Abstract
In this paper, we propose a new algorithm of dual predictive control for a system expressed by a linear autoregressive and exogenous (ARX) model with uncertain model parameters. The cost function, represented by the Bellman's equations, is based on the cost for the generalized predictive control (GPC). To avoid impractical computational burden, a new sub-optimal cost function which approximates the Bellman's equations is derived. The sub-optimal cost contains the variances of various future uncertainties, whose exact values are difficult to obtain. To cope with this, an algorithm to calculate the cost is devised with some appropriate approximations. The main difference from the preceding works on dual predictive control is the consideration of future uncertainties in control input and in the output values in the AR part of the model. Hence, the proposed control algorithm including the cost function is the closest to the optimal among all the dual predictive control algorithms. The control input to minimize the cost is obtained through nonlinear optimization. A numerical example illustrates the effectiveness of the algorithm.
