Details

Autor(en) / Beteiligte

• Popovic, Dobrivoje

Titel

Topics in extremum seeking

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2004

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Extremum Seeking is on-line optimization of unknown functions given as response maps of physical plants. A response map is the steady-state relationship between the input parameters of a plant and its performance output. Neither the dynamical model of the plant nor the model of the response map is available. Therefore, to optimize the map, an algorithm can rely only on map measurements, collected by assigning step commands to the parameters, and measuring the resulting plant performance after the large transients have settled. We start this dissertation with an investigation of stability properties of an extremum seeking loop created by an optimized plant and an optimization algorithm. In some extremum seeking problems; response maps are nonsmooth. Motivated by this, in this dissertation we design Direct Search algorithms for minimization of nonsmooth maps. Namely, the convergence properties of existing Direct Search methods were analytically established only recently, and only for continuously differentiable functions. We prove that our new algorithms will locate minima (stationary points) of locally Lipschitz maps. We present the theory behind the new algorithms, together with some numerical results. Next, we present a new stochastic optimization algorithm based on the currently popular Simultaneously Perturbed Stochastic Approximation. The reason for the new algorithm is that in some constrained problems the standard SPSA may exhibit slow convergence due to “iterate bouncing against the constraints.” We discuss the nature of this phenomenon, and present a modified SPSA algorithm that does not suffer from it. We used the modified SPSA algorithm in an important extremum seeking application: on-line optimization of an automotive engine. We show results developed in collaboration with Ford Research and Advanced Engineering. In a Ford engine test facility, we built an extremum seeking tool that automatically locates values of engine parameters that minimize the fuel consumption. This work demonstrates that extremum seeking can be used as a fast alternative to existing engine optimization methods, such as engine mapping.