Adaptive Prescribed-Time Control for a Class of Uncertain Nonlinear Systems

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Abstract
This paper focuses on the problem of prescribedtime control for a class of uncertain nonlinear systems. First, a prescribed-time stability theorem is proposed by following the adaptive technology for the first time. Based on this theorem, a new state feedback control strategy is put forward by using the backstepping method for high-order nonlinear systems with unknown parameters to ensure the prescribed-time convergence. Moreover, the prescribed-time controller is obtained in the form of continuous time-varying feedback, which can render all system states converge to zero within the prescribed-time. It should be noted that the prescribed-time is independent of system initial conditions, which means that the prescribed-time can be set arbitrarily within the physical limitations. Finally, two simulation examples are provided to illustrate the effectiveness of our proposed algorithm.
Funding Information
  • National Key R&D Program of China (2018YFB1308300)
  • National Natural Science Foundation of China (U20A20187, 618255304)
  • Science Fund for Creative Research Groups of Hebei Province (F2020203013)
  • Science and Technology Development Grant of Hebei Province (20311803D, 19011824Z)
  • National Defence Fundamental Project (2020A130)
  • National Defense Basic Scientific Research Project (JCKY2019407D001)

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