FAST ALGORITHMS FOR COMBINED SYNTHESIS OF DYNAMIC OBJECT CONTROL SYSTEMS

Abstract

The paper considers the issues of combined synthesis of a control system for a nonlinear dynamic object. The combined synthesis algorithms are based on the hybrid application of the theory of ordinary differential equations in the Cauchy form and the theory of automatic control. In this case, the dynamics of the control system are described in the input-output representation and by state-space equations. Algorithms for solving stabilization problems, finite control, and the inverse dynamics problem are presented in explicit form. These algorithms are based on the concept of reducibility of a general Cauchy-form system to the block-canonical Frobenius form. The combined use of these two approaches in the development of control system synthesis algorithms makes it possible to eliminate iterative search procedures, thereby ensuring high-speed execution of computational operations. A distinctive feature of the presented algorithms for solving stabilization problems is that these algorithms provide explicit solutions to the known problems mentioned above. Regarding the stabilization problem in the case of strong reducibility, it can easily be shown that such an implementation does not cause difficulties. In the case of weak reducibility, hardware implementation of the proposed algorithms is easily achieved for compensating the matrix companion polynomial of the block-canonical Frobenius form.