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This paper describes a novel technique for scenario generation aimed at closed loop stochastic nonlinear model predictive control. The key ingredient in the algorithm is the use of vector quantization methods.We also show how one can impose a tree structure on the resulting scenarios. Finally, we briefly describe how the scenarios can be used in large scale stochastic nonlinear model predictive control problems and we illustrate by a specific problem related to optimal mine planning.

This paper presents properties of a control law which quantizes the unconstrained solution to a unitary horizon quadratic programme. This nave quantized control law underlies many popular algorithms, such as -converters and decision feedback equalities, and is easily shown to be globally optimal for horizon one. However, the question arises as to whether it is also globally optimal for horizons greater than one, i.e. whether it solves a finite horizon quadratic programme, where decision variables are restricted to belonging to a quantized set. By using dynamic programming, we develop sufficient conditions for this to hold. The present analysis is restricted to first order plants. However, this case already raises a number of highly non-trivial issues. The results can be applied to arbitrary horizons and quantized sets, which may contain a finite or an infinite (though countable) number of elements.

By introducing psycho-acoustical aspects, the audio quantization problem is translated into a finite horizon optimal control problem with a finite input constraint set. An explicit solution is obtained. Its receding horizon implementation gives rise to the Receding Horizon Quantizer (RHQ). The RHQ corresponds to a closed loop, which embeds the widely-adopted Noise Shaping Quantizer in a broader framework and allows for enhanced performance. Furthermore, suboptimal algorithms are described and their behaviour illustrated by means of an example.