OPTIMAL CONTROL OF SYSTEMS WITH STOCHASTIC DISTURBANCES,
Abstract
The Optimal Control of a Linear System which is disturbed by white (or Linear Markov) additive noise is discussed. The state of the system cannot be measured directly, but is corrupted by additive white (or Linear Markov) noise. The Cost Function used is quadratic. It is proved that the Optimal Controller is a linear function of the observations only if both noises are Gaussian. This implies that the minimal cost of controlling this system, when subjected to Gaussian noise, is strictly higher than when subjected to any non-Gaussian noise, which has the same second order properties as the Gaussian. Besides this proof, Kalman's Best Linear Optimal Controller is extended to a Polynomial Controller. This controller retains the same features as Kalman's Best Linear Controller; namely, only the first few moments of the Best Estimate must be updated as the process evolves. While the Optimal Linear Controller requires the updating of only the mean and the variance, the n-th order Polynomial Controller requires the updating of the 2n first moments. These results can also be applied to Optimal Filtering. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 25, 1963
- Accession Number
- AD0430078
Entities
People
- Raphael Sussman
Organizations
- University of California, Berkeley