This article addresses the problem of prescribed performance tracking control for uncertain differential-drive mobile robots equipped with current sensorless electric motors. An improved line-of-sight distance control method with a desired heading angle switching strategy is proposed, which eliminates the singularity problem encountered in previous works when the line-of-sight distance approaches zero. In addition, an open issue of mobile robots control under unavailable motor current (or torque) and completely unknown motor parameters is tackled by combining differential homeomorphism transformations with a low-complexity prescribed performance control approach. Furthermore, the limitations imposed by initial high-order state errors in low-complexity control methods are overcome by introducing a time and space dependent amplifier. The proposed method guarantees the convergence of the position tracking error to the desired precision within the prescribed time, with rigorous proof provided. The effectiveness of the method is demonstrated through simulations and experiment comparisons.

This article investigates the optimal tracking control problem for high-order uncertain nonlinear systems by developing a simplified reinforcement learning (RL) framework with minimal neural networks (NNs). In contrast to conventional RL-based schemes that rely on recursive backstepping and require $3n$ NNs (where $n$ is the system order), the proposed method leverages high-order fully actuated (HOFA) system theory to reformulate the dynamics into a compact normal form. This enables a unified, nonrecursive controller design that requires only three NNs regardless of the system order, thereby significantly reducing computational complexity and facilitating practical implementation. Furthermore, this work overcomes a critical theoretical deficiency in existing simplified RL strategies, where the vanishing minimum eigenvalue of the NN basis function correlation matrix often leads to invalid Lyapunov stability analysis. A novel critic-actor weight update law is designed to bypass this problematic matrix, rigorously guaranteeing the semiglobal uniform ultimate boundedness of the closed-loop system without requiring persistent excitation (PE) conditions. Simulation results on a representative example demonstrate the effectiveness and computational efficiency of the proposed approach compared with existing methods.

The issue of fixed-time tracking control of nonlinear systems subject to time-varying uncertain parameters is investigated in this article. In contrast to previous adaptive approach-based fixed-time control results which focus on driving the tracking error to a bounded region, it is technically challenging yet highly desired to achieve zero-error trajectory tracking. The primary difficulty lies in how to construct and analyze adaptive estimation schemes to completely compensate for uncertain parameters within the fixed-time convergence setting. Furthermore, the presence of time-varying uncertainties renders the systems fundamentally different from those in existing works. To tackle this challenge, a new fixed-time stability lemma utilizing an exponential decay function is proposed. Then, we develop an adaptive fixed-time controller design framework, it is demonstrated that the tracking error ultimately converges to zero after converging to a small neighborhood around zero within a fixed time, with all the closed-loop signals remaining bounded. Besides, the singularity problem in fixed-time control is circumvented. Finally, simulation results substantiate the effectiveness of the proposed strategy.

This article investigates the problem of global full-state prescribed performance control (GFSPPC) for uncertain nonlinear systems with dead-zone and event-triggered input. By incorporating a unique time-varying funnel function and embedding it into the state transformation function of each step, we present a coordinate transformation. Then, based on the low-complexity methodology, a novel prescribed performance control (PPC) algorithm is developed, which guarantees predefined transient and steady-state performance for both the tracking error and system states in a global sense. Moreover, with our proposed 1-bit-triggered mechanism, only one bit signal (either 0 or 1) is transmitted on the controller-actuator channel from beginning to end, which reduces the bit of data transmission while saving communication resources. The designed control scheme is inherently robust against model uncertainties, external disturbances and dead-zone nonlinearity without the use of the adaptive technique, filters and approximators. Besides, the strictly increasing functions outside the dead-band in existing works are extended to a non-differentiable and locally decreasing form in the considered dead-zone model. Finally, the proposed approach’s effectiveness is confirmed through simulations of the resistance-inductance-capacitance (RLC) circuit system and the robotic manipulator system, respectively.

