This paper designs a predefined-time convergent continuous control algorithm to stabilize a permanent-magnet synchronous motor (PMSM) system. Three cases have been considered: disturbance-free, in presence of a deterministic disturbance satisfying a Lipschitz condition, and in presence of both a stochastic white noise and a deterministic disturbance satisfying a Lipschitz condition. The designed control law is free from the restrictions of exponential control growth and exact initial conditions knowledge. This is the first predefined-time convergent continuous control algorithm applied to stabilizing a PMSM system with both deterministic and stochastic disturbances, which enables one to a priori set the predefined convergence time even in presence of various disturbances of different nature. Numerical simulations are provided for a PMSM system to validate the obtained theoretical results in each of the three considered cases. The simulation results demonstrate that the employed values of the predefined-time convergent control inputs are applicable in practice.
This paper presents a fixed-time convergent super-twisting-like algorithm designed to provide a direct extension, without any additional terms, of the conventional super-twisting control system, whose state initial condition is unknown and the disturbance initial condition is bounded by a known constant or even completely unknown. The fixed-time convergent super-twisting-like algorithm is first designed for a scalar system and then generalized to a multivariable one. An upper estimate of its convergence (settling) time is calculated in each case. Several examples are provided to illustrate the obtained theoretical results.
This paper presents the drive-response synchronization problem for competitive neural networks in predefined time. The response system is considered in the presence of deterministic disturbances satisfying Lipschitz conditions and in the presence of both stochastic white noises and deterministic disturbances satisfying Lipschitz conditions. The effect of deterministic disturbances and stochastic noises is suppressed by designing a linear time-varying continuous control input driving the synchronization errors at the origin for an a priori predefined time, independently of initial conditions, deterministic disturbances, and stochastic noises. Finally, numerical simulations are conducted to demonstrate validity of the obtained theoretical results. The conducted comparisons with other predefined-time convergent synchronization algorithms reveal better performance of the proposed synchronization technique.
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