Algorithms of the Solutions of Linear Quadratic Optimal Control Problem with Nonseparated Boundary Conditions in Mixed (Continuous – Discrete) Typed Ömer AKIN Gazi University, Faculty of Arts and Sciences, Department of Mathematics 06500, Teknikokullar, Ankara-TURKEY, omerakin@gazi.edu.tr Fikret A. ALIEV Institute of Applied Mathematics,Baku State University,Azerbaijan. f_aliev@yahoo.com Mehmet CAN Technical University of İstanbul, Department of Mathematics İstanbul- TURKEY, mcan@itu.edu.tr Nurettin DOĞAN Gazi University, Faculty of Technical Education, Department of Electronics and Computer Education, 06500, Teknikokullar, Ankara-TURKEY, ndogan@gazi.edu.tr H. Hüseyin SAYAN Gazi University, Faculty of Technical Education, Department of Electrical Education, 06500, Teknikokullar, Ankara-TURKEY , hsayan@.gazi.edu.tr Abstract. In this article the mixed (continuous – discrete) optimal control problem with non seperated conditions is examined. In suggested algorithm the system has less number of equations than the number of equations used to solve continuous and discrete optimal control problems separately. Suggested algorithm is better than the others in the sense of computer realization. Finally we illustrated the algorithm with a concrete example. 1. Introduction Let the interval ( ) τ , 0 is devided into subintervals of the form ( ) 1 , + i i τ τ and the motion of the object is given by [1-3] () ( ) ( ) ( ) ( ) ( ) t t u t G t x t F t x υ + + = & (1) on each ( ) 1 , + i i τ τ and at each points of i τ is given by the discrete equations of [3-5] ( ) ( ) i i i i V x F x i τ τ τ δ Γ + − = + ) 0 ( . 0 (2) Finally at the boundary points of { } 0 , 0 + p τ the motion of the object is given by [3]