A design technique for fast sampled-data nonlinear model predictive control with convergence and stability results

ABSTRACT

In this study, a sampled-data nonlinear model predictive control scheme is developed. The control algorithm uses a prediction horizon with variable length, a terminal constraint set, and a feedback controller defined on this set. Following a suboptimal solution strategy, a defined number of steps of an iterative optimisation routine improve the current input trajectory at each sampling point. The value of the objective function monotonically decreases and the state converges to a target set. A discrete-time formulation of the algorithm and a discrete-time design model ensure high computational efficiency and avoid an ad hoc quasi-continuous implementation. This design technique for a fast sampled-data nonlinear model predictive control algorithm is the main contribution of the paper. Based on a benchmark control problem, the performance of the developed control algorithm is assessed against state-of-the-art nonlinear model predictive control methods available in the literature. This assessment demonstrates that the developed control algorithm stabilises the system with very low computational effort. Hence, the algorithm is suitable for real-time control of fast dynamical systems.

KEYWORDS:

• Nonlinear model predictive control
• receding horizon control
• real-time optimisation
• sampled-data control
• dynamic optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Natural Sciences and Engineering Research Council of Canada [grant number RGPIN/05252-2014].