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Stochastic diffrential equations on Banach spaces and their optimal feedback control

(2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems....

Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality

N.U. Ahmed (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the question of optimal control for a class of stochastic evolution equations on infinite dimensional Hilbert spaces with controls appearing in both the drift and the diffusion operators. We consider relaxed controls (measure valued random processes) and briefly present some results on the question of existence of mild solutions including their regularity followed by a result on existence of partially observed optimal relaxed controls. Then we develop the necessary conditions...

Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model

Nabil Rachdi, Jean-Claude Fort, Thierry Klein (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial...

Stochastic multivariable self-tuning tracker for non-gaussian systems

Vojislav Filipovic (2005)

International Journal of Applied Mathematics and Computer Science

This paper considers the properties of a minimum variance self-tuning tracker for MIMO systems described by ARMAX models. It is assumed that the stochastic noise has a non-Gaussian distribution. Such an assumption introduces into a recursive algorithm a nonlinear transformation of the prediction error. The system under consideration is minimum phase with different dimensions for input and output vectors. In the paper the concept of Kronecker's product is used, which allows us to represent unknown...

Strong average optimality criterion for continuous-time Markov decision processes

Qingda Wei, Xian Chen (2014)

Kybernetika

This paper deals with continuous-time Markov decision processes with the unbounded transition rates under the strong average cost criterion. The state and action spaces are Borel spaces, and the costs are allowed to be unbounded from above and from below. Under mild conditions, we first prove that the finite-horizon optimal value function is a solution to the optimality equation for the case of uncountable state spaces and unbounded transition rates, and that there exists an optimal deterministic...

The optimal control chart procedure

Jaroslav Skřivánek (2004)

Kybernetika

The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span k is specified by a partition of the space ℝ k into three disjoint parts. We call this partition as the control chart frame of span k . A shift in the process parameter is signalled at time t by having the vector of the last k sample characteristics fall out of the...

The risk-sensitive Poisson equation for a communicating Markov chain on a denumerable state space

Rolando Cavazos-Cadena (2009)

Kybernetika

This work concerns a discrete-time Markov chain with time-invariant transition mechanism and denumerable state space, which is endowed with a nonnegative cost function with finite support. The performance of the chain is measured by the (long-run) risk-sensitive average cost and, assuming that the state space is communicating, the existence of a solution to the risk-sensitive Poisson equation is established, a result that holds even for transient chains. Also, a sufficient criterion ensuring that...

The value function in ergodic control of diffusion processes with partial observations II

Vivek Borkar (2000)

Applicationes Mathematicae

The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equivalent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated discounted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular to a "martingale"...

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