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#optimal control #synthesis of control # equilibrium point #symbolic regression

This work considers a new approach to solution of the optimal control problem. Firstly, a stabilization system is synthesized for a control object. As a result, the control object has a stable of equilibrium point in the state space. A location of the equilibrium point depends on some vector of parameters in stabilization system. Secondly the vector of parameters, that influences on location of stable equilibrium point, is searched as a solution of the control optimal problem in the form of function of time. Such approach allows obtained the control system with the found function of time as a program control to set in real object without changes and additional controllers. This has become possible, because the differential equation system with a stable equilibrium point is a contraction manifold. All perturbations, mistakes, and differences of the mathematical model from real object are decreased at the approximation to a stable equilibrium point. The computation example is presented, that compares two functions of time for vector of parameters, piecewise-linear and piecewise constant.

New approach to solution of the optimal control problem is presented. Firstly, object is made a stable, and then it is controlled by position of equilibrium point. Such approach allows to put obtained optimal control on real object.

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