works, is its ability to completely eliminate the adverse effects caused by disturbances/uncertainties without inducing chattering. Moreover, the proposed scheme can not only achieve discrete information interactions between neighboring agents like most existing articles but also enable discrete updates of the controller. Finally, the theoretical results are demonstrated via a numerical example.

ABSTRACT This paper proposes an adaptive fuzzy fault‐tolerant tracking strategy for uncertain nonlinear systems subject to full‐state constraints and potential faults in sensors and actuators. To address the problems caused by full‐state constraints, a barrier function is employed as an analytical tool to ensure that the system's state remains within a safe operational range. Meanwhile, the combined use of parameter separation and multi‐adaptive law techniques effectively minimizes the influence of faults on system performance. Additionally, a finite‐time command filter with error‐compensation signals is embedded to prevent explosion of complexity. To further alleviate the communication load, an event‐triggered fault‐tolerant controller is designed, effectively avoiding Zeno behavior. The design of this controller ensures that all signals in the system remain bounded and enables the output signal to track the reference signal within a predetermined error range. In the end, the validity of the proposed strategy is confirmed by simulation results.

This paper focuses on the adaptive fixed-time control problem for uncertain nonlinear systems subject to input and output constraints. Distinct from the existing relevant literature, asymmetric constraints are considered and the bounds of the dead-zone parameters are not required to be known. Instead of adopting the piecewise Barrier Lyapunov Function, a nonlinear transformation is introduced to address the asymmetric output constraint. Furthermore, a switching-based adaptive control strategy is developed, which not only handles the unknown control signs but also compensates for the input constraint and system uncertainties. Based on the fixed-time stability theorem, an effective regulation algorithm is designed to tune the controller parameters such that the considered system is fixed-time stable and the output constraint can be ensured. Finally, a simulation example is provided to verify the effectiveness of the proposed control scheme.

Adaptive prescribed-time tracking control with guaranteed performance for uncertain nonlinear systems with arbitrary initial errors.

Output-feedback stochastic nonlinear adaptive control against Markovian jump actuator failures.

This paper proposes an adaptive backstepping control scheme for a class of uncertain nonlinear strict-feedback systems under a full-state event-triggering mechanism. Employing event-triggered (ET) mechanisms discretises state measurements, which renders the virtual control signals non-differentiable and poses challenges to the design of parameter adaptative laws. To address this challenge, we propose a group of adaptive chain filters to generate smooth and state estimates. Moreover, the monotonic tubular boundary functions (MTBFs) are introduced to constrain the tracking error, effectively mitigating overshoot and chattering during transients. The main results show that all closed-loop signals remain uniformly bounded and the tracking error converges asymptotically to zero, while Zeno behaviour is excluded. Finally, numerical simulations verified the effectiveness of this method.

This article addresses the global asymptotic stability problem of uncertain non-strict feedforward nonlinear systems. For multiple integrators with uncertain parameters and non-strict feedforward structure nonlinear perturbed terms, a novel nested saturated control design with state-dependent saturation levels is proposed, the complex perturbation terms of vector field homogeneity at least of first-order that destroy the strict feedforward structure and the uncertain parameters are dealt with successfully. By using direct calculation of inequalities, the reasonable control parameters are designed to ensure the non-integrability and slowly-varying property of the state-dependent saturation levels, then the convergence analysis can be carried out by calculating the time derivative of the boundary surface and simple Lyapunov function, besides, we can obtain explicit parameter conditions. A nonlinear liquid level control resonant circuit system is conducted to verify the validity of the saturated control scheme.

In this paper, an adaptive output feedback control scheme is proposed for a class of parametric strict feedback systems with asymmetric full-state constraints and unknown output gain. Firstly, an adaptive state observer is constructed to estimate the unmeasured system states. To compensate for the effect of the unknown output gain on the tracking performance, a new error signal incorporating an adaptive compensation coefficient is introduced into the backstepping design. Then, by combining the universal transformed function with a coordinate transformation, all system states are kept within time-varying asymmetric bounds, and the feasibility issues of conventional constrained control methods are avoided. Based on Lyapunov stability analysis, all signals in the closed-loop system are proven to be globally uniformly ultimately bounded. Finally, simulation results based on motor models demonstrate the effectiveness of the proposed scheme.

