Delay Systems Support Vector Machine Sliding Mode Control Study

In the actual system, the time-delay is a kind of common phenomena, and itsexistence will make the control quality poor, and even causes the systeminstablility, so the analysis and comprehensive of the systems with time-delayhas been a hot issue in the control field. As the younger content of StatisticalLearning Theory(SLT), Support Vector Machine(SVM) has strong learningability and better generalization performance. The combination of SVM andSliding Mode Control(SMC) can not only improve the self-adaption ability ofthe conventional sliding mode variable structure control, but also providemethods for the complex control systems and comprehensive problems. In thispaper, the sliding mode controllers based on support vector machine(SVM) areproposed for the systems with time-delay.First, for a class of the uncertain systems with state-delay, the sliding modesurface is designed by using the linear matrix inequality (LMI), and the slidingmode controller is proposed based on SVM, which can learn the upper bound ofthe uncertainty. This control scheme overcomes the limit that the upper bound ofthe uncertainty is known first in sliding mode control, ensures the asymptoticstability, effectively weakens the chattering and improves the robustness of thesystem.And then, for the uncertain system with the control-delay, a new integraltype sliding switch surface is put forward,which can change as the systemparameters of bounded perturbation. Based on SVM,the sliding mode controlleris got, where SVM with good self-learning and adaptive ability is introduced tocompensate for the uncertainty of the system. The control scheme has strongrobustness for the outside interference and nonlinear uncertainty, effectivelyinhibits the chattering and improves the control performance of the system.Finally, after analysising the sliding mode control for the fractional ordersystem, the sliding mode controllers based on SVM are presented respectivelyfor the fractional order system with state-delay and control-delay. Due to the small sample and the strong generalization ability of SVM, the model of thecontrol law parameter is established based on SVM,which can overcome thechattering problem in the sliding mode variable control. This method can notonly restrain the chattering, but also improve the system ability of theanti-interference.