Optimization by the Krasovskii Functional via the Bellman Quasilinearization Method

Abstract

Optimization by the generalized work functional using the Bellman quasilinearization method is shown to yield the well-known result due to A.A. Krasovskii.For the nonlinear dynamic system described by the vector equatioṅthe control that is optimal by the Krasovskii generalized work functionalwhere the function V (x, t) is the solution of the linear partial differential equationIn [2], the control that is optimal by the Krasovskii functional (2) and the control that is optimal by the Bolza functional (3) obtained in an example are compared and the former is found to be an approximation of the latter.Since the first iteration of the Bellman quasilinearization method under the Bolza criterion (3) coincides with the solution of optimization by the generalized work functional (2), the authors of [3] assert that there is a direct relationship between these two methods.According to [4], the solutions of minimization by criteria (2) and (3) are exact. As is known [1], minimization by the generalized work functional (2) is equivalent to minimization by the Bolza functional (3) under an additional isoperimetric condition

Task of Optimal Control of Gas Exchange in System qArtificial Lungs - Self-contained Breathing Apparatusq

“…Let the mathematical model of control object in accordance with (2) have the form: (11) where V 1 =V GAM (t) is the GAM volume removed from the system in the inhalation phase; The quality control criteria to be minimized for the object (11) will take the form: (12) where α i , β i are weighting factors (positive), which can be varied to achieve the predetermined quality of the transition process;…”