Stochastic H2/H∞-control for a dynamical system with internal noises multiplicative with respect to state, control, and external disturbance

Authors:
M. E. Shaikin
Affiliations:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Venue:
Automation and Remote Control
Year:
2013

Citing 4
Cited 0

Minimum entropy H∞ control

Minimum entropy H∞ control
Stochastic $H^\infty$

SIAM Journal on Control and Optimization
Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control

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Anisotropy-based robust performance analysis of finite horizon linear discrete time varying systems

Automation and Remote Control

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Abstract

We consider an optimal control problem for a dynamical system under the influence of disturbances of both deterministic and stochastic nature. The system is defined on a finite time interval, and its diffusion coefficient depends on the control signal. The controller in the feedback circuit is assumed to be static, nonstationary, linear in the state vector, and satisfying the condition 驴L驴驴驴 that bounds the norm of operator L: v 驴z for the transition of external disturbance to the controllable output signal. Solving the optimization H 2/H 驴-control problem, we get three matrix functions satisfying a system of two differential equations of Riccati type and one matrix algebraic equation. In the special case of a stochastic system whose diffusion coefficient does not depend on the control signal, the system is reduced to two related Riccati equations.