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• In this work, a new general control strategy for the asymptotic tracking problem of high-order uncertain nonlinear systems is proposed so that the convergence of tracking error is not affected by the initial value and the Lyapunov function. • The proposed approach ensures that all signals in the whole closed-loop system are bounded, the adaptive compensation is performed for each step, which avoids overestimating parameters and overcomes the inherent nonlinear obstacles of the system. • The flexibility of the control design is increased by introducing the ingenious coordinate transformations and algebraic transformations. The adaptive technology and the technique of adding a power integrator are successfully verified to update and extended to an universal adaptive asymptotic tracking control, which also provides guidance for constructing general adaptive controllers and verifying asymptotic convergence. This paper investigates the asymptotic tracking control of uncertain high-order nonlinear systems with time-varying desired signals.A new universal adaptive tracking control strategy is introduced, which combines the technique of adding a power integrator, adaptive technology and a series of algebraic transformations to achieve asymptotic tracking performance successfully. Compared to the traditional tracking control strategies, the proposed control scheme guarantees that the output tracking error of the high-order nonlinear system asymptotically converges to zero and is no longer limited to a time-varying compact domain. While ensuring that all signals in the closed-loop system are bounded, the controller also has sufficient ability to compensate for the unknown quantity, virtual control coefficient and parameter uncertainty of the system. Finally, the feasibility and effectiveness of the theoretical results are verified by a simulation example. [ABSTRACT FROM AUTHOR]

• This is the first work to design a finite-time controller with a new adaptive mechanism by constructing a novel preset region. The dynamical change of the control gain is dependent on the case whether the state trajectories enter or leave a pre-designed domain or not. • The novel adaptive control strategy is presented to avoid the overestimation of the developed adaptive gain based on the adding a power integrator technique and the Lyapunov method. Meanwhile, the novel practical adaptive finite-time controller could improve the dynamic performance of systems and reduce the potential chattering influence. • In practical applications, the system states are usually finite-time stabilized to a neighborhood of the origin, rather than the origin. From this point of view, the investigation of practical finite-time stability (PFTS) for nonlinear systems is more meaningful. In this paper, the PFTS of second-order nonlinear systems has been verified under the developed adaptive finite-time controller. This paper considers the practical adaptive finite-time stabilization problem for a class of second-order systems. Based on the adding a power integrator technique and the adaptive method, a novel adaptive control strategy is presented to assure the trajectories of the closed-loop systems converge to a small neighborhood of the origin in a finite time. Under the adaptive control strategy, the dynamical change of control gain is dependent on the cases whether the state trajectories enter or leave a pre-designed domain or not. In addition, the practical finite-time stability (PFTS) of systems is testified via utilizing the Lyapunov method and adaptive mechanism. Last of all, the validity of the obtained practical adaptive finite-time algorithm is verified via simulation results. [ABSTRACT FROM AUTHOR]

• The paper projects a finite-time output feedback control framework subject to asymmetric output constraints. • The proposed control strategy can assure the finite-time stability of the whole system under output constraints. • Via an observer, only partial state knowledge is demanded to be measured in the proposed control method. This work has addressed the output-feedback finite-time stabilization issue for a type of asymmetric output-constrained planar systems. The innovation involved in the results of the work owes to the construction of a barrier Lyapunov function (BLF) to the handling of the asymmetric output constraint. By incorporated the BLF into the backstepping-like technique, a state feedback controller is first developed. An implementable observer is subsequently designed to estimate the unmeasurable system state. Lastly, an observer-based finite-time output feedback controller is explicitly proposed. Theoretically, the Lyapunov stability theory is adopted to show that the system states are finite-time stabilized under the presented control scheme. Meanwhile, the violation of a pre-established asymmetric output constraint is circumvented. To testify the derived theoretical results, the case studies of a permanent magnet linear motor system are offered. [ABSTRACT FROM AUTHOR]

