A novel event-triggered adaptive finite-time control strategy is developed for a class of uncertain fractional-order stochastic nonlinear systems (SNSs). The fractional orders of the systems can be represented by the ratio of arbitrary two positive odd integers, so that the target systems could contain both highorder SNSs and low-order SNSs. A new more general and flexible asymmetric barrier Lyapunov function (BLF) is established to fulfill the requirement of asymmetric dynamic output constraints. By adoptingadding a power integraltechnique and backstepping method, a finite-time controller with the adaptive laws is codesigned. The ubiquitous system uncertainty is directly estimated by adaptive method, and no extra approximation errors are introduced. An event-triggered mechanism is presented to reduce the update frequency of the controller, overcoming the difficulties caused by the system’s stochastic characteristics and fractional power of the control input. It is strictly proved that the trivial solution of the system is finite-time attractive and stable in probability, meanwhile the system output is constrained within the prescribed asymmetric time-varying boundaries. Simulation experiments demonstrated the effectiveness of the main result.

This paper studies the global finite-time control problem for uncertain high-order nonlinear systems (HNSs) with event-triggered input and deferred output constraint. The bounds of control coefficients are not required to be known and odd rational powers are allowed in the system. In this case, unlike the existing adaptive estimation control results can only achieve bounded or asymptotic stability, the proposed control strategy focuses on ensuring finite-time stability (FTS). Specially, two sets of distinct power-type parameters are introduced in control process to reconstruct the adaptive law and integral-type candidate Lyapunov functions respectively, such that the residual terms containing uncertainties can be dominated by the stabilizing terms. To reduce communication burden, an event-triggered mechanism is developed with a state-dependent function instead of a constant, enabling a timely update for controller as all state variables reach zero. Based on Lyapunov analysis and FTS theory, it is proven that the deferred output constraint can be guaranteed and all state variables reach the origin in a finite time under the designed controller. Two simulation examples are illustrated to verify the validity of theoretical results.

This article proposes a finite-time prescribed performance control (FTPPC) method for interconnected nonlinear systems with input saturation. By adding nonnegative auxiliary signals to the setting time of finite-time prescribed performance functions (FTPPFs), we present saturation-tolerant FTPPFs, which are easy to observe the convergence time. Compared with traditional FTPPFs, saturation-tolerant FTPPFs are able to expand from or restore to the expect constraint boundaries based on the input saturation error as well as whether the system enters the collision avoidance regions. Thus, the potential conflicts between input saturation and FTPPFs are resolved. Combined with saturation-tolerant FTPPFs, a low-complexity control algorithm is proposed, which omits the need for a function to estimate the unknown terms and reduces the computation. With the designed control scheme, the boundedness of all closed-loop signals is strictly proved when the feasibility condition is satisfied. Ultimately, simulations are presented to show the capability of the designed controller.

The problem of command-filter-based adaptive fixed-time tracking control is investigated for nonlinear systems with time-varying uncertain parameters and disturbances in this article. Existing fixed-time control strategies via an adaptive approach are primarily bounded-error, trajectory tracking-oriented. Different from previous results, we propose a new fixed-time stability lemma utilizing an exponential decay function. Then, by leveraging the proposed lemma and command filtered backstepping technique, a novel adaptive fixed-time control scheme is constructed, which can reduce the computational complexity and completely counteract uncertain parameters. We demonstrate that the tracking error enters a neighborhood near zero within a fixed-time and ultimately converges to zero. Furthermore, through the incorporation of a piecewise function into both the filter error compensation system and virtual control laws, the second-order derivability of virtual control laws is guaranteed, thereby ensuring the validity of the command filter. Finally, the proposed strategy's effectiveness is confirmed through simulation results.

This paper focuses on the leader-following consensus control problem for nonlinear multiagent systems (MASs) under output event-triggered communication. A novel distributed discontinuous backstepping control strategy is presented, which utilizes information exclusively from intermittent output instants. First, a distributed adaptive event-triggered mechanism (ETM), along with a continuous-discrete time compensator and observer are designed jointly to compensate for consensus errors and reconstruct the system state, where all parameters designed are flexibly chosen. The triggering sampling instants are asynchronous and aperiodic, eliminating the necessity for continuous neighbor information monitoring. Second, we introduce a dynamic variable into the coordinate transformation to overcome the challenge of intermittent output in backstepping design, which is the key to address input errors caused by triggering mechanisms. Compared with the widely used backstepping method using the first-order filter to address intermittent signals, the proposed scheme does not require additional triggering design for the filter and achieves a full-state consensus in the global sense. Theoretical analysis shows that the system is asymptotically stable, all consensus errors converge to zero, and Zeno behavior is excluded. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical result.

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 paper focuses on output feedback prescribed-time control problem of nonlinear system subject to bounded disturbance. Firstly, in order to observe and deal with unmeasurable states and disturbances, the prescribed-time observer and filter are constructed. The prescribed-time state stabilization problem of the original system is translated into how to design the controller to make the state of filter stable in a predetermined time. Then, to overcome the effect of unknown disturbance during the design process, a novel switched prescribed-time high-order sliding mode (HOSM) is constructed. The output feedback prescribed-time control scheme is presented in conjunction with the proposed prescribed-time HOSM to guarantee the prescribed-time stability of system. Finally, the effectiveness of the main result is demonstrated through two numerical simulations, a third order nonlinear system and the single-link robot system.

