Three extended horizon adaptive nonlinear predictive control schemes based on the parametric Volterra model

Abstract

Extended horizon one-step-ahead predictive control algorithm is given for the parametric Volterra model (which includes also the generalized Hammerstein model). A quadratic cost function is minimized which considers the quadratic deviation of the reference signal and the output signal in a future point beyond the dead time and also punishes big control signal increments. For prediction of the output signal, a prediction equation is applied which uses information about the input and output signals up to the current time. It is advantageous to use the control increments instead of the control signal in the prediction equation, since the cost function contains the control increment and not the control signal itself. Assuming a functional relation between the subsequent control increments in the control horizon leads to a one-dimension minimization of the control cost function. This sub-optimal solution of the nonlinear predictive control approximates the optimal solution with few computational efforts. Three adaptive schemes are presented and compared: estimation of the parameters of the process model, estimation of the parameters of the prediction equation using the control signal, and estimation of the parameters of the prediction equation using the control increments.