Adaptive Information Processing and Global Optimization
Abstract
In the area of global optimization, we have analyzed the necessary and sufficient condition for the simulated annealing algorithm to hit the global minimum with probability. This entailed the development of a new theory of balance of recurrence orders for time-inhomogeneous Markov chains. In the area of adaptive control and filtering, we have developed the first convergence theory for least-squares based adaptive control - the most popular scheme. We have also developed a theory of parallel model adaptation which resolves the question of convergence of the output error identification and adaptive IIR filtering algorithms, which has been an open problem for about a decade now. Also we have proposed new algorithms for adaptive feedforward control and adaptive active noise canceling, and developed their analysis. We have applied for a patent on the latter scheme. In the area of robustness, we have shown that the simple modification of projecting the parameter estimates to stay in a compact convex set gives robustness not only with respect to bounded disturbances but also unmodeled dynamics. This resolves a question open for more than a decade.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 29, 1991
- Accession Number
- ADA248450
Entities
People
- P. R. Kumar
Organizations
- University of Illinois Urbana–Champaign