This article investigates fixed-time prescribed tracking control based on a command filter for a class of nonlinear systems with unknown control coefficients. A novel switching control mechanism is proposed to address the challenge of unknown control coefficients and introduce a dual-parameter switching strategy with online parameter adjustment based on the designed conditions. To address the limitation in existing research, where prescribed performance functions depend on the initial conditions of systems, this work designs a new class of prescribed performance functions that eliminates this dependency. A command-filter-based backstepping approach effectively avoids the computational complexity of high-order derivatives in traditional backstepping methods. In addition, the issue of the nondifferentiability of the virtual controller at switching moments in existing switching control methods has been resolved. Ultimately, the boundedness of all signals in the closed-loop system is ensured. Moreover, a simulation example of a second-order system verifies the effectiveness of the algorithm in this article.

The global asymptotic stabilization control algorithm is proposed for interconnected nonlinear systems utilizing intermittent output feedback. A dynamic double side event-triggered mechanism (ETM) is designed to make the available output intermittent, reducing the frequency of signal updates. In this case, we relax some restrictive conditions from related studies. The considered system features unknown time-varying parameters, mismatched uncertainties, and uncertain functions that satisfy nonlinear growth conditions. These complexities render the standard backstepping recursive design scheme inapplicable, as the derivative of the virtual controller does not exist. To address the intermittent output feedback problem, we introduce a novel dynamic backstepping control method. First, we establish a dynamic gain observer using the triggered output signals to reconstruct the unmeasurable state variables. Next, the concept of dynamic gain is introduced through a coordinate transformation, with its derivative employed to offset discontinuous terms, which solves the challenges in recursive backstepping design caused by intermittent output and regulates that the state variable converges asymptotically to the origin in the global sense. Final, the simulation example is proposed to show the validity of the developed algorithm.

The issue of event-based asymmetric predetermined performance control (PPC) has been addressed for$p$-normal nonlinear systems with time-varying unknown control coefficients. A set of Nussbaum functions is introduced, capable of addressing both single and multiple unknown control coefficients. To achieve asymmetric PPC, a switching constraint scheme is proposed. Subsequently, an adaptive fuzzy controller based on dynamic events is developed. Improved techniques for approximating the unknowns of a system using fuzzy logic systems, while dynamic events are employed to reduce the frequency of controller updates. Using Lyapunov stability theory, it is proven that all signals in the closed-loop system remain bounded, and the tracking error is confined within the specified asymmetric boundaries. Eventually, the effectiveness of the present scheme is demonstrated by the simulation of three examples.

In this article, the adaptive backstepping control problem is investigated for a class of mismatched uncertain nonlinear systems with input and state quantization. All available states are generated by the static bounded quantizers, which can cause the failure of the recursive backstepping design. Previous results are based on linear-like virtual controllers to ensure that the partial derivatives of virtual controllers are constants, therefore, the systems are required to be an integral form or to meet matched conditions. Based on a dynamic gain approach, this article presents a new compensation mechanism to solve the difficulty of recursive backstepping design caused by discontinuous states, the control problem is transformed into a design problem of the dynamic variable. First, the dynamic variable is introduced based on a coordinate transformation, its derivative is used to compensate for discontinuous mismatched nonlinear terms. Then, with the help of the Lyapunov stability theorem, it is strictly proved that all signals of the closed-loop system are globally uniformly bounded. Finally, numerical simulations are provided to validate the effectiveness of the developed algorithm.

In order to improve the efficiency of data transmission and save communication resources, the problems of double event-triggered control are investigated for a class of high-order nonlinear random systems. Under more general system conditions, in addition to overcoming the difficulty of recursive design caused by signal discontinuity, the effects of high-order nonlinearity and random disturbances also need to be addressed. Based on the adding power integral technique, a practical finite-time stable result is established for the nonlinear random systems under a double event-triggered mechanism (ETM) and proved that there is no Zeno phenomenon. Compared with the existing results, the update frequency of the signals is effectively reduced, and the upper bound of the stable error is independent of trigger parameters, thus can be made sufficiently small by tuning design parameters. Furthermore, the result is expanded to finite-time stabilization, state variables converge to the origin in a finite time. Finally, numerical simulations verify the effectiveness of the proposed algorithm.

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 considers the tracking control problem for an uncertain feedback nonlinear system with asymmetric time-varying full-state constraints and unknown control directions. We propose a new low-computation full-state constrained robust control algorithm, that removes the feasibility conditions of virtual controllers and solves the unknown control direction problem without using the Nussbaum gain technique. By introducing nonlinear transformation functions, the original constrained systems are converted into new unconstrained tracking error systems, and the new systems eliminate the limitation of the initial conditions. Then, to seek the correct control directions, an orientation function with error conversion is constructed, which avoids introducing Nussbaum-type functions and logic switching rules. The proposed method possesses inherent robustness against model uncertainties and disturbances, and guarantees that the full-state constraints and the tracking error of systems enter into a prescribed set in a fixed time. Finally, simulation examples are presented to demonstrate the superiority and effectiveness of the developed control algorithm.