A fixed time convergent dynamical system to solve linear programming

The aim of this paper is to present a new dynamical system which solves linear programming. Its design is considered as a sliding mode control problem, where its structure is based on the Karush-Kuhn-Tucker optimality conditions, and its multipliers are the control inputs to be implemented by using fixed time stabilizing terms with vectorial structure, based on the unit control, instead of common terms used in other approaches. Thus, the main features of the proposed system are the fixed convergence time to the programming solution and the fixed parameters number despite of the optimization problem dimension. That is, there is a time independent to the initial conditions in which the system converges to the solution and, the proposed structure can be easily scaled from a small to a higher dimension problem. The applicability of the proposed scheme is tested on real-time optimization of an electrical Microgrid prototype.