Unfalsified Adaptive Control For Time-varying Systems

With today’s highly developed science and technology, the requirement of system control precision in modern industrial processes continues to increase. And it’s becoming more difficult to control the system through the establishment of the accurately model of the system. At the same time, the society today is a society of information. Lots of data and information is generated continuously, providing the status changes of the systems and other relevant information during the system operation in their industrial production processes. We need to know how to take advantage of all these information and data to control the system whose accurate mathematical model is difficult to establish, and so the concept of data-driven has emerged.The concept of data-driven comes from the fields of computer science and computational intelligence originally, and has been applied to the control field in recent years. Unfalsified control method belongs to data-driven control, which controls the system directly from the system’s input and output data. Based on the past study of the unfalsified control, this paper extends this method to the time-varying systems, and proposes a new cost function with fading memory factor, combining it to a new algorithm, and chooses PID controllers as a candidate controller set, then formulate the unfalsified adaptive PID control for time-varying systems.Firstly, the PID controller parameters have been chosen as a set of candidate controllers and certain improvements have been made. Then combine the controller set with the unfalsified adaptive control to formulate the unfalsified adaptive PID control.Secondly, based on the original cost function, the new cost function with a fading memory has been proposed for time-varying systems, to accelerate the speed of controller switching and reduce the transient response of the switches. At the same time, a new controller switching algorithm LICLA has been proposed based on the new cost function. And then compared it with the original switching algorithm, theoretical analysis has been given to illustrate the effectiveness.Thirdly, in order to ensure the stability of the system during the controller switches, the new definitions of stability have been proposed based on the original ones. And then based on the new definitions, the stability analysis and proof have been given, to illustrate that the unfalsified adaptive control can ensure the system stability effectively for time-varying systems.Finally, simulations based on previous theoretical analysis have been given. The simulation results show that the introduction of fading memory can make the time-varying systems switch to a stable controller with a faster speed and a lower transient response.