607 research outputs found
Linear estimation in Krein spaces. Part II. Applications
We have shown that several interesting problems in H∞-filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in Part I. We show that all these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models and error Gramians, we can use the Krein-space estimation theory to calculate the stationary points and study their properties. The approach discussed here allows for interesting generalizations, such as finite memory adaptive filtering with varying sliding patterns
H
With the help of a stochastic bounded real lemma, we deal with finite horizon H2/H∞ control problem for discrete-time MJLS, whose Markov chain takes values in an infinite set. Besides, a unified control design for H2, H∞, and H2/H∞ is given
Mean-Field Stochastic Linear Quadratic Optimal Control Problems: Closed-Loop Solvability
An optimal control problem is studied for a linear mean-field stochastic
differential equation with a quadratic cost functional. The coefficients and
the weighting matrices in the cost functional are all assumed to be
deterministic. Closed-loop strategies are introduced, which require to be
independent of initial states; and such a nature makes it very useful and
convenient in applications. In this paper, the existence of an optimal
closed-loop strategy for the system (also called the closed-loop solvability of
the problem) is characterized by the existence of a regular solution to the
coupled two (generalized) Riccati equations, together with some constraints on
the adapted solution to a linear backward stochastic differential equation and
a linear terminal value problem of an ordinary differential equation.Comment: 23 page
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