Enhanced Collocation Method for Dynamical Systems Subject to Finite Set Control

摘要

An enhanced optimizationmethod, rooted in direct collocation, is formulated to treat a specific class of continuous-rntime hybrid control systems; specifically, dynamical systems that depend on continuous state variables and spatiallyrndiscrete control variables. In this study, a spatially discrete control variable refers to one that is defined over therncontinuous-time domain yet is constrained to a range of discrete finite values. This subset of hybrid control systems isrntermed here as finite set control. Traditionally, optimal control for hybrid systems of this class is formulated in therncontext of mixed-integer nonlinear programming. The numerical efficiency of these methods, however, is adverselyrnaffected by the number of independent control variables and the range of the combined set. The methodologyrnpresented in this study focuses on this class of problems: multiple independent control variables, each with a uniquernrange and a switching schedule independent from the others. The resulting formulation leads to a morerncomputationally efficient nonlinear program suitable for the identification of optimal control solutions for this classrnof hybrid systems.