Discrete-time algebraic Riccati inequation neuro-LMI solution

In this article we present a proposal for solving the discrete-time algebraic Riccati inequation (DARI). This associate linear matrix inequality (LMI) is solved using a multilayer recurrent neural network (RNN) approach. Systems of coupled matricial nonlinear differential equations are derived describing the neural dynamics of the neuro-LMI. By solving these coupled matrix equations using recurrent neural networks, our approach is capable of obtaining a symmetric and positive definite solution for this problem. Examples demonstrate the effectiveness of this proposal and respective implementation, for different learning rates.