Low complexity suboptimal explicit NMPC

Abstract We present a method for calculating suboptimal explicit solutions to NMPC problems that guarantee stable closed-loop behavior. These explicit solutions are piecewise affine functions that are defined on a polytopic partition of the state space. In contrast to other approaches, we do not only calculate an inner approximation, but also an outer approximation, of the closed-loop stable set. The approximation gap can be used to control the resolution of the state space partition. The proposed approach is illustrated with an example. Despite the simplicity of the example, the results show that the combination of a piecewise affine function and a polytopic partition results in an explicit control law of significantly lower complexity than those from previous approaches.

[1]  Frank Allgöwer,et al.  A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability , 1997, 1997 European Control Conference (ECC).

[2]  G. Goodwin,et al.  Global analytical model predictive control with input constraints , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  Martin Mönnigmann,et al.  Approximate explicit NMPC with guaranteed stability ensured by a simple auxiliary controller , 2012, 2012 IEEE International Symposium on Intelligent Control.

[4]  Martin Mönnigmann,et al.  Explicit feasible initialization for nonlinear MPC with guaranteed stability , 2011, IEEE Conference on Decision and Control and European Control Conference.

[5]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[6]  M. Morari,et al.  Fast explicit nonlinear model predictive control via multiresolution function approximation with guaranteed stability , 2010 .

[7]  Lorenzo Fagiano,et al.  Set Membership approximation theory for fast implementation of Model Predictive Control laws , 2009, Autom..

[8]  Tor Arne Johansen,et al.  Approximate explicit receding horizon control of constrained nonlinear systems , 2004, Autom..

[9]  Thomas Parisini,et al.  Approximate off-line receding horizon control of constrained nonlinear discrete-time systems , 2009, 2009 European Control Conference (ECC).

[10]  Eduardo F. Camacho,et al.  On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach , 2003, 2003 European Control Conference (ECC).