Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning
- 27 Downloads
We establish necessary conditions for the optimality of smooth boundary and initial controls in a semilinear hyperbolic system of the first order. The problem adjoint to the original problem is a semilinear hyperbolic system without initial conditions. The suggested approach is based on the use of special variations of continuously differentiable controls. The existence of global generalized solutions for a semilinear first-order hyperbolic system in a domain unbounded in time is proved. The proof is based on the use of the Banach fixed-point theorem and a space metric with weight functions.
KeywordsOptimal Control Problem Hyperbolic System Boundary Control Exponential Dichotomy Adjoint Problem
Unable to display preview. Download preview PDF.
- 1.A. V. Arguchintsev, Optimal Control over Hyperbolic Systems [in Russian], Fizmatlit, Moscow (2007).Google Scholar
- 4.O. V. Peliushkevych, “On one problem for a loaded hyperbolic system of semilinear equations with horizontal characteristics,” Visn. Lviv Univ., Ser. Mech. Math., Issue 76, 109–118 (2012).Google Scholar
- 5.V. M. Kyrylych and A. D. Myshkis, “Boundary-value problem without initial conditions for one-dimensional linear hyperbolic system,” Differents. Equat., 28, No. 3, 463–469 (1992).Google Scholar
- 7.S. M. Aseev and A. V. Kryazhymskii, “A class of optimal control problems encountered in mathematical economics,” in: Trudy Steklov Mat. Inst. [in Russian], 262 (2008), pp. 16–31.Google Scholar
- 8.B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics [in Russian], Nauka, Moscow (1978).Google Scholar
- 9.I. P. Natason, The Theory of Functions of Real Variable [in Russian], GITTL, Moscow (1957).Google Scholar
- 10.H. I. Matveev and V. A. Yakubovych, Optimal Control Systems: Ordinary Differential Equations. Special Problems [in Russian], S.-Petersburg (2003).Google Scholar
- 11.G. M. Fichtenholz, A Course in Differential and Integral Calculus [in Russian], Nauka, Moscow, Vol. (1970),Google Scholar