Modal synthesis of nonstationary linear and relay stabilization systems

The synthesis problem of nonstationary linear and nonlinear stabilization s ystems using the performance index of transition processes is urgent. The a im of the synthesis is to approximate the transition process of minimizing the initial error in the synthesized system to the transition process of th e standard system with the standard position of zeros and poles. In this pa per, this type of approach is called the modal synthesis of nonstationary s ystems. The maximum principle is used as a method for the approximation of functions. The cases of absence and presence of control constraints are con sidered. In both cases, the main difficulty of the modal synthesis is relat ed to the necessity of solution of a two-point boundary value problem. The synthesized systems contain the standard system in its structure as a suppo rt structure. Examples of modal synthesis of the linear nonstationary syste m of an airplane's final approach and of the nonlinear control law of a spa cecraft's reorientation are presented. The possibility of using the quadrat ic optimization method for the approximation of the transition functions is also studied. The proposed synthesis methods are flexible, ensure high qua lity of the stabilization processes, and can be extended to tracking system s, as well as multiconnected systems.