The arbitrary-time (AT) nonovershoot adaptive tracking control issue is investigated for uncertain high-order nonlinear systems with guaranteed-performance (GP). Superior to the existing prescribed-time prescribed-performance control strategies that are vulnerable to suddenly unexpected external disturbances, a novel globally segmented AT guaranteed-performance (ATGP) function is proposed to overcome such limitations. First, the tracking errors of the system are driven to zero not only within the GP constraints but within an AT, which greatly enhances the execution efficiency. Then, a robust error-induced time-triggered disturbance-rejection mechanism is proposed to eliminate the singularity issue in conventional prescribed-performance control and enable a stabilized system to regain ATGP convergence under unexpected disturbances. Furthermore, compared with traditional adaptive algorithms that only achieve the ultimately uniform boundedness, an AT parameter adaptive law is proposed, driving the adaptive estimation error to zero. Finally, a practical example on a manipulator and a numerical example on a general nonlinear system are taken to authentically corroborate the efficacy of the proposed control algorithm.

This article focuses on stabilizing uncertain nonlinear systems with limited communication resources. Traditional approaches relying on static quantizers or fixed-gain observers face significant limitations. To solve this, an adaptive observer-based quantized output feedback control framework is proposed. A dynamic-gain state observer is developed, with observer gains adjusted by a differential equation to handle nonlinearities and quantization effects. A criterion for choosing quantization parameters is established, linking them to control gains, observer dynamics, and bounded uncertainties. This confines quantization errors and ensures global asymptotic stability of the closed-loop system. Simulations on a robotic manipulator system validate the superiority of the proposed method. The work integrates dynamic observer adaptation and quantizer design, promoting resource-efficient control in bandwidth and resource-constrained applications.

This article proposes an adjustable-error neural network (NN) approximator and incorporates it into the adaptive neural tracking controller design of uncertain nonlinear systems. Noted that the error between the unknown nonlinear function and the NN approximator cannot be adjusted under the traditional NN control framework, as it is solely determined by the selection of neurons, basis functions, and the estimation of the ideal weight vector. This inherent constraint compromises the precision of the NN approximation and the convergence accuracy of the tracking error. To improve the approximation accuracy of unknown nonlinear functions in adaptive neural control systems, an adjustable-error NN approximator is designed, in which the error between the approximator and the unknown nonlinear function can be adjusted by designed parameters. Based on the proposed NN approximator, an adaptive neural tracking controller is designed for a class of uncertain nonlinear systems, which achieves higher accuracy of the tracking error compared with traditional methods. The stability of the resulting closed-loop system is proved in the Lyapunov sense, and the convergence of the tracking error is also analyzed. The effectiveness of the proposed scheme is verified by simulation and experiment.

Fixed-time adaptive fault-tolerant control for uncertain nonlinear systems with actuator faults

To address long convergence time and state constraint challenges in high-order uncertain nonlinear systems, this paper proposes a fixed-time command filtered adaptive prescribed performance control strategy. It constructs an adaptive dynamic constraint boundary via error transformation, overcoming fixed-boundary conservatism in traditional prescribed performance control. A fixed-time command filter with error compensation eliminates the “differential explosion” problem in backstepping. Fuzzy logic approximates unknown dynamics with adaptive parameter tuning. Rigorous analysis proves all closed-loop signals are bounded within a fixed time, and tracking error meets prescribed performance. Simulations verify its superiority in convergence speed and dynamic constraints over existing methods.

This paper proposes a robust tracking control approach for a class of uncertain non-linear systems with external disturbances whose dynamics are globally linearisable and can be represented as a polytopic linear differential inclusion. The method involves solving a non-linear open-loop control problem (OCP) that gives the desired optimal tracking behaviour, followed by the design of a pole-placement constrained multi-objective H ∞ state-feedback controller from a global linearisation model of the plant to robustly stabilise the system around the optimal trajectory. Offset-free tracking is ensured by augmenting the state vector with the integral of the tracking error of the states to be controlled. The effectiveness of the proposed approach is demonstrated on a highly non-linear, cross-coupled quadruple-tank system subject to parametric uncertainties and external disturbances.

