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Orthonormal function parametrisation of model-predictive control for linear time-varying systems

ABSTRACT It is well known that some practical difficulties are involved in the implementation of stabilising model predictive control for time-varying systems. In order to address the difficulty of computational load, this paper extends the orthonormal function method for model predictive control to linear time-varying systems. We provide sufficient conditions for a sub-optimal model predictive controller to be stabilising for a time-varying system. It is also shown that the orthonormal parametrisation method enables us to reduce the number of decision variables significantly and with a satisfactory performance. In addition, it is shown that orthonormality and, the called for, long prediction horizons are not necessary for stability. Examples are provided, illustrating the effectiveness of the method for linear time-varying systems.