Preview Control Of Descriptor Continuous-time Systems

Descriptor system theory and preview control theory have had a rich theoretical basis, but also achieved fruitful research results. Thus, the investigation that preview control theory is applied to the descriptor system the attention of scholars. So far, researchers are focused on the preview control of discrete-time descriptor systems, but seldom on the preview control of descriptor continuous-time systems. This paper combined descriptor continuous system and nonlinear descriptor discrete-time systems with preview control to design controller, The main research work is as follows:(1) The preview control problem for the impulse-free linear descriptor continuous-time systems is studied. The system is first decomposed into a traditional control system (i.e., slow subsystem) and an algebraic equation set by restricted equivalent linear transformation. Next, we apply the method from preview control theory to the slow subsystem. That is, we take derivatives on both the error vector and both sides of the state function of the slow subsystem. This constructs an augmented system in which a part of the state vector is the error vector. The problem is also transformed into an optimal control problem for an augmented system. Its optimal preview control input can be obtained from the related results in preview control theory, which is the derivative of the input of the original system. Integrating on this input, we obtain the controller of the original descriptor system with preview function.(2) The optimal controller problem of linear descriptor continuous-time system with impulse signal is discussed. Based on impulse-controllable, firstly, descriptor augmented error system is constructed that contains previewable target signal. Secondly, by introducing state feedback to eliminate impulses, descriptor augmented error system is transformed into normal error system by restricted equivalent linear transformation, then original the tracking problem is transformed into the optimal preview contorl problem of normal augmented error system. Finally, by applying the related results, and the relationship between inputs, we obtained controller of descriptor system with previewable action.(3) Design of optimal preview controller for a class of time-varying descriptor continuous-time system is presented. First, introduction of a preliminary feedback control, descriptor system is transformed into the normal of an algebraic equation and a part of state variables by restricted equivalent. Second, by differentiating both the two sides of the state equation and the output error signal, an augmented error system is constructed by use of the methods in preview control theory, which contains the error vector, the state vector, the state vector derivative and the input vector, then the tracking problem is transformed into the optimal regulating problem. We utilize optimal control theory to design optimal controller by introducing the performance index function, further, we deduced controller of the original time-varying continuous descriptor system with the preview feedforward compensation.(4) An optimal preview controller design method for nonlinear descriptor discrete-time control systems is proposed. Firstly, based on the idea of the direct control method of nonlinear control system, the part of nonlinear feedback is taken as formal input in order to make the nonlinear system into a "formal" linear system. Secondly, this linear descriptor system transformed into normal system by restricted equivalent, then an optimal preview controller is designed by using the basic methods in the optimal preview control. Finally, by the application of the relationship between the formal input and actual input, the optimal preview controller for the nonlinear descriptor discrete-time system is obtained.We do simulation by Matlab for the aboving the systems, and illustrate correctness and validity of the results and the methods.