Assessment and Future Directions of Nonlinear Model Predictive ...

Interval Arithmetic in Robust Nonlinear MPCD. Limon 1 ,T.Alamo 1 ,J.M.Bravo 2 ,E.F.Camacho 1 ,D.R.Ramirez 1 ,D. Muñoz de la Peña 1 ,I.Alvarado 1 , and M.R. Arahal 11 Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla,Sevilla, Spain{limon, alamo, eduardo, danirr, davidmps, alvarado,arahal} @cartuja.us.es2 Departamento de Ingeniería Electrónica, Sistemas Informáticos y Automática.Universidad de Huelva, Huelva, Spaincaro@uhu.esSummary. This paper shows how interval arithmetic can be used to design stabilizingrobust MPC controllers. Interval arithmetic provides a suitable framework to obtaina tractable procedure to calculate an outer bound of the range of a given nonlinearfunction. This can be used to calculate a guaranteed outer bound on the predictedsequence of reachable sets. This allows us to consider the effect of the uncertaintiesin the prediction and to formulate robust dual-mode MPC controllers with ensuredadmissibility and convergence. Interval arithmetic can also be used to estimate thestate when only outputs are measurable. This method provides a guaranteed outerbound on the set of states consistent with the output measurements. Generalizing thecontrollers based on reachable sets, a novel robust output feedback MPC controller isalso proposed.1 IntroductionConsider a process described by an uncertain nonlinear time-invariant discretetime modelx + = f(x, u, w) (1)y = g(x, u, v) (2)where x ∈ R n is the system state, u ∈ R m is the current control vector, y ∈ R pis the measured output, w ∈ R nw is the disturbance input which models theuncertainty, v ∈ R pv is the measurement noise and x + is the successor state. x k ,u k , y k , w k and v k denote the state, input, output, uncertainty and noise of theplant at sampling time k, respectively.It is assumed that the uncertainty is bounded and contained in a compactset,w ∈ W (3)which contains the origin and the noise is bounded in the compact setv ∈ V. (4)R. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 317–326, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007