Theory Of Hybrid Systems Deterministic And Stochastic PDF Download

"Deterministic and stochastic hybrid optimal control problems are studied for systems where autonomous and controlled state jumps are allowed at the switching instants and, in addition to running costs, switching between discrete states incurs costs. Features of special interest in this work are the possibility of state space dimension change, and existence of low dimensional switching manifolds. In other words, the hybrid state space is considered as the direct product of a set of discrete state components with finite cardinality and a set of Euclidean spaces whose dimensions depend upon the discrete state components; and Euclidean spaces contain switching manifolds which correspond to autonomous switchings and jumps, and which are allowed to be codimension k submanifolds of the corresponding Euclidean state spaces, where k is greater than or equals to one. Statements of the Hybrid Minimum Principle (HMP) and Hybrid Dynamic Programming (HDP) are presented and it is shown that under certain assumptions the adjoint process in the HMP and the gradient of the value function in HDP are identical to each other almost everywhere along optimal trajectories. Furthermore, results for stochastic hybrid optimal control problems are established which generalize those of the deterministic case. A key feature of the stochastic hybrid systems framework under consideration is the presence of the hard constraints imposed by switching manifolds on diffusion-driven state trajectories; these constraints influence the boundary conditions in the Stochastic Hybrid Minimum Principle (SHMP). In addition to analytic examples, an electric vehicle equipped with a dual-stage planetary transmission is modelled in this framework, where, due to the special structure of the transmission, the mechanical degree of freedom changes during the transition period. Hybrid control problems for energy and time optimality of an electric vehicle acceleration task are studied which reveal unanticipated aspects of optimal energy saving strategies for the transmission control. " --