Extended separation theorem and exact analytical solution of stochastic control
✍ Scribed by T.J Tarn
- Publisher
- Elsevier Science
- Year
- 1971
- Tongue
- English
- Weight
- 606 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0005-1098
No coin nor oath required. For personal study only.
✦ Synopsis
Le th6or~me de s6paration 6tendu et la solution analytique exacte de la commande al6atoire
Erweitertes Separations-Theorem und exakte analytische L6sung einer stochastischen Steuerung Pactur~peHHa~ TeopeMa pa3)/e.qeHr~ rf TOqHOe aHa.qHTtaqecKoe pemeHrte c~yqafiHoro ynpaBaeHrtn T. J. TARNS"
The separation theorem has been extended to hold when the noises have unknown variances. When the mean and variance of the plant noise are unknown, the analytical solution of the control law may be obtained.
Summary--The stochastic optimal control of linear, discrete scalar systems are studied. A method is presented for relaxing the usual assumption that the probability distributions of the disturbances are perfectly known. Two problems are considered here: (1) the problem where the plant noise variance and the measurement noise variance both are unknown but fixed, and it is shown that the well-known separation theorem for the filtering and control still holds; and (2) the problem where the mean and variance of the plant disturbance are unknown but fixed with perfect measurement. The exact analytical solution of the feedback control law is obtained.