Neural approximations for receding-horizon controllers

A receding-horizon (RH) optimal control scheme for a discrete-time nonlinear dynamic system is presented. A nonquadratic cost function is considered and constraints are imposed on both the state and control vectors. Two main results are reported. The first consists in deriving a stabilizing regulator without imposing, as is usually required by existing RH control schemes, that either the origin (i.e. the equilibrium point of the dynamic system) or a suitable neighbourhood of the origin be reached within a finite time. Stability is achieved by adding a proper terminal penalty function to the process cost. The second result consists in generating the control vector by means of a feedback control law computed off line instead of computing it on line, as is done for existing RH regulators. The off-line computation is performed by approximating the RH regulator by means of a multilayer feedforward neural network.