Minimum variance control based on an uncertain neural networks and global optimization method

In this paper, we propose a robust minimum variance controller for nonlinear systems based on feedforward neural networks. Based on input-output system measurements, a neural network model with uncertain parameters is trained to approximate the unknown dynamic behavior of the system. The control law is formulated as a min-max optimization problem which minimizes the worst case of the quadratic objective function subject to the uncertain parameters of the model and the control signal constraints. When classic optimization methods are used to optimize this kind of problem, a local solution is then obtained. In order to reach the global solution of the control problem which corresponds to the optimal control actions, the Generalized Geometric Programming technique is used to reduce the constrained non-convex problem to a convex one. The performances of the proposed neural controller are illustrated by a simulation example.