Fetisov

pp. 17-31

pp. 32-43

pp. 281-293

A new method was proposed to solve terminal control problems for multidimensional affine systems. The system under consideration is supposed to be equivalent to a regular system of a quasi-canonical form. A necessary and sufficient condition for existence of a solution of terminal control problems for transformed systems was formulated. A sufficient condition for solvability of terminal control problems was proved for quasi-canonical systems with nonlinear subsystem dimension not exceeding control dimension. An algorithm was designed to construct a solution of terminal control problems for this class of systems. A numerical example was presented to illustrate the proposed algorithm.

In this paper a new approach was proposed to solve terminal control problems for affine systems. This approach is based on transformation of a system under consideration to a quasi-canonical form system. Moreover, it was assumed that all subsystems of the canonical form are two-dimensional. A sufficient condition for existence of a solution for the terminal control problem was proved. A numerical procedure was also proposed to construct a solution of the terminal control problem for affine systems which are equivalent to systems of the quasi-canonical form with two-dimensional subsystems of the canonical form. An example was given to illustrate the proposed approach.

The new method is proposed to solve a terminal problem for regular systems of a quasicanonical form with two-dimensional zero dynamics and scalar control. The example of terminal problem solving by means of the method proposed is given. The controllability sufficient condition for regular systems of a quasicanonical form with scalar control and two-dimensional zero dynamics is proven. The example is represented to illustrate the condition received.

This note deals with a controllability condition for affine systems with scalar control. The main assumption – the considered system is equivalent to system of a quasicanonical form, regular on all space of states. For regular system of a quasicanonical form the solution existence sufficient condition of a terminal task is received. By means of this condition it is shown that under some conditions the terminal task for regular system of a quasicanonical form has the decision for any initial and final conditions of system on any final interval of time. Thereby the sufficient condition of controllability for a considered class of systems is proved. A possible scope of the received results is the solution of technical systems control problems.

 This note deals with a controllability condition for affine systems with scalar control on all space of states for any final interval of time. Research is based on system transformation to a quasicanonical form and the further analysis of terminal problem solution existence for the transformed system. It is shown that for system with the right part of a special form the terminal problem has the solution for any initial and final states of system and any interval of time. Thereby it is proved that such system is controlled on all space of states for any final interval of time. A possible scope of the received results is the solution of technical systems control problems.