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Predictive Control Algorithms: Stability despite Shortened Optimization Horizons

The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a suitable optimization horizon length for nonlinear control systems governed by ordinary differential equations. In this context, we firstly show how the essential growth assumption involved in this methodology can be derived and demonstrate this technique by means of a numerical example. Secondly, inspired by corresponding results, we develop an algorithm which allows to reduce the required optimization horizon length while maintaining asymptotic stability or a desired performance bound. Last, this basic algorithm is further elaborated in order to enhance its robustness properties.