Adaptive control of linear stochastic evolution systems
- 1 August 1991
- journal article
- research article
- Published by Taylor & Francis in Stochastics and Stochastic Reports
- Vol. 36 (2) , 71-90
- https://doi.org/10.1080/17442509108833711
Abstract
An adaptive control problem for some linear stochastic evolution systems in Hilbert spaces is formulated and solved in this paper. The solution includes showing the strong consistency of a family of least squares estimates of the unknown parameters and the convergence of the average quadratic costs with a control based on these estimates to the optimal average cost. The unknown parameters in the model appear affinely in the infinitesimal generator of the C 0 semigroup that defines the evolution system. A recursive equation is given for a family of least squares estimates and the bounded linear operator solution of the stationary Riccati equation is shown to be a continuous function of the unknown parameters in the uniform operator topologyKeywords
This publication has 12 references indexed in Scilit:
- Adaptive control of continuous-time linear stochastic systemsMathematics of Control, Signals, and Systems, 1990
- Identification of an Infinite-Dimensional Parameter for Stochastic Diffusion EquationsSIAM Journal on Control and Optimization, 1988
- Adaptive control of linear delay time systems *Stochastics, 1988
- Regularity of solutions of linear stochastic equations in hilbert spacesStochastics, 1988
- On minimum-contrast estimation for hilbert space-valued stochastic differential equationsStochastics, 1986
- Semilinear stochastic evolution equations: boundedness, stability and invariant measurestStochastics, 1984
- Stochastic differential equations in Hilbert spacesBanach Center Publications, 1979
- Remarks on the algebraic Riccati equation in Hilbert spaceApplied Mathematics & Optimization, 1975
- Une formule d'isométrie pour l'intégrale stochastique hilbertienne et équations d'évolution linéaires stochastiquesProbability Theory and Related Fields, 1975
- Extending a theorem of A. M. Liapunov to Hilbert spaceJournal of Mathematical Analysis and Applications, 1970