Optimal Control of Switching Diffusions With Application to Flexible Manufacturing Systems

Abstract

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Stochastic Reachability Analysis of Hybrid Systems

“…The original formulation of many of these models includes control inputs [19,34,64,[103][104][105] but other models are autonomous [122]. To allow a uniform presentation we discuss only the autonomous versions for all models.…”

“…Switching diffusion processes (SDPs) were introduced by Ghosh In the following we introduce formally SDP following [103][104][105]. To allow a comparison with other SHP we restrict our attention to autonomous SDP.…”

“…For i, j ∈ Q and z ∈ R n let Δ(i, j, z) be consecutive, with respect to lexicographic ordering on Q × Q, left closed, right open intervals of the real line, each having length λ ij (z) (for details see [103][104][105]). Now define a function…”

“…There has been considerable current interest in stochastic hybrid systems due to their ability to represent such systems as manoeuvring aircraft [132] and switching communication networks [117]. Other areas to which stochastic hybrid systems have found applications include insurance pricing [63], capacity expansion models for the power industry [66], flexible manufacturing and fault tolerant control [104,105].…”

Exponential stability of nonlinear ito differential systems with time-delay and Markovian switching

“…, , , , , , , , Markovian [1] Markovian , Markovian , Markovian Markovian Basak [2] Ghosh [3] Ji Chizeck [4] Mao [5] Mao [6] Skorohod [7] , Mao [5] Mao [6] Lyapunov [8] , , [ …”