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This article studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibitpredefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-timestable, and an upper bound of the settling-time function can be arbitrarily chosen a priori through a suitable selection of the system parameters. We show that the studied Lyapunov-like conditions allow usto demonstrate the equivalence between previous Lyapunov theorems for predefined-time stability forautonomous systems. Moreover, the obtained Lyapunov-like theorem is extended for analyzing theproperty of predefined-time ultimate boundedness with predefined bound, which is useful when ana-lyzing uncertain dynamical systems. Therefore, the proposed results constitute a general framework foranalyzing the predefined-time stability, and they also unify a broad class of systems that present thepredefined-time stability property. On the other hand, the proposed framework is used to designrobust controllers for affine control systems, which induce predefined-time stability (predefined-timeultimate boundedness of the solutions) w.r.t. to some desired manifold. A simulation example ispresented to show the behavior of a developed controller, especially regarding the settling timeestimation.
This article studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibitpredefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-timestable, and an upper bound of the settling-time function can be arbitrarily chosen a priori through a suitable selection of the system parameters. We show that the studied Lyapunov-like conditions allow usto demonstrate the equivalence between previous Lyapunov theorems for predefined-time stability forautonomous systems. Moreover, the obtained Lyapunov-like theorem is extended for analyzing theproperty of predefined-time ultimate boundedness with predefined bound, which is useful when ana-lyzing uncertain dynamical systems. Therefore, the proposed results constitute a general framework foranalyzing the predefined-time stability, and they also unify a broad class of systems that present thepredefined-time stability property. On the other hand, the proposed framework is used to designrobust controllers for affine control systems, which induce predefined-time stability (predefined-timeultimate boundedness of the solutions) w.r.t. to some desired manifold. A simulation example ispresented to show the behavior of a developed controller, especially regarding the settling timeestimation.
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In this paper, we study the practical tracking control problem for a class of pure-feedback systemssubject to full states asymmetric and time-varying constraints, non-vanishing uncertainties andexternal disturbances. A new robust control scheme is proposed to deal with state constraints.Unlike some existing results for practical tracking control, the proposed method does not involve anyswitching and is able to deal with asymmetric and time varying state constraints without the need forfeasibility conditions. Furthermore, with proper choice of scaling function, three different trackingcontrol results (i.e., ultimately uniformly bounded tracking, practical tracking and asymptotic tracking)can be achieved. Simulation verification further confirms the effectiveness of the proposed approach.
In this paper, we study the practical tracking control problem for a class of pure-feedback systemssubject to full states asymmetric and time-varying constraints, non-vanishing uncertainties andexternal disturbances. A new robust control scheme is proposed to deal with state constraints.Unlike some existing results for practical tracking control, the proposed method does not involve anyswitching and is able to deal with asymmetric and time varying state constraints without the need forfeasibility conditions. Furthermore, with proper choice of scaling function, three different trackingcontrol results (i.e., ultimately uniformly bounded tracking, practical tracking and asymptotic tracking)can be achieved. Simulation verification further confirms the effectiveness of the proposed approach.
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This paper discusses the adaptive control problem for a class of nonlinear systems with polynomialgrowing conditions. By introducing a Lyapunov function which carries the quadratic terms and higher-order terms of the transformed variables and constructing an appropriate dynamic gain, a new controlstrategy is presented to design an adaptive controller using only one parameter estimation. Comparedwith the existing results, the presented method avoids the over-parameterization and significantlysimplifies the control design. A modified version of the method which adopts no parameter estimationis also provided. It shows that all the signals of the closed-loop system are bounded and the solution ofthe original system converges to zero. A simulation example is given to show the validness of themethod.
This paper discusses the adaptive control problem for a class of nonlinear systems with polynomialgrowing conditions. By introducing a Lyapunov function which carries the quadratic terms and higher-order terms of the transformed variables and constructing an appropriate dynamic gain, a new controlstrategy is presented to design an adaptive controller using only one parameter estimation. Comparedwith the existing results, the presented method avoids the over-parameterization and significantlysimplifies the control design. A modified version of the method which adopts no parameter estimationis also provided. It shows that all the signals of the closed-loop system are bounded and the solution ofthe original system converges to zero. A simulation example is given to show the validness of themethod.
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This paper studies the stabilization problem for switched systems in the presence of denial-of-service(DoS) attack using the event-triggered scheme. Unlike the traditional switching signal design withDoS attack, some challenges arise in the joint influence on the constraints of DoS duration/frequency,and the asynchronous behavior caused by the controller and the subsystem mode. To this end, a novelmultiple Lyapunov function involving the joint effects of DoS attack and controller mode isconstructed. This allows that there are no events between two consecutive switching instants. Byincorporating the dwell-time switching signal with the event-triggered scheme, the considered systemcan be globally exponentially stabilizable when the frequency and duration of DoS attack meet certainrequirements. It also shows that apart from the co-design associated the event-triggered parameterswith controller gain, the maximum allowable sampling period can be offline calculated. Moreover, theZeno behavior is eliminated by
calculating a lower bound of the event-triggered interval, over which the DoS attack is inactive.Finally, simulations are carried out to verify the effectiveness of the theoretical results.
This paper studies the stabilization problem for switched systems in the presence of denial-of-service(DoS) attack using the event-triggered scheme. Unlike the traditional switching signal design withDoS attack, some challenges arise in the joint influence on the constraints of DoS duration/frequency,and the asynchronous behavior caused by the controller and the subsystem mode. To this end, a novelmultiple Lyapunov function involving the joint effects of DoS attack and controller mode isconstructed. This allows that there are no events between two consecutive switching instants. Byincorporating the dwell-time switching signal with the event-triggered scheme, the considered systemcan be globally exponentially stabilizable when the frequency and duration of DoS attack meet certainrequirements. It also shows that apart from the co-design associated the event-triggered parameterswith controller gain, the maximum allowable sampling period can be offline calculated. Moreover, theZeno behavior is eliminated by
calculating a lower bound of the event-triggered interval, over which the DoS attack is inactive.Finally, simulations are carried out to verify the effectiveness of the theoretical results.
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In this paper, we investigate the adaptive control problem for robot manipulators with both theuncertain kinematics and dynamics. We propose two adaptive control schemes to realize the objectiveof task-space trajectory tracking irrespective of the uncertain kinematics and dynamics. The proposedcontrollers have the desirable separation property, and we also show that the first adaptive controllerwith appropriate modifications can yield improved performance, without the expense of conservativegain choice. The performance of the proposed controllers is shown by numerical simulations.
In this paper, we investigate the adaptive control problem for robot manipulators with both theuncertain kinematics and dynamics. We propose two adaptive control schemes to realize the objectiveof task-space trajectory tracking irrespective of the uncertain kinematics and dynamics. The proposedcontrollers have the desirable separation property, and we also show that the first adaptive controllerwith appropriate modifications can yield improved performance, without the expense of conservativegain choice. The performance of the proposed controllers is shown by numerical simulations.
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