Abstract
In this paper, we use an information geometric algorithm to solve the distribution control problem. The new designed algorithm is called principal whitened gradient-projection algorithm. In the principal natural gradient step, we use principal whitened gradient algorithm to obtain an optimal trajectory of the weight vector on the B-spline manifold from the viewpoint of information geometry. In the projection step, we project the selected points on B onto M. The coordinates of the projections on M give the trajectory of the control input u.
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References
Donson C, Wang H. Itertative approximation of statistical distribution and relation to information geometry. J Stat Infer Stoch Proc, 2001, 147: 307–318
Gao Z, Wang H, Chai T. A robust fault detection filtering for stochastic distribution systems via descriptor estimator and parametric gain design. IET P-Contr Theor Ap, 2007, 1: 1286–1293
Wang H. Detect unexpected changes of particle size distribution in paper-making white water system. In: Proceedings of IFAC Fault Detection and Diagnosis Lyon. New York: Marcel Dekker Inc, 1998. 78–84
Wang H. Minimum entropy control of non-Gaussian dynamic stochastic systems. IEEE Trans Automat Contr, 2002, 47: 398–403
Zhang Z, Sun H, Zhong F. Natural gradient-projection algorithm for distribution control. Optim Contr Appl Met, 2009, 30: 495–504
Wang H, Baki H, Kabore P. Control of bounded dynamic stochastic distributions using squre root models: an applicability study in papermaking systems. Trans I Meas Control, 2001, 23: 51–68
Wang H. Model reference adaptive control of the output stochastic distributions for unknown linear stochastic systems. Int J Syst Sci, 1999, 30: 707–715
Wang H. Bounded Dynamic Stochastic Systems: Modeling and Control. London: Springer-Verlag, 2000
Amari S. Differential Geometrical Methods in Statistics. New York/Tokyo: Springer-Verlag, 1985. 15–24
Amari S. Natural gradient works efficiently in learning. Neural Comput, 1998, 10: 251–276
Yang Z, Laaksonen J. Principal whitened gradient for information geometry. Neural Networks, 2008, 21: 232–240
Amari S. Information geometry of the EM and em algorithm for neural networks. Neural Networks, 1995, 8: 1379–1408
Amari S, Kurata K, Nagaoka H. Information geometry of Boltzmann machines. IEEE Trans Neural Networ, 1992, 3: 260–271
Ohara A, Suda N, Amari S. Dualistic differential geometry of positive definite matrices and its applications to related problems. Linear Algebra Appl, 1996, 247: 31–53
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Zhang, S., Sun, H. & Li, C. Principal whitened gradient-projection algorithm for distribution control. Sci. China Inf. Sci. 56, 1–8 (2013). https://doi.org/10.1007/s11432-011-4500-8
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DOI: https://doi.org/10.1007/s11432-011-4500-8