Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Homotopy Method in the Problem of Robust Mixed Criterion Control Synthesis in Hindrances Action

Author(s):

Alexander Anatolievich Rogoza

Bauman Moscow State Technical University (BMSTU),
Kaluga, Bazenova st, 2.

aemaeth_eternity@mail.ru

Abstract:

The work deals with the synthesis problem of the robust control for a mixed criterion in the conditions of action of hindrances minimizing anisotropic norm of a linear discrete system with structured uncertainty. The task may be considered as a part of a more general problem which does not contain any uncertainty, but has an additional input bounded on the capacity half-norm. Analytically the problem of the synthesis is reduced to the solving coupled system of nonlinear algebraic equations: Lyapunov equation, four Riccati equations and nonlinear equation of a special form. The homotopy method for the obtained system and the difference from the Davydenko classical method are discussed. The convergence of the method is justified. The analytical dependences for the implementation of the numerical procedures for the solution of nonlinear system of algebraic equations have been obtained. The mathematical modeling on the example of the aircraft in landing mode in conditions of wind shear has been performed.

Keywords

• homotopy method with
• Lyapunov equation
• mathematical modeling
• mixed optimization criterion
• Newtonian iteration
• Riccati equation

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