Estimation and control of systems with unknown covariance and multiplicative noise
- 1 January 1989
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 34 (10) , 1075-1078
- https://doi.org/10.1109/9.35279
Abstract
The problem of estimation and control for systems with multiplicative noise and unknown second-order statistics is considered. Conditions are found for the existence of a solution based on game theoretic ideas. The conditions for the existence of a saddle point for the time-invariant filtering problem are necessary and sufficient, whereas for all other cases only necessary. The central idea of the solution is to convert the stochastic problem to a deterministic optimal control problem whose minimax point is sought with respect to the control, filter, and unknown statistics parameters. The results that are derived show that the problem of estimation for systems with unknown covariances depends on the costate matrix, which in turn is a function of the performance measure. Thus, the filter loses one of its best known properties, that of independence of the performance functional. This property holds not only for the classical Kalman filter but also for multiplicative systems.Keywords
This publication has 9 references indexed in Scilit:
- Robust static and dynamic output-feedback stabilization: Deterministic and stochastic perspectivesIEEE Transactions on Automatic Control, 1987
- Robust controller synthesis using the maximum entropy design equationsIEEE Transactions on Automatic Control, 1986
- The optimal projection/maximum entropy approach to designing low-order, robust controllers for flexible structuresPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1985
- Controller design of systems with multiplicative noiseIEEE Transactions on Automatic Control, 1985
- Minimax linear observers and regulators for stochastic systems with uncertain second-order statisticsIEEE Transactions on Automatic Control, 1984
- Noncausal minimax linear state estimation for systems with uncertain second-order statisticsIEEE Transactions on Automatic Control, 1984
- Robust filtering and prediction for linear systems with uncertain dynamics: A game-theoretic approachIEEE Transactions on Automatic Control, 1983
- Minimax control of linear stochastic systems with noise uncertaintyIEEE Transactions on Automatic Control, 1983
- Minimax state estimation for linear stochastic systems with noise uncertaintyIEEE Transactions on Automatic Control, 1981