On Dynamic Programming Of Discrete Descriptor Systems Based On Data-driven Methods

The optimal control methods based on data-driven of aclass of descriptor system are concerned. The descriptor system model isfound in many fields, such as electric power systems, petrochemicalindustry, economic field, robot systems, communication networks, andaerospace systems. With the research of descriptor systems, the theory ofdescriptor system has become an independent branch of modern controltheory. Different from the normal systems, which are described inordinary differential equations or difference equations, descriptor systemsare established in a more general form. Especially, when the systemparameter index is greater than1, the system may have potential impulsebehavior. This characteristic brings great difficulties to the theoreticalresearch of descriptor system. However it brings the big challenge at thesame timeRecently, with the development of computer technology, it is easy tostore and process data. The data-driven control methods can beimplemented more effectively. Data-driven methods are applicable whenthe global model of controlled system is unknown, or that the structure ofcontrolled process changed a lot. Compared with traditional methods foroptimal control, data-driven methods do not need to complete informationof system. The controller is designed only depending on the inputs and outputs data of target system. This characteristic make such controlmethods more flexible and applicable.The main contribution of this thesis is that the optimal controlmethod based data-driven for the discrete time descriptor system areestablished. Firstly, based on the controllability and observability, theoptimal control problem is solved with no information of system states.Secondly, the controller is designed in the form of auto regressive movingaverage (ARMA) of the inputs and outputs data of the system, and is withno need for the information of system states or system matrices. Finally,based on the theoretical analysis, value iteration (VI) and policy iteration(PI) algorithms are discussed in detail. Simulation indicates that thepresented algorithms can solved the optimal problem of the targetdescriptor system not only when the index is less or equal1, but when theindex is greater than1as well.