Optimization of hybrid discrete/continuous dynamic systems

Many engineering applications call for the open loop optimization of a hybrid (discrete/continuous) dynamic system. Examples include the design of operating procedures for process start-up, shut-down and changeovers, the design of emergency shutdown systems, or the optimal design of inherently dynamic processes such as those operated in a batch, semi-continuous and/or periodic manner. The most intriguing class of problems are those in which the optimal trajectories an characterized by a sequence of switches and/or jumps at events, some of which are dependent on the state of the system satisfying certain conditions (state or implicit events), and it is necessary to search over several alternative sequences of events to find the optimal one. The potential for numerical optimization procedures to make optimal sequencing decisions in hybrid dynamic systems is explored. A general formulation of the hybrid optimal control problem is presented. Novel existence and uniqueness results for the parametric sensitivity functions of a hybrid system show that parameter optimization of hybrid dynamic systems (including sequencing decisions) is in general nonsmooth, but also smooth in many important cases. For illustration, the design of a minimum time changeover operation for a pressure vessel avoiding the formation of explosive mixtures is considered. In closing, progress on more systematic approaches to the solution of the resulting nonsmooth optimization problems are discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.