Optimal Distributed Globally Bounded Control for Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions and a Linear Quality Criterion

Abstract

For the problem of optimal control of a parabolic-hyperbolic process with nonlocal point boundary conditions, an explicit form of the solution is obtained in the form of formal series according to the system of eigenfunctions, which are generated by the spatial differential operator and boundary conditions. At the same time, the unequivocal solvability of the intermediate problems is established for each iteration. In addition, sufficient conditions for the convergence of the series are established, which determine the obtained formal solution of the optimal control problem, which justifies its correctness system of differential equations; Lyapunov exponents; fractal dimension

Keywords

• optimal control problem
• parabolic-hyperbolic equations
• fourier coefficients
• approximation