From modern, creative, algorithmic positions, mathematical methods for the study of optimal control on the class of piece-constant controls . are presented. The solution of the actual problem of the theory of optimal control is presented - algorithms were created and tested on test and real models , Moving to , For various reasons , from continuous optimal control to quasi-optimal piecewise-linear or piecewise-constant control of objects. The analysis of methods for studying the local optimality of controls in deterministic systems has been performed, the problem of developing a method for studying the local optimality of control systems in the class of piecewise constant functions has been set and solved. An improved method of numerical location of local-optimal control in the class of piecewise constant controls is presented and a method of reducing the optimal control problem to the finite-dimensional problem of studying uniform forms of higher order. is developed. Practical application of the developed algorithms implemented in LabVIEW 9. environment is considered 0 on the example of a low-flying object. For academics, management theory specialists, graduate students and senior students of technical universities.