Improved indirect method for air-vehicle trajectory optimization

An improved indirect method is presented for air-vehicle vertical-plane, two-point boundary-value trajectory optimization. The performance index is related to minimizing an integral weighted sum of quadratic terms in aerodynamic angle and propulsive thrust, modified to exclude all penalties associated with non-maneuvering flight. For this index, costate rates are constants if the dynamic model is continuous, assuring costale system stability, increasing radii of convergence in costate initializations, and facilitating propagation of costates. A multimodal, four-dimensional search initializes costates using predictive trajectory shooting. Multiple modes of the costate space are investigated in the search via simultaneous, parallel threads of computation. Within each thread, trial variances are adjusted adaptively to find a modal region of global quality and converge rapidly toward its best point. Costate-rate adaptation refines the initialization and subsequently provides compensation for identifiable changes in system parameters. Collocated analytical solutions, polynomial networks, and neural models are not used. Simulation results are presented for ascent and descent maneuvers of a notional unmanned air vehicle.