Date of Award
Doctor of Philosophy (PhD)
Professor J.W. Bandler
This thesis concerns itself with computer-aided techniques for design centering, tolerancing and tuning, fault location and model parameter identification from measurements.
Since many of the engineering system problems discussed in this thesis are formulated as optimization problems we examine algorithms and techniques for nonlinear optimization. Our attention is focused on minimax and ℓ₁ algorithms since many formulations of engineering system problems exploit the characteristic features of these two norms.
A novel approach for worst-case network design is proposed and an algorithm for the fixed tolerance problem embodying worst-case search and selection of sample points is presented.
The features of the ℓ₁ norm in the tuning problem are discussed in detail and explained using necessary conditions for optimality of the nonlinear ℓ₁ problems with nonlinear constraints. Regular and singular ℓ₁ problems are defined and a criterion for determining a singularity present in the ℓ₁ problem is formulated.
New formulations using the ℓ₁ norm are given for fault isolation and model parameter identification in analog circuits.
Practical engineering problems have been solved illustrating the wide applicability of the concepts used and the robustness of the algorithms employed.
A new algorithm for minimizing the cardinality of a set subject to nonlinear, nondifferentiable constraints is presented and illustrated by solving the best mechanical alignment problem. The load shedding and generation rescheduling problem in power systems is formulated using the ℓ₁ norm. The formulation is tested on 6-bus and 26-bus power systems. A general microwave multiplexer design procedure exploiting exact network sensitivities is introduced and illustrated by designing 5-channel, 11 GHz and 12-channel, 12 GHz multiplexers.
Kellermann, Witold, "Advances in Optimization of Circuits and Systems Using Recent Minimax and ℓ₁ Algorithms" (1985). Open Access Dissertations and Theses. Paper 1081.