Estimation and Detection with Chaotic Systems
Abstract
Chaotic systems have received much attention in the mathematics and physics communities in the last two decades; and they are receiving increasing attention in various engineering disciplines as well. Experimental evidence suggests that these systems may be useful models for a wide variety of physical phenomena, including turbulence, vibrations of buckled elastic structures, and behavior of certain feedback control devices. This thesis deals with both the analysis and synthesis of chaotic maps and time-sampled chaotic flows, with a focus on the problems and issues that arise with noise-corrupted orbit segments generated by these maps and flows. Both dissipative and nondissipative systems are considered, with both types of systems considered in the context of analysis and the latter type also considered in the context of synthesis. With respect to dissipative systems, three probabilistic state estimation algorithms are introduced and applied to three problem scenarios, with the scenarios distinguished by the amount of a priori knowledge of the dynamics of the underlying chaotic system. Cramer-Rao, Barankin, and Weiss-Weinstein upper bounds on state estimator performance are derived and both experimentally and qualitatively analyzed. The analysis reveals that intrinsic properties of chaotic systems-positive Lyapunov exponents and boundedness of attractors-have a fundamental influence on achievable state estimator performance with these systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1994
- Accession Number
- ADA459508
Entities
People
- Michael D. Richard
Organizations
- Massachusetts Institute of Technology