Idempotent method for dynamic games and complexity reduction in min-max expansions

— In recent years, idempotent methods (specifically, max-plus methods) have been developed for solution of nonlinear control problems. It was thought that idempotent linearity of the associated semigroup was required for application of these techniques. It is now known that application of the max-plus distributive property allows one to apply the maxplus curse-of-dimensionality-free approach to stochastic control . Here, we see that a similar, albeit more abstract, approach can be applied to deterministic game problems. The main difficulty is a curse-of-complexity growth in the computational cost. Attenuation of this effect requires finding reduced-complexity approximations to min-max sums of maxplus affine functions. We demonstrate that that problem can be reduced to a pruning problem.

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: William M. McEneaney
• Keywords: CDC 2009, Control Systems, Max-plus Distributive Property, Maxplus Curse-of-dimensionality-free Approach, Nonlinear Control Problems