Jianfeng Feng et al 2003 J. Phys. A: Math. Gen. 36 7469 doi:10.1088/0305-4470/36/27/301
Jianfeng Feng1, Kewei Zhang2 and Yousong Luo3
Show affiliationsWe present an analytical and rigorous study on a TOPS (task optimization in the presence of signal-dependent noise) model with a hold-on or an end-point control. Optimal control signals are rigorously obtained, which enables us to investigate various issues about the model including its trajectories, velocities, control signals, variances and the dependence of these quantities on various model parameters. With the hold-on control, we find that the optimal control can be implemented with an almost 'nil' hold-on period. The optimal control signal is a linear combination of two sub-control signals. One of the sub-control signals is positive and the other is negative. With the end-point control, the end-point variance is dramatically reduced, in comparison with the hold-on control. However, the velocity is not symmetric (bell shape). Finally, we point out that the velocity with a hold-on control takes the bell shape only within a limited parameter region.
87.10.-e General theory and mathematical aspects
92Bxx Mathematical biology in general
92B20 Neural networks, artificial life and related topics (See also 68T05, 82C32, 94Cxx)
Issue 27 (11 July 2003)
Received 26 February 2003, in final form 20 May 2003
Published 25 June 2003
Jianfeng Feng et al 2003 J. Phys. A: Math. Gen. 36 7469
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