Deterministic Approaches to Transient Trajectory Generation

Abstract

This chapter studies a deterministic approach to transient trajectory generation and control as applied to the forced Van der Pol oscillatory system. This type of system tends towards a strongly nonlinear system, which can be considered chaotic. A classical tuning method, targeted exponential weighting, and isolated trajectory fractionalization trajectory generation methods are examined. Illustrating the given deterministic approach via the Van der Pol system highlights the potentially iterative nature of deterministic methods, and that traditional optimal linear time-invariant control techniques are unable to perform as desired whereas even an idealized nonlinear feedforward control significantly outperforms at the steady-state. It will be shown that utilizing a-priori knowledge of the system dynamics will enable the isolated trajectory fractionalization method to minimize the nonlinear transient effects due to miss-modeled or unmodeled plant dynamics, and that this benefit can be coupled with the targeted exponential weighting approach for greatly decreased trajectory tracking error on the order of a 92% reduction of the objective cost function in the presented case study based on the forced Van der Pol system.