On input-to-state stability of min-max nonlinear model predictive control

In this paper we consider discrete-time nonlinear systems that are affected, possibly simultaneously, by parametric uncertainties and disturbance inputs. The min-max Model Predictive Control (MPC) methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium. The aim is to provide a priori sufficient conditions for stability of the resulting closed-loop system via the input-to-state stability framework. First, we show that only input-to-state practical stability can be ensured in general for perturbed nonlinear systems in closed-loop with min-max MPC schemes. Then, we derive new sufficient conditions that guarantee input-to-state stability of the min-max MPC closed-loop system, via a dual-mode approach. An illustrative example is also presented. Key words: Min-max, Nonlinear model predictive control, Input-to-state stability

• Type: Journal
• Year: 2008
• Where: SCL
• Authors: Mircea Lazar, David Muñoz de la Peña, W. P. M. H. Heemels, Teodoro Alamo
• Keywords: Input-to-state Stability, Model Predictive Control, Nonlinear Systems, SCL 2008