A novel approach solving for linear matrix inequalities using neural networks
Linear matrix inequalities (LMIs) play a very important role in postmodern control by providing a framework that unifies many concepts. While numerous papers have appeared cataloging applications of LMIs to control system analysis and design, there have been few publications in the literature describing the numerical solution of these problems. Specially, neural network processing has rarely been used to solve those problems. This paper attempts to propose a new approach to solving a class of LMIs using recurrent neural networks. The nature of parallel and distributed processing renders these networks, which possess the computational advantages over the traditional sequential algorithms in real-time applications. The proposed networks are proven to be largely asymptotical and capable of solving LMIs. Some illustrative examples are provided to demonstrate the proposed results.
linear matrix inequality recurrent neural network lyapunov equation riccati equation quadratic stability