Optimality Conditions for Minimization Problem of Piecewise-Linear Functional in Optimization of the Oscillation Processes
Abstract
In the article, the minimization problem is investigated of piecewise linear functional in non-linear optimization of oscillation processes described by Fredholm integro-differential equations. An algorithm has been developed for constructing a generalized solution to boundary value problem that describes the oscillation process. Using the maximum principle for systems with distributed parameters, optimality conditions are determined in the form of equality and inequality.
Keywords
Optimal control, optimal process, piecewise linear functional, generalized solution, maximum principle, optimality condition
References
- [1]. Polyanin A.D., Zaitsev V.F. A.N. , “Handbook of Nonlinear Partial Differential Equations.” Chapman & Hall/CRC, 2004.
- [2]. Evans L.C. “Partial Differential Equations sport”, 2nd ed. — Providence: AMS, 2010.
- [3]. Samarskii A.A., Mikhailov A.P., “Principles of Mathematical Modelling: Ideas, Methods, Examples”, Taylor & Francis, 2001.
- [4]. Egorov A.I., “Optimal control of thermal and diffusion processes”,Moscow:Nauka, 1978, P.37.
- [5]. Krasnov M.L. “Integral equation”, - Moscow:Nauka, 1975, P.29.
- [6]. Komkov Vadim. “Optimal Control Theory For The Damping Of Vibrations Of Simple Elastic Systems”, Springer-Verlag, Berlin-Heidelberg-New York, 1972
- [7]. Lions J.L. Optimal Control of Systems Governed by Partial Differential Equations., Springer, 2001 (reprint).
- [8]. Plotnikov V.I. “ Energy inequality and the property of overdetermination of system of eigenfunctions", Mathematical collection, 32, №4 (1968), pp.743-755.
- [9]. Abdyldaeva E., Gulbarchyn Taalaibek kyzy, Аnarkulova B. Generalized solution of boundary value problem with an inhomogeneous boundary condition» Manas Journal of Engineering, Bishkek, 2019.
- [10]. The Control Handbook: Control System Advanced Methods / Ed. W.S. Levine. — Boca-Raton; London; New York: CRC Press, 2010. — 942 p.