This article concentrates on the event-triggered control problem for interconnected nonlinear systems under hybrid stochastic faults. Unlike existing results, our work considers both, sensor stochastic faults and process stochastic faults, which are referred to as hybrid stochastic faults. First, under hybrid stochastic faults, an observer is constructed to estimate all states, which converts the process stochastic faults into a processable form. Second, an event-triggered mechanism is proposed for the estimated states to reduce their update frequency. To deal with the problem that the triggered estimated states are nondifferentiable, a continuous controller with continuous estimated states is developed, and the event-triggered controller with triggered estimated states is established accordingly. By the use of Lyapunov stability theory, it can be rigorously shown that all signals of the closed-loop systems are bounded in probability. The proposed approach is illustrated with the simulation of two interconnected pendulums.

This article focuses on the problem of adaptive event-triggered output feedback control for a class of uncertain nonlinear systems under the output constraint. Different from the existing works, the time-varying parameters and the global output constraint are taken into account. First, by means of multifilters, the unmeasurable state variables are reconstructed, under which the unknown time-varying parameters and sensor sensitivity are transformed into the estimation problem of unknown parameters. Second, based on a barrier function, a novel constraint algorithm is established to make the output enter into asymmetric time-varying constraint boundaries, which is independent of the initial value of the output. To avoid continuous sampling of the controller, an event-triggered mechanism is proposed without the Zeno phenomenon. By means of the Lyapunov stability theory, it is strictly proved that the output enters into the pregiven asymmetric constraint boundaries, and never exceeds. Finally, the validity of our proposed control algorithm is illustrated by a numerical simulation.

This article studies the event-triggered output feedback consensus problem for a class of high-order uncertain nonlinear multiagent systems with totally unknown non-identical control directions. Firstly, the reduced-order filters are constructed by utilizing the dynamic gain technique to compensate the system uncertainties and unmeasurable states of the followers. Based on the filter states and output information, the asymptotic output consensus result is guaranteed with the developed distributed adaptive output feedback control protocol, while the inherent issue “complexity explosion” in backstepping design is avoided. Then, to solve the interaction of multiple Nussbaum functions in a single inequality, the Nussbaum functions with different frequencies are adopted, with which the unknown directions of multiagent system are no longer limited in identical. In addition, we propose a dynamic triggering strategy with time-varying threshold parameters to reduce the updates of controller without Zeno phenomenon. Finally, simulation results are provided to illustrate the effectiveness of theoretical algorithm.

This paper focuses on the adaptive output feedback control problem for nonlinear stochastic systems with unknown measurement sensitivity based on dynamic event-triggered mechanism (ETM). Different from the existing works, a novel adaptive output feedback control algorithm is proposed for unknown measurement sensitivity (its sign and bounds are unknown) by means of Nussbaum-type function. First, a reduce-order dynamic gain K-filter is proposed to reconstruct the unmeasurable state variable. Second, a tangent-type barrier Lyapunov function with a predefined-time performance function is established to constrain system output into the given region in a predefined time. Third, a dynamic ETM is put forward to reduce trigger times, and then the controller is designed accordingly. Based on the Lyapunov stability theory, it is proved that system state variables converge to zero in probability and other signals of the closed-loop system are bounded in probability. Finally, the validity of the proposed algorithm is demonstrated by the numerical simulation on a single-link manipulator.

This article studies the global prescribed-time stabilization problem for a class of time-delay nonlinear systems with uncertain parameters. First, we design two time-varying gains with special properties, in which one is introduced into virtual controllers to achieve prescribed-time convergence and the other one is used to construct the Lyapunov-Krasovskii (L-K) functional and Lyapunov function to handle the nonlinear time-delay term and unknown parameters, respectively. Then, by utilizing double time-varying gains and the scaling-free backstepping design approach, a dynamic state feedback controller is constructed, which guarantees that all state variables reach zero within a prescribed time, and the prescribed time can be specified in advance. Then, based on new functionals and regular differential inequality, we figure out the explicit expression for the upper bound of all variables, which plays an important role in proving the boundedness of all system variables. Final, a simulation example is given to demonstrate the effectiveness of the proposed method.

