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Research Papers

Stochastic Recruitment Control of Large Ensemble Systems With Limited Feedback

[+] Author and Article Information
Lael U. Odhner1

Department of Mechanical Engineering, Yale University, New Haven, CT 06520lael.odhner@yale.edu

Harry Asada

Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139asada@mit.edu

Real physical systems, such as muscle actuators, often exhibit transient dynamics and time delays. In this paper we assume that the sampling interval of discrete-time models is long enough to absorb all transient dynamics and time delays.

Consider, for instance, the example of a bang-bang controlled positioning stage having position confirmation switches at preset locations.

These results were found using the value iteration algorithm, for a controller with measurements of the exact number of on agents.

1

Corresponding author.

J. Dyn. Sys., Meas., Control 132(4), 041008 (Jun 17, 2010) (9 pages) doi:10.1115/1.4001706 History: Received February 25, 2008; Revised October 16, 2009; Published June 17, 2010; Online June 17, 2010

A new approach to controlling the ensemble behavior of many identical agents is presented in this paper, inspired by motor recruitment in skeletal muscles. A group of finite state agents responds randomly to broadcast commands, each producing a state-dependent output that is measured in aggregate. Despite the lack of feedback signal and initial state information, this control architecture allows a single central controller to direct the aggregate output of the ensemble toward a desired value. First, the system is modeled as an ensemble of statistically independent, identically distributed, binary-state Markov processes with state transition probabilities designated by a central controller. Second, steady-state behavior, convergence rate, and variance of the aggregate output, i.e., the total number of recruited agents, are analyzed, and design trade-offs in terms of accuracy, convergence speed, and the number of spurious transitions are made. Third, a limited feedback signal, only detecting if the output has reached a goal, is added to the system, and the recruitment controller is designed as a stochastic shortest path problem. Optimal convergence rate and associated transition probabilities are obtained. Finally, the theoretical results are verified and demonstrated with both numerical simulation and control of an artificial muscle actuator made up of 60 binary shape memory alloy motor units.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

A conceptual diagram of the ensemble control problem

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Figure 2

A small two-state random state machine, governing the behavior of a single distributed unit

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Figure 3

A schematic of recruitment in muscles

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Figure 4

A graph showing the minimal impact of convergence time on the steady-state variance

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Figure 5

The contour lines of the cost function for N=500, Nref=200

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Figure 6

A simulation of the constant policy recruitment algorithm

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Figure 7

The cumulative distribution of Nton in steady-state, for the two simulations shown in Fig. 6

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Figure 8

A comparison of the constant and one-shot policies

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Figure 9

Simulation of the feedback policy, showing the expected convergence time

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Figure 10

A histogram showing the observed convergence time of the feedback policy for many trials

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Figure 11

The experimental apparatus

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Figure 14

A plot of the variance in the steady-state force output as a function of xss, compared with Eq. 11

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Figure 13

The step response of the actuator for parameter values xss=0.8, λ=0.0,0.4,0.8

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Figure 12

A plot of the average steady-state force output as a function of xss, for varying values of λ

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