Abstract
By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG control problem decomposes, or separates, into an optimal state-feedback control problem and an optimal state estimation problem. That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation, but also can be used to solve the estimated state from the time-variant differential equations. The high precision of precise integration is of advantage for the control and estimation. Numerical examples demonstrate the high precision and effectiveness of the algorithm.
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References
ZHENG Da-zhong.Linear System Theory [M]. Beijing: Tsinghua University Press, 1990, (in Chinese).
Green M, Limebeer D J N.Linear Robust Control [M]. Prentice-Hall, 1995.
Meirovitch L.Dynamic and Control of Structures [M]. J Wiley & Sons, 1990.
Doyal J C, Glover K, Khargoneker P P et al., State space solutions to standardH 2 andH ∞ control problems[J].IEEE Trans Automat Control 1989,34(8):831–847.
SHEN Tue-long.H ∞ Control Theory and Application [M]. Beijing: Tsinghua University Press, 1996. (in Chinese)
ZHONG Wan-xie et al.Computation Structural Mechanics and Optimal Control [M], Dalian: Dalian University of Technology Press, 1993. (in Chinese)
ZHONG Wan-xie.A New Systematic Methodology for Theory of Elasticity [M]. Dalian: Dalian University of Technology Press, 1995. (in Chinese)
ZHONG Wan-xie. The precise integration for matrix Riccati equations[J].Computational Struct Mech Applic, 1994,11(2):113–119. (in Chinese)
ZHONG Wan-xie. The precise integration of LQ control problems[J]. {jtJ Automat}, {dy2000}, {vn26}({sn5}).
ZHONG, Wan-xie. The precise integration of Kalman-Bucy filtering problems[J].J Dalian University of Technology, 1999,39(2):191–200. (in Chinese)
LU Kai, TIAN Wei-fengOptimal Estimation Theory and Applications to Navigation [J]. Shanghai: Shanghai Jiaotong University Press, 1990 (in Chinese)
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Paper from ZHONG Wan-xie, Member of Editorial Committee, AMM
Foundation item: the National Natural Science Foundation of China (19732020)
Biographies: ZHONG Wan-xie (1934-) CAI Zhi-qin (1961-)
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Wan-xie, Z., Zhi-qin, C. Precise integration method for LQG optimal measurement feedback control problem. Appl Math Mech 21, 1417–1422 (2000). https://doi.org/10.1007/BF02459220
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DOI: https://doi.org/10.1007/BF02459220
Key words
- precise integration
- LQG measurement feedback control
- Riccati differential equation
- time-variant differential equation