A Parameter Estimate Associated with the Adaptive Control of Stochastic Systems
Many physical phenomena are modeled by stochastic systems. Typically some parameters of the system are unknown so that these parameters must be estimated and often it is required to control this system. In this paper the parameter estimation problem is considered for this combined adaptive control problem. The unknown parameters appear affinely in the drift term of the stochastic differential equation that describes the nonlinear stochastic system. It is shown that the family of maximum likelihood estimates based on the observations of the system for increasing time are strongly consistent.
Unable to display preview. Download preview PDF.
- 4.T. E. Duncan and B. Pasik—Duncan, Adaptive control of continuous time linear systems, preprint.Google Scholar
- 5.T. E. Duncan and B. Pasik—Duncan, Adaptive control of linear delay time systems, preprint.Google Scholar
- 6.P. Hall and C. C. Heyde, Martingale Limit Theory and Its Applications, Academic Press, 1980.Google Scholar
- 7.K. It6 and H. P. McKean, Duffusion Processes and their Sample Paths, Springer—Verlag, 1965.Google Scholar
- 10.P. Mandl, The use of optimal stationary policies in the adaptive control of linear systems, Proc. Symp. to Honour Jerzy Heyman, Warsaw, 1974, 223–243.Google Scholar