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A Multiscale Approximation Scheme for Explicit Model Predictive Control with Stability, Feasibility, and Performance Guarantees


S. Summers

IEEE Conference on Decision and Control, Shanghai, China

In this paper, an algorithm is introduced based on classical wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second order interpolating wavelets. It is proven that the resulting interpolation is everywhere feasible. Further, tests to confirm stability and to compute a bound on the performance loss are introduced. Since the controller approximation is built on a gridded hierarchy, the evaluation of the control law in real-time systems is naturally fast and runs in a bounded logarithmic time. A simple example is provided which both illustrates the approach and motivates further research in this direction.


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