Abstract
This paper announces initial results of studies on partially observed linear quadratic Gaussian (LQG) models where the stochastic disturbances depend on both states and controls and the measurements may be bilinear in the noise and the states/controls. While the Separation Theorem of standard LQG design does not apply in any strict sense, suboptimal linear state estimate feedback laws are derived based on certain linearizations. The controllers may well be useful for nonlinear stochastic systems where linearized models which include terms bilinear in the noise and states/controls are significantly more accurate than if these terms are set to zero. These controllers are calculated by solving a generalized discrete time Riccati equation. The properties of this equation relating to well posedness of the associated LQG problem are discussed.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35359-3_40
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Keywords
- Riccati Equation
- Nonlinear Stochastic System
- Stochastic Disturbance
- Linear Quadratic Gaussian
- Matrix Riccati Equation
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References
B.D.O. Anderson and J.B. Moore. Optimal Control: Linear Quadratic Methods. Prentice Hall, New Jersey, 1989.
B.D.O. Anderson and J.B. Moore. Optimal Filtering. Prentice Hall, New Jersey, 1978.
M.H.A. Davis. Linear Estimation and Stochastic Control Chapman and Hall, London, 1977.
R.J. Elliott, L Aggoun and J.B. Moore. Hidden Markov Models: Estimation and Control. Springer-Verlag, 1995.
J.B. Moore, X.Y. Zhou and A.E.B. Lim. Suboptimal LQG control of linear systems with control dependent noise. (submitted).
S.P. Chen, X.J. Li and X.Y. Zhou. Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Contr. Optim., to appear.
A.E.B. Lim and X.Y. Zhou. Optimal stochastic LQR control with integral quadratic constraints and indefinite control weights. (preprint)
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© 1999 IFIP International Federation for Information Processing
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Moore, J.B., Zhou, X., Lim, A.E.B. (1999). On LQG Control of Linear Stochastic Systems with Control Dependent Noise. In: Chen, S., Li, X., Yong, J., Zhou, X.Y. (eds) Control of Distributed Parameter and Stochastic Systems. IFIP Advances in Information and Communication Technology, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35359-3_30
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DOI: https://doi.org/10.1007/978-0-387-35359-3_30
Publisher Name: Springer, Boston, MA
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