Dual predictive control considering future uncertainties in parameters, input, output and output reference

In this paper, the author proposes an algorithm of dual predictive control for a system expressed by a linear ARX (auto-regressive and exogenous) model with uncertain plant model parameters. Previously, the author proposed a dual predictive control algorithm which first considered the uncertainties in future control input values and in future output values included in an ARX model. The future input uncertainty is due to future unknown changes of further-future output predictions. The cost function, represented by the Bellman´s equations, was based on that for GPC (generalized predictive control). To avoid impractical computational burden, the cost function must be simplified; hence, a sub-optimal algorithm including the procedure for simplification and cost evaluation was derived. The algorithm proposed here has improved the previous one through the consideration of future uncertainties in output reference and in parameter changes. These uncertainties have not been fully taken into consideration in other dual predictive control algorithms. The sub-optimal control input is obtained through nonlinear optimization. A numerical example illustrates the effectiveness of the algorithm.