This article concerns with the adaptive fixed-time control problem for classes of nonlinear cascade systems with parametric uncertainty. The majority of existing finite/fixed-time control strategies for uncertain nonlinear systems can only make system states approach to the neighborhood of origin over a finite/fixed time. Different from these results, we put forward a time-varying gain-based control algorithm to ensure that all system states return to the origin in a fixed time. With the help of the backstepping method, a time-varying adaptive controller is designed for a high-order nonlinear systems subject to uncertain parameters. Through constructing appropriate dynamic gain-based Lyapunov functions and utilizing our proposed stability criterion, it is proved that all states of the uncertain system can be adjusted to the origin in a fixed-time interval. Moreover, the settling time is not depend on the initial conditions of system and can be preset according to the actual requirements. Finally, the simulation results are provided to illustrate the effectiveness of the developed dynamic time-varying feedback control algorithm.

In this paper, global event-triggered adaptive prescribed tracking output feedback control is investigated for a class of nonlinear uncertain systems with unknown control direction. Different from the existing works, the design of the tracking error-dependent normalized function and prescribed boundary is based on our uniformly defined blow-up function rather than a specific function, and the asymmetric constraint requirements on tracking error can be achieved by appropriately selecting the blow-up function. By utilizing the Kalman filter ($K$-filter) and dynamic gain technique, a new reduce-order observer is proposed, which can make the estimated error exponentially converge to zero. In addition, by introducing a dynamic signal into the trigger condition, a novel event-triggered mechanism is proposed, which can extend the trigger time interval and completely counteract the event-triggered errors in terms of asymptotic stability by sacrificing part of the system transient performance. Furthermore, an adaptive controller is designed based on the backstepping method, which ensures the boundedness of the state of the closed-loop system, while regulating the tracking error meets the global prescribed performance requirements and approaches to zero asymptotically. Two examples are given to illustrate the effectiveness of the proposed control scheme.

This article is concerned with the fixed-time prescribed tracking control problem for the uncertain stochastic nonlinear systems subject to input quantization and unknown measurement sensitivity. Different from existing results, the sensitivity on the sensor for measuring the system state is considered as an unknown parameter instead of the known one. Due to unknown measurement sensitivity on the sensor, the real system state cannot be obtained by measurement; hence, we put forward a new feedback control algorithm by the use of the unreal measured value of the system state. Moreover, the fixed-time prescribed performance on the output tracking error is investigated by developing a novel performance function. By means of the backstepping method, an adaptive quantized controller is designed for the system. Based on the Lyapunov stability theory, it is proved that the controller can render the output tracking error that satisfies the fixed-time prescribed performance and all signals of the resulting closed-loop system are bounded in probability. Finally, simulation results are provided to illustrate the effectiveness of the proposed control algorithm.

This article focuses on the problem of adaptive finite-time tracking control for nonlinear stochastic systems under asymmetric constraints based on dynamic event-triggering control. Different from the existing works, a novel adaptive tracking control algorithm is proposed with asymmetric time-varying constraints and dynamic event-triggering mechanism. First, to constrain the state variable within given time-varying boundaries, a novel predefined-time performance function is constructed. Second, a novel barrier function related to state variable is constructed, by means of which the state variable is directly constrained within the asymmetric time-varying boundaries without the virtual controller. In addition, by establishing a novel dynamic function, we propose a dynamic event-triggering mechanism, and then design controller accordingly, which can reduce computation burdens and save the network resources. By the aid of the Lyapunov stability theory, it is proved that the system tracking error converges to an adjustable bounded set in probability in a finite time and all state variables are successfully constrained into the asymmetric time-varying boundaries. Finally, the effectiveness of the proposed control algorithm is verified by a simulation example.