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Method of additional argument in problems of optimal control

Ramiz RAFATOV

The problem of control of the process described by the nonlinear differential equation with partial derivatives of the first order, with conditions at t 0 and in a sequence n of points x1 < x2 ... < xn is solved. The criterion of quality of control is the integrated quadratic functional, which depends on a final state of system and set n of controlling parameters. The method of increment of functional is applied to reception of conditions of optimality, and the method of additional argument (MAA) is applied for the decision of the nonlinear equations with partial derivatives.

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Method of spherical harmonic series in the problem of minimization of atmosphere pollution by fractions of harmful admixtures

Ramiz RAFATOV

The problem of minimization of atmosphere pollution by fractions of harmful admixtures is studied. It is supposed that a controlled object is described by non-stationary integral–differential transfer equation with special boundary conditions and control parameters, which are included in the right part of equation as delta-functions. Minimized integral quadratic functional characterizes energy expenditure for control and depends on the average squared deflection of fraction concentration from the desired final state. Optimal conditions are obtained with the help of Pontryagin’s maximum princip ...More

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