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General Lyapunov stability and Its Application to time-Varying Convex Optimization

IEEE/CAA Journal of Automatica Sinica 2024年第11期11卷 2316-2326页

作者： Zhibao Song Ping Li the College of Mathematics and Systems Science Shandong University of Science and Technology

In this article, a general Lyapunov stability theory of nonlinear systems is put forward and it contains asymptotic/finite-time/fast finite-time/fixed-time stability. Especially, a more accurate estimate of the settling-time function is exhibited for fixedtime stability, and it is still extraneous to the initial *** can be applied to obtain less conservative convergence time of the practical systems without the information of the initial conditions. As an application, the given fixed-time stability theorem is used to resolve time-varying(TV) convex optimization *** the Newton's method, two classes of new dynamical systems are constructed to guarantee that the solution of the dynamic system can track to the optimal trajectory of the unconstrained and equality constrained TV convex optimization problems in fixed time, respectively. Without the exact knowledge of the time derivative of the cost function gradient, a fixed-time dynamical non-smooth system is established to overcome the issue of robust TV convex optimization. Two examples are provided to illustrate the effectiveness of the proposed TV convex optimization algorithms. Subsequently, the fixed-time stability theory is extended to the theories of predefined-time/practical predefined-time stability whose bound of convergence time can be arbitrarily given in advance, without tuning the system parameters. Under which, TV convex optimization problem is solved. The previous two examples are used to demonstrate the validity of the predefined-time TV convex optimization algorithms.

关键词： Fixed-time stability nonlinear system predefined-time stability time-varying(TV)convex optimization

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predefined-time Command Filtering Control for High-Order Strict Feedback System

Predefined-Time Command Filtering Control for High-Order Str...

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第43届中国控制会议

作者： Guoju Zhang Xiaoli Li Faculty of Information Technology Beijing University of Technology Beijing Key Laboratory of Computational Intelligence and Intelligent System

This article investigates the predefined-time tracking problem for high-order strict feedback *** command filter can not only avoid the "computational complexity explosion" phenomenon in traditional backstepping methods,but also alleviate the chattering problem caused by signum in conventional filters.A novel predefined-time compensation system is proposed to compensate for the decrease in control accuracy caused by filtering ***-time command filtering controller is proposed by combining the backstepping mechanism and predefined-time theory,ensuring that the controlled system converges within a user-defined ***,mathematical simulation demonstrates the rationality and effectiveness of the proposed control scheme.

关键词： predefined-time stability Modified command filter Error compensation mechanism

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predefined-time Air-Ground Cooperative Control with Actuator Faults and Communication Attacks

Predefined-Time Air-Ground Cooperative Control with Actuator...

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第43届中国控制会议

作者： Yongyan Zhao Mou Chen College of Automation Engineering Nanjing University of Aeronautics and Astronautics

The cooperative tracking control strategy of heterogeneous Unmanned Aerial Vehicles(UAVs) and Unmanned Ground Vehicles(UGVs) systems under unknown actuator fault and communication signal attack is studied. Fuzzy logic system(FLSs) is used to approximate the uncertain nonlinear terms in the system. A predefined time(PT) distributed observer is designed to observe the unmeasurable state of the system when the communication is attacked. Then,a fault-tolerant controller is designed based on the theory of predetermined time Lyapunov stability to realize cooperative control unaffected by faults,ensuring the stability of the closed loop and effective tracking performance in predetermined time. Finally,the effectiveness of the control method is verified by numerical simulation.

关键词： heterogeneous UAVs-UGVs systems cooperative control communication attacks predefined-time stability

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