Mixed–Integer Real–Time Iterations
In this chapter we present an algorithmic framework for mixed–integer Nonlinear Model Predictive Control (NMPC) that builds on the MIOCP and NLP techniques and algorithms of the previous chapters. We present the real–time iteration scheme for moving horizons, cf. [51, 53] that allows to deal with challenges every real–time on–line optimal control algorithm has to face. Conditions for local contractivity of this algorithm are given. As one central part of this thesis we develop a new real–time iteration scheme for mixed–integer NMPC problems treated by the outer convexification reformulation of the previous chapter. Relying on local contractivity of the classical real–time iteration scheme, we give a proof of local contractivity for the mixed–integer case in the presence of an arbitrary rounding scheme. A sufficient condition coupling the contractivity statement to the sampling time is derived and an upper bound on the allowable sampling time is given that depends on Lipschitz and boundedness properties of the problem.
KeywordsOptimal Control Problem Model Predictive Control Time Iteration Time Optimal Control Optimal Feedback Control
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