Practical Fixed-Time Synchronization for a Class of Markov Switching Stochastic Complex Networks Based on Energy Consumption Estimation

Abstract

The practical fixed-time synchronization issue is investigated for complex networks with stochastic disturbance, Markov switching and energy consumption. First, a relaxed practical fixed-time stability theorem is established for stochastic systems, which improves the range of the convergence parameter and the accuracy of convergence time in existing results, and yields some new expectation-based residual sets. On this basis, by developing an energy consumption-based control scheme, several sufficient conditions for synchronization are derived, which do not require the system to converge exactly to the origin, but only to a bounded region. Furthermore, an upper bound on the energy consumption is obtained, and the restrictive unboundedness assumption on the parameter commonly used in previous studies is removed. Finally, simulation results on a motor system are provided to illustrate the effectiveness of the proposed theoretical method. Note to Practitioners—This study stems from the common engineering pain points in modern networked control systems, such as energy consumption and complex operating environments. In practical scenarios including wireless sensor networks, synchronization performance degrades under stochastic interference and Markov switching, hindering exact convergence to the origin. To address these challenges, a practical fixed-time synchronization method is proposed for stochastic complex networks, suitable for application scenarios such as UAV formation and multi-motor coordination. For example, under gust interference and switching, UAV formation synchronization can be achieved in a bounded region, reducing excessive attitude adjustments and energy consumption. Theoretically, some relaxed stochastic practical fixed-time convergence criteria are established, which achieve improvements in convergence parameters, convergence time accuracy and residual sets. The simulation on the motor system verifies the feasibility of the method, which offers an efficient control solution for energy-constrained networked systems with stochastic disturbances and mode switching, showing promising application prospects.