Kasatkina

pp 266-280

pp. 781- 797

The authors consider an affine third order system which describes action of a chemical batch reactor with a ternary working mixture. The terminal control problem for this system with restrictions on state variables was investigated. Solution to this problem is based on the orbital linearization approach by which the original problem is transformed to a terminal problem for a non-stationary second-order system in a canonical form. For the transformed terminal problem conditions for solution existence were obtained; a method of obtaining this solution was also proposed. Operability of the proposed method was illustrated by mathematical simulation.

Change of the independent variable (time-scaling) gives an additional degree of freedom for equivalence conversions of dynamical systems. Affine system transformation to the canonical form is a standard technique in the design of nonlinear control systems. In this paper transformations of a stationary affine system to the canonical form, using time-scaling, were investigated. Integratable and non-integratable changes of the independent variable were considered. It was shown, that the affine system can't be transformed to the canonical form using integratable time-scaling. Conditions of the possibility of transformation to the regular canonical form using non-integratable time scaling were obtained for single-input affine systems of the third order.

The model of the wheeled robot with automobile configuration of wheels in a problem of path stabilisation is considered. Conditions at which transition from the Cartesian coordinates to the trajectory coordinates at the path stabilization problem is correct are investigated. Performance of these conditions for the elementary types of a trajectory of the robot is analyzed.