Governing Parameter Changes in Nonlinear Parameter-Dependent Optimization Problems

The paper treats a class of parameter-dependent optimization/root finding problems where the minimizer or a real root need to be determined as a function of parameter. Applications of parameter-dependent optimization include spacecraft debris avoidance, adaptive control of Hybrid Electric Vehicles, engine mapping and model predictive control. In these and other problems, the parameter changes can be controlled either directly or indirectly. In this paper, the error analysis of a dynamic predictor-corrector Newton’s type algorithm is presented. Based on this analysis, an approach to govern the changes in the parameter to enable the algorithm to track the minimizer within an acceptable error bound is described. Two simulation examples are presented. In the first example the objective is to minimize the distance between points on a curve and a given set and simultaneously move as fast as possible along the given curve. In the second example we illustrate the use of this technique for aircraft flight envelope estimation. Specifically, we estimate maximum speed of an aircraft as a function of its altitude and flight path angle.