JJPC 456 Disk used No. pages 12, DTD=4.3.1 Version 7.51e ARTICLE IN PRESS UNCORRECTED PROOF A note on stability, robustness and performance of output feedback nonlinear model predictive control Lars Imsland a, *, Rolf Findeisen b , Eric Bullinger b , Frank Allgower b , Bjarne A. Foss a a Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491 Trondheim, Norway b Institute for Systems Theory in Engineering, University of Stuttgart, 70550 Stuttgart, Germany Abstract In recent years, nonlinear model predictive control (NMPC) schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in the framework of nonlinear predictive control. This paper combines stabilizing instantaneous state feedback NMPC schemes with high-gain observers to achieve output feedback stabilization. For a uniformly observable MIMO system class it is shown that the resulting closed loop is asymptotically stable. Furthermore, the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme can be recovered to any degree of accuracy for large enough observer gains, thus leading to semi-regional results. Additionally, it is shown that the output feedback controller is robust with respect to static sector bounded nonlinear input uncertainties. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nonlinear model predictive control; Output feedback stabilization; High gain observers; Nonlinear separation principle 1. Introduction Model predictive control (MPC), also referred to as moving horizon control or receding horizon control, has become an attractive feedback strategy, especially for linear or nonlinear systems subject to input and state constraints. In general, linear and nonlinear MPC are distinguished. Linear MPC refers to a family of MPC schemes in which linear models are used to predict the system dynamics, even though the dynamics of the closed loop system is nonlinear due to the presence of constraints. Linear MPC approaches have found suc- cessful applications, especially in the process industries [23]. By now, linear MPC theory is fairly mature. Important issues such as the online computations, the interplay between modeling, identification and control as well as system theoretic issues like stability are well addressed. Linear models are widely and successfully used to solve control problems. However, many systems are inherently nonlinear. Higher product quality specifica- tions, increasing productivity demands, tighter environ- mental regulations and demanding economical considerations require systems to be operated closer to the boundary of the admissible operating region. Often in these cases, linear models are not adequate to describe the process dynamics and nonlinear models must be used. This motivates the application of non- linear model predictive control. Model predictive control for nonlinear systems (NMPC) has received considerable attention over the past years. Many theoretical and practical issues have been addressed. Several existing schemes guarantee stability under full state information, see [1,7,19] for recent reviews. In practice, however, not all states are directly available by measurements. A common approach to output feedback NMPC is to employ a state feedback NMPC controller in combination with a state observer. If this approach is used, in general little can be said about the stability of the closed loop, since no universal separation principle for nonlinear systems exists. Different approaches addressing the output feedback problem in NMPC exist. In [21] a moving horizon observer is presented, that together with the so called dual-mode NMPC scheme [20] lead to semi-regional 0959-1524/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0959-1524(03)00006-4 Journal of Process Control & (&&&&) &–& www.elsevier.com/locate/jprocont 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 * Corresponding author. E-mail address: lars.imsland@itk.ntnu.no (L. Imsland); findeise@ ist.uni-stuttgart.de (R. Findeisen); bullinger@ist.uni-stuttgart.de (E. Bullinger); allgower@ist.uni-stuttgart.de (F. Allgo¨wer); bjarne. foss@itk.ntnu.no (B.A. Foss).