Optimal Design of Adaptive Robust Control for Fuzzy Swarm Robot Systems

Motion control for an uncertain swarm robot system consisting of N robots is considered. The robots interact with each other through attractions and repulsions, which mimic some biological swarm systems. The uncertainty in the system is possibly fast time varying and bounded with unknown bound, which is assumed to be within a prescribed fuzzy set. On this premise, an adaptive robust control is proposed. Based on the proposed control, an optimal design problem under the fuzzy description of the uncertainty is formulated. This optimal problem is proven to be tractable, and the solution is unique. The solution to this optimal problem is expressed in the closed form. The performance of the resulting control is twofold. First, it assures the swarm robot system deterministic performances (uniform boundedness and uniform ultimate boundedness) regardless of the actual value of the uncertainty. Second, the minimization of a fuzzy-based performance index is assured. Therefore, the optimal design problem of the adaptive robust control for fuzzy swarm robot systems is completely solved.