Recurrent neural networks with fixed time convergence for linear and quadratic programming

In this paper, a new class of recurrent neural networks which solve linear and quadratic programs are presented. Their design is considered as a sliding mode control problem, where the network structure is based on the Karush-Kuhn-Tucker (KKT) optimality conditions with the KKT multipliers considered as control inputs to be implemented with fixed time stabilizing terms, instead of common used activation functions. Thus, the main feature of the proposed network is its fixed convergence time to the solution. That means, there is time independent to the initial conditions in which the network converges to the optimization solution. Simulations show the feasibility of the current approach.