Advertisement

Discrete-time stochastic H2 optimal control

  • Vasile Drăgan
  • Toader Morozan
  • Adrian-Mihail Stoica
Chapter

Abstract

In this chapter the problem of H2 control of a discrete-time linear system subject to Markovian jumping and independent random perturbations is considered. Several kinds of H2-type performance criteria (often called H2 norms) are introduced and characterized via solutions of some suitable linear equations on the spaces of symmetric matrices. The purpose of such performance criteria is to provide a measure of the effect of additive white noise perturbation over an output of the controlled system. Different aspects specific to the discrete-time framework are emphasized. Firstly, the problem of optimization of H2 norms is solved under the assumption that a full state vector is available for measurements. One shows that among all stabilizing controllers of higher dimension, the best performance is achieved by a zero-order controller. The corresponding feedback gain of the optimal controller is constructed based on the stabilizing solution of a system of discrete-time generalized Riccati equations. The case of discrete-time linear stochastic systems with coefficients depending upon the states both at time t and at time t-1 of theMarkov chain is also considered. Secondly, the H2 optimization problem is solved under the assumption that only an output is available for measurements. The state space realization of the H2 optimal controller coincides with the stochastic version of the well-known Kalman-Bucy filter. In the construction of the optimal controller the stabilizing solutions of two systems of discrete-time coupled Riccati equations are involved. Because in the case of the systems affected by multiplicative white noise the optimal controller is hard to implement, a procedure for designing a suboptimal controller with the state space realization in a state estimator form is provided. Finally a problem of H2 filtering in the case of stochastic systems affected by multiplicative and additive white noise and Markovian switching is solved.

Keywords

Feedback Gain Optimal Controller Markovian Switching Fundamental Matrix Solution State Space Realization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vasile Drăgan
    • 1
  • Toader Morozan
    • 1
  • Adrian-Mihail Stoica
    • 2
  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucuresti 1Romania
  2. 2.Faculty of Aerospace EngineeringUniversity “Politehnica” of BucharestBucurestiRomania

Personalised recommendations