The Anokhin-Pareto interaction principle in control system theory (Q1335860)

It is well-known that many (if not most) physical processes can be formulated as variational problems of minimal time, or minimal energy etc. The authors of the present paper try to formulate a somewhat similar principle applicable to biological, physiological and possibly sociological processes. The model for this type of processes are ``dynamical systems with redundant control'', where there are more controls than differential equations. Specifically, the considered systems are of the type \[ dx_i/ dt= f_i(x_1,\dots, x_n, u_1,\dots, u_r, t),\quad\text{for}\quad i= 1,\dots, h, \] and \[ dx_i/dt= g_i(x_1,\dots, x_n, t)\quad\text{for}\quad i= h+ 1,\dots, n. \] Based on considerations of optimality of possible controls, the authors find it reasonable to define an objective functional, to be minimized, measuring ``the control energy which is lost because the control actions are mismatched with the system''. This is related to work of \textit{A. V. Anokhin} [``Essays on the physiology of systems'', Meditsina, Moscow (1975)], where an ``Anokhin-Pareto'' principle is established.