Prescribed-time synchronization in networks of piecewise smooth systems via a nonlinear dynamic event-triggered control strategy

Distributed optimization in predefined-time for multi-agent systems over a directed network

This paper addresses conditions and synthesis of adaptive prescribed-time controllers. The sufficient condition says that a system can achieve prescribed-time stabilization if its certain variant can be made globally bounded (on infinite time interval). From the condition one can know far more varieties of (uncertain nonlinear) systems can achieve prescribed-time control, rather than just special varieties in the related literature. The necessary condition states that a system can achieve prescribed-time stabilization attached global uniform boundedness (GUB) on finite time interval only if it, by some feedback type, can achieve GUB on infinite time interval. From the condition, or rather, its converse-negative version, one can see that what kind of systems cannot virtually achieve the prescribed-time stabilization attached GUB for some feedback type. The sufficient condition builds on two crucial transformations which change prescribed-time convergence on finite-time interval into global boundedness on infinite-time interval. With the aid of the conditions and transformations, we conduct the synthesis of adaptive prescribed-time controllers for general uncertain nonlinear systems typically with unknown control directions. By integrating time-varying factors into Lyapunov functions, an adaptive smooth controller is devised such that the system states converge to zero before an arbitrarily prescribed time, while the controller and its dynamic gains are bounded. 

Conditions and Synthesis of Adaptive Prescribed-time Controllers

Fixed-time control of a class of fractional-order chaotic systems via backstepping method

This paper investigates the fractional order chaotic systems synchronization with input delay. To reduce the utilization of communication resources and achieve system synchronization, an adaptive neural network backstepping sliding mode controller is proposed based on event-triggered scheme without Zeno behavior. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. The sliding term is introduced to enhance robustness. The Pade delay approximation method is used to handle the input delay, which can reduce the analysis complexity of fractional order chaotic systems with input delay. The unknown nonlinear functions and uncertain disturbances are approximated by the RBF neural network. An observer is used for state estimation of the fractional order system. By applying the Lyapunov stability theory, we can prove that the all closed-loop signals are bounded. Examples and simulations prove the feasibility of the proposed control method.

/pdf/event-triggered-adaptive-neural-network-backstepping-sliding-412zmdx7os.pdf

Event-Triggered Adaptive Neural Network Backstepping Sliding Mode Control for Fractional Order Chaotic Systems Synchronization With Input Delay

This paper devotes to the adaptive globally synchronization within predefined-time of two time-delayed fractional-order chaotic systems. Firstly, through fractional calculus, two novel different fractional-order systems with time-delay are proposed, whose convergence is guaranteed and phase trajectory is given. Secondly, by exploiting the non-negative Lyapunov function and inequality theorem, a novel global predefined-time stability theorem is proposed, which can ensure the settling time tunable. And the upper bound of the settling time estimation is more accurate compared with the classical results. With the help of novel predefined-time stability theorem, two active controllers are designed, namely the fixed-time synchronization controller and predefined-time synchronization controller, to achieve the fixed-time synchronization and the predefined-time synchronization of two different time-delayed fractional-order chaotic systems respectively. Finally, several numerical simulations are presented in order to show the effectiveness of the proposed methods.

/pdf/adaptive-predefined-time-synchronization-of-two-different-293dooyf84.pdf

Adaptive Predefined-Time Synchronization of Two Different Fractional-Order Chaotic Systems With Time-Delay

To solve the problem that the fractional-order system is difficult to implement on FPGA, the chaotic behavior of a single fractional-order Chen system is realized on the FPGA platform in this article by using Laplace transform and Bode-domain approximation to transform the fractional-order operator. Then the System Generator model of two different fractional-order systems is studied, and FTS/PTS (fixed/predefined time synchronization) algorithms are designed to realize the FTS/PTS of the FOTD (fractional-order time-delay) chaotic systems on FPGA. By changing the initial conditions and parameters of the FOTD chaotic systems, several groups of experiments are carried out on FPGA. The experimental results show that the FTS/PTS controllers of two different FOTD chaotic systems are feasible on FPGA.

FPGA Realization of Two Different Fractional- Order Time-Delay Chaotic System With Predefined Synchronization Time

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Adaptive Predefined-Time Synchronization of Two Different Fractional-Order Chaotic Systems With Time-Delay

FPGA Realization of Two Different Fractional- Order Time-Delay Chaotic System With Predefined Synchronization Time