INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2005; 15:219–231 Published online 27 January 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/rnc.982 Extension of efficient predictive control to the nonlinear case M. Bacic n,y , M. Cannon z and B. Kouvaritakis } Department of Engineering Science, Oxford University, Parks Rd., Oxford OX1 3PJ, U.K. SUMMARY The combined use of the closed-loop paradigm, an augmented autonomous state space formulation, partial invariance, local affine difference inclusion, and polytopic invariance are deployed in this paper to propose an NMPC algorithm which, unlike earlier algorithms that have to tackle online a nonlinear non-convex optimization problem, requires the solution of a simple QP. The proposed algorithm is shown to outperform earlier algorithms in respect of size of region of attraction and online computational load. Conversely, for comparable computational loads, the proposed algorithm outperforms earlier algorithms in terms of optimality of dynamic performance. Copyright # 2005 John Wiley & Sons, Ltd. KEY WORDS: nonlinear predictive control; invariant sets; feedback linearization; quadratic programming 1. INTRODUCTION The theoretical framework of Nonlinear Model Predictive Control (NMPC) that guarantees feasibility and stability is now well understood [1] and consists of the optimization of a finite horizon cost with a terminal penalty term subject to system constraints in addition to a terminal stability constraint. This formulation, however, is not amenable to practical implementation, especially for application with fast dynamics. The reason for this is that both the cost and constraints bear a nonlinear dependence on the degrees of freedom so that the online optimization problem is non-convex, and as such can be computationally exceedingly demanding. This is especially pertinent for long prediction horizons and/or models of large dimension. Furthermore, non-convex optimization has no guarantees of terminating in finite time. It is the purpose of the current paper to overcome these difficulties through the extension of a framework that was developed for use in linear MPC [2,3]. Thus use is made of the ‘closed loop paradigm’, according to which the degrees of freedom are reformulated as perturbations on the Received 21 January 2004 Revised September 2004 Accepted 30 November 2004 Copyright # 2005 John Wiley & Sons, Ltd. y E-mail: marko.bacic@eng.ox.ac.uk n Correspondence to: Marko Bacic, Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, U.K. z E-mail: mark.cannon@eng.ox.ac.uk } E-mail: basil.kouvaritakis@eng.ox.ac.uk Contract/grant sponsor: EPSRC; contract grant number: GR/N05499/01 Contract/grant sponsor: UK (ORS) and Emden Scholarship Fund