The objective of this article is to make the analysis of the muscular force response to optimize electrical pulses train using Ding et al. force-fatigue model. A geometric analysis of the dynamics is provided and very preliminary results are presented in the frame of optimal control using a simplified input-output model. In parallel, to take into account the physical constraints of the problem, partial state observation and input restrictions, an optimized pulses train is computed with a model predictive control, where a non-linear observer is used to estimate the state-variables.
Citation: Toufik Bakir, Bernard Bonnard, Jérémy Rouot. A case study of optimal input-output system with sampled-data control: Ding et al. force and fatigue muscular control model[J]. Networks and Heterogeneous Media, 2019, 14(1): 79-100. doi: 10.3934/nhm.2019005
The objective of this article is to make the analysis of the muscular force response to optimize electrical pulses train using Ding et al. force-fatigue model. A geometric analysis of the dynamics is provided and very preliminary results are presented in the frame of optimal control using a simplified input-output model. In parallel, to take into account the physical constraints of the problem, partial state observation and input restrictions, an optimized pulses train is computed with a model predictive control, where a non-linear observer is used to estimate the state-variables.
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Figures(15) / Tables(1)
Toufik Bakir, Bernard Bonnard, Jérémy Rouot. A case study of optimal input-output system with sampled-data control: Ding et al. force and fatigue muscular control model[J]. Networks and Heterogeneous Media, 2019, 14(1): 79-100. doi: 10.3934/nhm.2019005
Time evolution of the permanent control (thin continuous line) and sampled-data control for several values of the sampling period
Evolution of
Relative error of the force for a well known and erroneous
General MPC strategy diagram
(left half plane)
Evolution of
Evolution of
Evolution of
Evolution of
Evolution of
Evolution of the force for a reference force of
Evolution of the interpulse (control) for a reference force of
Evolution of the amplitude (control) for a reference force of
Evolution of the interpulse (control) for a reference force of 425N and a preditive horizon of 10
Evolution of the amplitude (control) for a reference force of 425N and a preditive horizon of 3
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