关键词：物理系统；大规模分布式系统；最优控制配方；混合动力系统；控制理论
摘 要：This thesis presents three new computational tools that bring the strength of hybrid dynamical models and optimal control to applications in Cyber-Physical systems. The first tool is an algorithm that nds the optimal control of a switched hybrid dynamical system under state constraints, the second tool is an algorithm that approximates the trajectories of autonomous hybrid dynamical systems, and the third tool is an algorithm that computes the optimal control of a nonlinear dynamical system using pseudospectral approximations. These results achieve several goals. They extend widely used algorithms to new classes of dynamical systems. They also present novel mathematical techniques that can be applied to develop new, computationally efficient, tools in the context of hybrid dynamical systems. More importantly, they enable the use of control theory in new exciting applications, that because of their number of variables or complexity of their models, cannot be addressed using existing tools.