Optimization of systems governed by hyperbolic partial differential equation with equality and inequality constraints

Kazemi-Dehkordi, M. A.

doi:10.1007/bf02850702

Cited by 3 publications

(1 citation statement)

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“…The important role of the Goursat–Darboux problem is in the optimization theory of distributed systems (Vasil’ev, 2002; Vasil’ev et al, 1990). The authors of Egorov (1965), Egorov (1966), Kazemi–Dehkordi (1986), Plotnikov and Sumin (1972a), Plotnikov and Sumin (1972b), Srochko (1984), Suryanarayana (1972) and Suryanarayana (1973) have studied the continuous Goursat–Darboux optimal control problem from the point of view of Pontryagin’s maximum principle. Though in Belbass (1990), the author has utilized the dynamic programming approach to optimal control problem for the continuous Goursat–Darboux systems with distributed controls.…”

Section: Introductionmentioning

confidence: 99%

On the numerical scheme of a 2D optimal control problem with the hyperbolic system via Bernstein polynomial basis

Mamehrashi

Yousefi

Soltanian

2018

Transactions of the Institute of Measurement and Control

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A numerical method for solving a 2D optimal control problem (2DOCP) governed by a linear time-varying constraint is presented in this paper. The method is based upon the Bernstein polynomial basis. The properties of Bernstein polynomial functions are presented. These properties, together with the Ritz method, are then utilized to reduce the given 2DOCP to the solution of an algebraic system of equations. By solving this system, the solution of the proposed problem is achieved. The main advantage of this scheme is that the approximate solutions satisfy all initial and boundary conditions of the problem. We extensively discuss the convergence of the method. Finally, an illustrative example is included to demonstrate the validity and applicability of the new technique.

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