### Convergence of The Discrete Classical Optimal Control Problem To The Continuous Classical Optimal Control Problem Including A Nonlinear Hyperbolic P.D. Equation

*Engineering and Technology Journal*

2010, Volume 28, Issue 14, Pages 4687-4702

2010, Volume 28, Issue 14, Pages 4687-4702

#### Abstract

Our focus in this paper is to study the behaviour in the limit of the discrete classical optimal control problem including partial differential equations of nonlinear hyperbolic type. We study that the discrete state and its discrete derivative are stable in Hilbert spaces 1 H0(W) and L2(W) respectively. The discrete state equations containing discrete controls converge to the continuous state equations. The convergent of a subsequence of the sequence of discrete classical optimal for the discrete optimal control problem, to a continuous classical optimal control for the continuous optimal control problem is proved. Finally the necessary conditions for optimality of the discrete classical optimal control problem converge to the necessary conditions for optimality of the continuous optimal control problem, so as the minimum principle in blockwise form for optimality.

#### Keywords

Optimal Control, Nonlinear Systems, State Constrains, Classical Controls, Converges, Stability#### Metrics