Stochastic differential equations and their application to randomly time varying control systems
Sibul, Leon H.
MetadataShow full item record
Let a control system be represented by a system of n first-order stochastic differential equations / ;(t, (I))=a(t, (I))y(t, (1))+ Ux(t, (I)) wEn on (n,!E, P) and tET / where the coefficient matrix a(t, m) is a sum of a deterministic matrix and a. stochastic matrix a(t, 0»). It is assumed that the deterministic part of the system is stable in the sense of Lyapunov. The stochastic differential equation becomes now an integral equation with a stochastic kernel. This integral equation is solved by constructing a resolvent kernel by means of a Neumann series expansion. Sufficient conditions for almost sure unifonn convergence of the Neumann series expansion are given. Integral expressions for the expectation and covariance matrix of the stochastic vector y(t. m) are found. These results have many applications in control systems theory.
The article of record as published may be found at https://doi.org/10.1080/00207177708922260
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Blackner, Ronald Keith (Monterey, California. Naval Postgraduate School, 1967);A least squares estimator is derived for the state transition matrix phi of a linear, stationary sampled data system operating in a stochastic environment. The estimator is shown to be unbiased and minimum variance under ...
On the implementation of reduced, sub-optimal Kalman filters, for discrete, linear, stochastic processes with time-invariant dynamics. Lara, Juan Francisco (Monterey, California. Naval Postgraduate School, 1969-12);Three different approaches to the problem of implementing a reduced-order, sub-optimal Kalman filter for a discrete, linear stochastic process, with time-invariant dynamics, are presented. A first method, A, is based ...
Goggins, David A. (Monterey, California. Naval Postgraduate School, 1995-09);This thesis is a continuation of optimization modeling research conducted at the Naval Postgraduate School for the U.S. Air Force Studies and Analyses Agency. That work resulted in Throughput II, a multi-period model for ...