This paper investigates the control design problem for the second-order sliding mode (SOSM) dynamics with mismatched uncertainty subject to the output constraint by means of the adding a power integrator technique. An unified method through the barrier Lyapunov function (BLF) technique and adding a power integrator technique has been proposed. The contributions of the paper can be summarized as follows. • This is the first time to investigate the stabilization problem for the SOSM dynamics with mismatched uncertainty subject to output constraint. • The homogeneity of the SOSM control method holds due to the modified BLF. • The proposed method can deal with the symmetric output constraint as well as the asymmetric output constraint. • The developed SOSM controller has the generic property since it is also valid in the absence of the output constraint or the mismatched uncertainty. This paper investigates a control design problem for the second-order sliding mode (SOSM) dynamics with mismatched uncertainty subject to the output constraint by means of the adding a power integrator technique. Firstly, a SOSM dynamics with mismatched uncertainty is constructed by retaining some information in the mismatched channel so as to reduce the uncertainty in the control channel, thereby relaxing the control requirement. Secondly, a barrier Lyapunov function (BLF) is designed in consideration of the output constraint to prevent the considered system from escaping from the output constraint. Moreover, the output constraint can be either symmetric or asymmetric. Thirdly, by embedding the above BLF into the adding a power integrator technique, a SOSM controller can be eventually constructed for the SOSM dynamics with the mismatched uncertainty to solve the output constraint problem. The finite-time stability analysis is proved by Lyapunov theory. The simulation results considering the symmetric constraint as well as the asymmetric constraint are provided to demonstrate the validity of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finite-time stabilization in probability for a class of high-order stochastic nonlinear systems with output constraints in which the fractional powers are only required to be positive rather than not less than one. Based on a modified version of adding a power integrator technique and a novel tan-type barrier Lyapunov function, a systematic design approach is developed and a state-feedback controller is constructed. Rigorous mathematical proof shows that the origin of the system is finite-time stable in probability and the constraint requirement on the output is not violated. The effectiveness of the proposed finite-time control scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

• A modified design process of finite-time control (FTC) is achieved by utilizing prescribed performance control (PPC) and pre-assigned finitetime function (PFTF). • The states can converge to a predefined region within the pre-assigned finite-time. • The proposed method is more flexible and simpler since the convergence time is not related with the design parameters and initial values. • Nussubaum gain is employed to tackle the FTC problem for parameter systems with unknown signs. This paper mainly studies an adaptive finite-time control problem for a kind of uncertain strict feedback systems with unknown control gains. First, the original strict-feedback system is transformed into a pure-feedback system. And then, we propose a modified adaptive finite-time design idea on the basis of the property of pre-assigned finite-time function (PFTF) and Nussbaum gain. The designed controller can make sure that all states converge to an arbitrarily region in finite-time and signals in the closed-loop system are finite-time bounded. Moreover, the presented controller is smooth and the settling time does not rely on the initial values and design parameters. Finally, the simulation study is made to illustrate the innovativeness for the proposed scheme. [ABSTRACT FROM AUTHOR]

• This is the first work to investigate the design of SOSM controller with mismatched uncertainty and time-varying output constraint, and to further verify the stability of the uncertain system. • A new time-varying BLF has been constructed to handle the time-varying output constraint. By modifying the API technique and using the time-varying BLF, a SOSM controller for the SOSM dynamics under the time-varying output constraint is systematically projected such that the finite-time stability of closed-loop system can be guaranteed. Meanwhile, the time-varying output condition is never violated during operation. • In accordance with the Lyapunov approach, the finite-time stability of the closed-loop sliding mode dynamics is confirmed. Notably, the proposed method can handle nonlinear systems with the time-varying output constraint, static symmetrical output constraint, and can also be used to deal with nonlinear systems without output constraint. Therefore, the SOSM controller which is developed in this paper is more general. The current work develops a new approach to handle the second-order sliding mode (SOSM) controller design with mismatched term and time-varying output constraint. A novel time-varying Barrier Lyapunov Function (BLF) is firstly constructed to deal with the time-varying output constraint. A new SOSM dynamics subject to mismatched terms is established for the purpose of uncertainty reduction in control input channels. Meanwhile, by incorporating the time-varying BLF into the adding a power integrator (API) technique, a new finite-time SOSM controller, which can ensure that the system output variable will not violate the boundary of the constrained region, is explicitly constructed. Finally, a simulation example is given to illustrate the feasibility of the proposed SOSM algorithm. [ABSTRACT FROM AUTHOR]

• A new concept, called fixed-time funnel boundary (FFB), is defined for the first time in this paper. • This work is first to introduce a new control mechanism for TCP/AWM system to ensures that the tracking error satisfies certain transient performances. • The proposed control scheme has the better performance and faster convergent rate than results without FFB or ACT. In this paper, TCP/AWM network congestion control problem is investigated. First, a new funnel boundary (FB) is proposed. And then, in the framework of backstepping, a new control technique is given by virtue of free-will arbitrary time stability and the novel FB, which guarantees that the tracking error converges to the origin within an arbitrary setting time. Besides, the transient performances of the error can also be achieved. Finally, simulation results verify the efficacy and superiority of the presented theoretical findings. [ABSTRACT FROM AUTHOR]

This paper has developed a finite-time controller design for a category of multiple integrator nonlinear systems subject to input saturation. First of all, an unsaturated finite-time controller is constructed without considering input saturation. On this basis, by combining the saturation technique, a saturated controller is presented to finite-time stabilize the closed-loop system and to guarantee no transgression of pre-set input saturation. In simulation studies, an academic example is given to confirm the validity of the proposed approach. Moreover, the presented theoretical results are successfully applied to the saturated finite-time control of an agricultural vehicle straight-line tracking system (AVSTS). [ABSTRACT FROM AUTHOR]