Limited Complexity and Parallel Implementation of Polytope Updating

The methods introduced in this paper aim at helping the practical applications of polytope based parameter and state bounding, and for this purpose parallel computing and limited complexity procedures are introduced to update convex polytopes. As opposed to the case of covariance based recursive statistical estimation where parallel computation can only result moderate improvement for lower dimensions of parametervectors, polytope updating can be parallelized more efficiently. The increase in the speed of the procedure can be made proportional to the number of applied processors. This result means that using sufficent number of processors polytope based parameter bounding can be made even faster than statistical estimation. Another development of this paper is the introduction of some schemes to limit the complexity of the updated polytopes. Combining limited complexity calculations with parallel processing helps the way towards on-line applications of polytope-based parameter and state bounding in adaptive control and signal processing.