Optimum design of multiresolutional hierarchical control systems

The theoretical foundations of optimum design based on complexity analysis are outlined for hierarchical control systems. Using analytical expressions for the complexity, the optimum design parameters are computed for a multiresolution hierarchical controller. It is demonstrated that hierarchies for multiresolution control should have a definite number of levels which in order to minimize the complexity of computations. The optimum number of levels is found analytically. It is shown that complexity has an asymptotic limit, as the number of levels grows. Two important interconnected design parameters are found: the ratio of level-to-level refinement, and the contraction factor for determining the subset of attention at the adjacent lower level. It is demonstrated that in optimal hierarchies the ratio between two consecutive resolutions is not generally a constant value, and it is shown how this value can be computed