Robust simulation and analysis of nonlinear systems

Citation

Kantner, Michael James (1997) Robust simulation and analysis of nonlinear systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/BDXE-V419. https://resolver.caltech.edu/CaltechETD:etd-01102008-080147

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. For linear systems, robust analysis techniques are well developed. For non-linear systems, they are not. Most nonlinear analysis techniques use extensive simulation to examine system performance. However, these simulations do not give guarantees, they only describe local performance. This thesis presents a simulation technique, called robust simulation, that answers the nonlinear robust analysis question. For an uncertain nonlinear system and a set of initial conditions, robust simulation calculates the set of all possible trajectories. By applying a measure to the set of all trajectories, a performance guarantee is obtained. To allow efficient robust simulation, only discrete time piecewise linear systems are considered. This class of systems admits a wide variety of nonlinearities and can approximate generic nonlinear systems to any degree of accuracy. To measure performance, a generalized [...] norm is used. As in the linear case, the robust nonlinear analysis question cannot be answered exactly. Instead, upper and lower bounds are calculated. Many techniques, including traditional simulation, exist for finding lower bounds. Robust simulation provides efficient methods for calculating an upper bound. Robust simulation also supports simulation when multiple models exist for a single system. When modeling a physical system, any amount of complexity is possible. Traditional simulation of these models with different levels of detail yields different individual trajectories. Which is correct? By explicitly quantifying the uncertainty as noise, robust simulation calculates sets of possible trajectories. For each model the result is guaranteed to contain the true output. More detailed models yield smaller sets of possible trajectories. To test the algorithms, robust simulation is applied to a variety of examples. Algorithm performance is generally very good. Three other applications of robust simulation are also presented. In addition to measuring robust non-linear performance, robust simulation also generates lower bounds for model predictive control optimizations, verifies the stability of piecewise linear systems, and analyzes gain scheduled systems.

Thesis Files