Optimal containment control for a class of stochastic systems perturbed by poisson and wiener processes

Mean-square filtering problem for stochastic polynomial systems with Gaussian and Poisson noises

“…Theorem 1. The mean-square finite-dimensional filter for the third degree state (1), where the polynomial f (x,t) is defined by (12), is given by the equations (15) and (16) for the estimate m(t) = m G (t)+m P (t) and the equations (17) and (18) for the estimation error variance P(t) = P G (t) + P P (t).…”

“…x 2 (t) = 0.1x 3 2 (t) + ψ 1 (t) + N 1 (t), x 2 (0) = x 20 , and the scalar observation process be given by the linear equation (20) where N 1 (t) and N 2 (t) are Poisson white noises, which are the weak mean square derivatives of standard Poisson processes, and ψ 1 (t) and ψ 2 (t) are white noises, which are the weak mean square derivatives of standard Wiener processes (see [16]). The equations (19), (20) present the conventional form for the equations (1), (2), which is actually used in practice [27], [28].…”

“…The equations (19), (20) present the conventional form for the equations (1), (2), which is actually used in practice [27], [28].…”

Robust stabilization design for nonlinear stochastic system with Poisson noise via fuzzy interpolation method

“…Poisson processes should be also considered when a dynamic system is exposed to sudden, infrequent, highly localized changes that occur in a short period of time such as earthquakes, large random weather fluctuations, or occasional mass mortalities [8,4,1]. Poisson processes quite frequently arise in engineering, manufacturing, economics, and biosystem applications [17]. In manufacturing systems, the Poisson processes may represent the effects of the machine breakage or repair [34].…”

Mean-square filter design for stochastic polynomial systems with Gaussian and Poisson noises

“…It is known that the mean-square filter for linear systems with Poisson white noises coincides with the Kalman-Bucy filter (Liptser and Shiryayev 1989;Pugachev and Sinitsyn 2001). Other results related to non-linear Poisson systems can be found in Lu, Liang, and Chen (2001), Kolmanovsky and Maizenberg (2002a), Hannequin and Mas (2002), Kolmanovsky and Maizenberg (2002b), Zhang, Fadili, Starck, and Dige (2008b), Dupé, Fadili, and Starck (2008), Zhang, Fadili, and Starck (2008a), , Basin, Maldonado, and Karimi (2011), Basin and Maldonado (2012). However, to the best of authors' knowledge, no filtering algorithms solving the mean-square filters * Corresponding author.…”