This article introduces a safe sliding mode controller designed to ensure both stability and safety in nonlinear uncertain systems. The proposed architecture combines two feedback loops: an inner sliding mode controller that ensures robust asymptotic stability, and an outer safeguarding loop that enforces safety constraints. By augmenting the system with a state variable whose dynamics are derived from Lyapunov theory, we establish a control barrier function (CBF) framework that guarantees finite-time convergence to a stabilizing sliding manifold while maintaining safety. The method features two key innovations: 1) a noninvasive safeguarding control that limits interference with the robust stability objective by employing a risk-set-triggered mechanism, and 2) closed-form expressions for the control input, which eliminate the need for solving quadratic programs (QP), significantly reducing computational burden. Theoretical analysis proves that the proposed controller ensures system stability and provides robust safety assurances under matched uncertainties. Simulation studies validate the approach across three representative scenarios. Results show the controller maintains safety without significant performance degradation, while outperforming QP-based safety-critical controllers in terms of computational efficiency.

This article presents a new higher-order sliding mode control (HOSMC) technique for coupled uncertain nonlinear systems (MIMO). This new rth order sliding mode control relies primarily on the judicious choice of a Lyapunov function that depends on the sliding surfaces and their derivatives. It extends the generality of sliding mode control to higher orders by taking into account uncertainties and perturbations in the system parameters. This method has the advantage of being resistant to parametric uncertainties, perturbations and the coupling term, which is itself considered a perturbation. The performance and applicability of this strategy are first tested through a simulation of a three-tank interconnected system and then through a comparative study with the Twisting control method. The results demonstrate the robustness of the presented approach in the face of parametric uncertainties, system coupling and disturbances, as well as its applicability and efficiency while mitigating the chatter phenomenon.

For uncertain strict-feedback nonlinear systems with self-restructuring structures and nonaffine dynamics, this article addresses the challenge of achieving exact full state zero-error stabilization within a prescribed finite time. An adaptive prescribed-time control scheme is proposed, which guarantees that all system states converge to zero within the user-specified settling time, irrespective of initial conditions. The controller is designed based on a time-varying scaling state transformation and incorporates the Nussbaum function to handle unknown self-restructuring control gains. The self-restructuring structures are treated as a time-state-dependent lump, which is effectively estimated by freezing both time and system states and then applying an adaptive estimation strategy. Numerical simulations on a piezoelectric-actuated stage and a second-order nonlinear system are conducted to demonstrate the effectiveness of the proposed scheme.

This article investigates the sliding mode control problem of uncertain nonlinear systems and its application in tracking periodic motion. Traditional sliding mode control fulfils perfect tracking at the cost of chattering, especially in the case of high-frequency scenarios. To address the limitations of this method, this article introduces the internal model of the reference signal in building the sliding manifold, which fully takes the advantages of two fundamental methodologies. Specifically, the internal model of the reference signal is involved in the closed-loop system dynamics after the sliding manifold is reached. Thence, all terms related to the reference signal in the tracking error can be eliminated and high-precision tracking can be achieved while reducing chattering phenomenon. Remarkably, the detailed expressions of the derivatives of the reference signal are unnecessarily required, which simplifies the controller design and implementation. It is rigorously proved mathematically that the closed-loop system is asymptotically stable. Finally, the proposed control algorithm is applied for solving the position tracking control problem for permanent magnet synchronous motor servo systems, and experimental results verify the effectiveness and superiority.

When disturbances or nonlinearities couple the observer and the controller, implementing active fault-tolerant control (AFTC) via the separation principle (SP) becomes challenging. This article proposes a novel AFTC framework with the goal of decoupling design for a class of uncertain nonlinear systems, thereby recovering the use of SP in AFTC design. An observer is developed for fault diagnosis and state estimation based on the system outputs, and the boundedness of the estimation errors is guaranteed. Next, an active fault-tolerant controller integrated with an adaptive mechanism is constructed for fault accommodation using the obtained fault information. To mitigate bidirectional influences between the observer and controller designs, all estimation errors and disturbances are treated as new disturbances in the AFTC system (AFTCS), and adaptive updating terms are designed to compensate for these disturbances. The stability of the AFTCS is analyzed, ensuring that all signals in the closed-loop system remain bounded and that the output tracking error converges to a neighborhood around zero. The effectiveness of the proposed approach is illustrated through a numerical simulation example.

Adaptive intrusion tolerant control for uncertain nonlinear cyber-physical systems under actuator attacks