Practical control design method of hybrid systems

近年来，控制界对由连续动态和离散动态组成的混杂系统的研究受到了极大的关注，并取得了许多成果，发展了一些智能控制系统的系统设计方法。然而，由于几个关键问题仍然悬而未决，因此很少有实际应用。因此，在本研究项目中，对建模、高效分析、实时优化和应用四个主题进行了研究。首先，建立了一种新的离散动力学模型，使我们能够有效地解决最优控制问题。其次，提出了一种适用于大规模系统的混杂系统概率能控性分析方法。第三，开发了基于预计算的混合逻辑规划问题的高效求解器。最后，通过在步行机器人上的应用验证了该算法的有效性。

Recently in the control community, much attention has been paid on research topics on hybrid systems, which are composed of continuous dynamics and discrete dynamics, and many results have been obtained so far toward to developments on systematic design methods for some kind of intelligent control systems. However, there are few practical applications because several crucial issues are still open. Thus in this research project, four topics on modeling, efficient analysis, real-time optimization, and applications have been studied. First, a new modeling on discrete dynamics has been developed, which allows us to solve the optimal control problem in an efficient way. Next, a probabilistic controllability analysis of hybrid systems has been proposed, which can be applied to a large-scale class of systems. Third, an efficient solver to mixed logical programming problems has been developed based on the precalculation. Finally, an application to walking robot has been executed to verify the efficiency of the proposed algorithm.