Research on designing control system to realize useful functions of complicated mechanical systems by learning or adaptive system considering competition or cooperation between the uncertain complex systems was performed.
In our researches, systems with deterministic and un-structured uncertainties, systems with deterministic and structured uncertainties, and systems with stochastic uncertainties were considered, and we proposed several design methods of robust controllers by using neural networks. We found that the very simple order that is power law is formed in the relation between the performance and the robustness of the set of controllers which are trained by the proposed methods in which uncertainties of the controlled object are taken into account. From the viewpoint of the optimization, design methods of robust controllers by learning is equals to the multi objective optimization problems. One of main causes of forming simple order, which is widely found in many natural systems, is forming of the set of Pareto solutions in the state space of multi-objective optimization. Therefore the competitive learning against the environmental uncertainties to improve robustness has close relation to simple order formation. Fixed robust controllers are robust against the considered robustness but they may be fragile to uncertainties which are never considered in designing controllers. Therefore not only the competitive learning against considered uncertainties but also adaption is important. Task decomposition by adaptation of modular controller and its order formation was investigated. We proposed an reinforcement learning algorithm for adaptive modules, which are able to decompose tasks of the complicated mechanical system. We applied the proposed method to design flight controllers, especially altitude controllers, for an unmanned helicopter. In designing controllers, vertical wind was considered as uncertainties. We found that the adaptive modules decomposed the task of the altitude control and the modules formed the simple order. As a result, controller's task was decomposed according to the direction of the helicopter's motion to improve the robustness against vertical wind and suitable controllers for each tasks were adaptively obtained by learning.