关键词：切换系统；最优控制；混合动力；人体运动
摘 要：The goal of this thesis is to address these two problems. First, a hybrid dynamical system representation is introduced that is shown to be capable of describing the discontinuities in dynamics that occur during locomotion. In particular, such a representation is constructible from observation given an unconstrained Lagrangian which is intrinsic to the biped after the identification of the sequence of contact points that are enforced during the observed motion. Second, a specific hybrid dynamical system representation is shown to be constructible from observed data by optimally switching between the set of vector fields corresponding to all possible combinations of contact point enforcements. At this point an algorithm for the computation of an optimal control of constrained nonlinear switched dynamical systems is devised. The control parameter for such systems include a continuous-valued input and discrete-valued input, where the latter corresponds to the mode of the switched system that is active at a particular instance in time.