Approximate Linear Regulator and Kalman Filter
Abstract
Practical dynamic systems constantly face unpredictable fluctuations and disturbances for which Kalman filter has been shown to be effective in estimating the states from the outputs corrupted by white noises. This is the Kalman filtering problem. On the other hand, the Linear regulator problem, which is the mathematical dual of the Kalman filtering problem, plays an important role in modern optimal control theory. Both problems can be formulated as quadratic synthesis problems. A geometric-series approach is used to approximate the exponentials of Hamiltonian matrices for the quadratic synthesis problems. The approximants of the discretized transition matrices are then used to construct piecewise-constant gains and piecewise time-varying gains for approximating time-varying optimal gains and time-varying Kalman gains. Simple and fast algorithms are developed and can be easily implemented on a low cost minicomputer or microprocessor. The proposed methods have been successfully applied to the analysis of practical control systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1980
- Accession Number
- ADA092176
Entities
People
- Leang S. Shieh
- Willon B. Wai
Organizations
- University of Houston