Synthesis of optimum types of feedback for systems with internal restrictions on control. II: An operation algorithm for an optimal controller. (Q1284300)

In Part I [Autom. Remote Control 58, No. 2, Part 1, 165--172 (1997); translation from Avtom. Telemekh. 1997, No. 2, 18--26 (1997; Zbl 1050.93512)], the authors obtained the governing equations of an optimal controller for the problem \[ J(u) = h'_0\,x(t^\ast)\to \text{max,}\quad \dot x = Ax + v(u), \quad x(0) = x_0, \] \[ Hx(t^\ast)=g,\quad | u(t)|\leqslant1,\quad t\in T=[0,t^\ast]. \] In the present paper a numerical method for solving these equations in the real-time mode is described. Based on this solution, an operation algorithm for the optimal controller is synthesized within the interval of control regularity and within the interval of sliding. An example is given to illustrate the operation of the optimal controller.