Model predictive control of constrained Markovian jump nonlinear stochastic systems and portfolio optimization under market frictions

Automatica ◽  
2018 ◽  
Vol 87 ◽  
pp. 61-68 ◽  
Author(s):  
Vladimir Dombrovskii ◽  
Tatiana Obyedko ◽  
Maria Samorodova
Keyword(s):  
Model Predictive Control ◽  
Portfolio Optimization ◽  
Predictive Control ◽  
Stochastic Systems ◽  
Market Frictions ◽  
Markovian Jump ◽  
Nonlinear Stochastic Systems

scholarly journals Stationary Response of a Class of Nonlinear Stochastic Systems Undergoing Markovian Jumps

2015 ◽  
Vol 82 (5) ◽  
Author(s):  
Rong-Hua Huan ◽  
Wei-qiu Zhu ◽  
Fai Ma ◽  
Zu-guang Ying
Keyword(s):  
Stochastic Systems ◽  
Original System ◽  
Stochastic Averaging ◽  
Kolmogorov Equation ◽  
Markovian Jump ◽  
Nonlinear Stochastic Systems ◽  
Stationary Response ◽  
Set Up ◽  
Jump Systems ◽  
Stationary Probabilities

Systems whose specifications change abruptly and statistically, referred to as Markovian-jump systems, are considered in this paper. An approximate method is presented to assess the stationary response of multidegree, nonlinear, Markovian-jump, quasi-nonintegrable Hamiltonian systems subjected to stochastic excitation. Using stochastic averaging, the quasi-nonintegrable Hamiltonian equations are first reduced to a one-dimensional Itô equation governing the energy envelope. The associated Fokker–Planck–Kolmogorov equation is then set up, from which approximate stationary probabilities of the original system are obtained for different jump rules. The validity of this technique is demonstrated by using a nonlinear two-degree oscillator that is stochastically driven and capable of Markovian jumps.

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