Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesized that some symptoms originate from the inability to spontaneously transition from one attractor to another. Using external perturbations, such as electrical pulses delivered by deep brain stimulation devices, it may be possible to induce such transition out of the pathological attractors. However, the induction of transition may be non-trivial, rendering the current open-loop stimulation strategies insufficient. In order to develop next-generation neural stimulators that can intelligently learn to induce attractor transitions, we require a platform to test the efficacy of such systems. To this end, we designed an analog circuit as a model for the multistable brain dynamics. The circuit spontaneously oscillates stably on two periods as an instantiation of a 3-dimensional continuous-time gated recurrent neural network. To discourage simple perturbation strategies, such as constant or random stimulation patterns from easily inducing transition between the stable limit cycles, we designed a state-dependent nonlinear circuit interface for external perturbation. We demonstrate the existence of nontrivial solutions to the transition problem in our circuit implementation.
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Adaptive Quasi-Static Control of Multistable Systems
In some applications of control, the objective is
to optimize the constant asymptotic response of the system by
moving the state of the system from one forced equilibrium to
another. Since suppression of the transient response is not the
main objective, the feedback control law can operate quasistatically,
that is, extremely slowly relative to the open-loop
dynamics. Although integral control can be used to achieve the
desired setpoint, three issues must be addressed, namely, nonlinearity,
uncertainty, and multistability, where multistability
refers to the fact that multiple locally stable equilibria may
exist for the same constant input. In fact, multistability is the
mechanism underlying hysteresis. The present paper applies an
adaptive digital PID controller to achieve quasi-static control
of systems that are nonlinear, uncertain, and multistable. The
approach is demonstrated on multistable systems involving
unmodeled cubic and backlash nonlinearities.
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- Award ID(s):
- 1634709
- NSF-PAR ID:
- 10190786
- Date Published:
- Journal Name:
- Proc. American Control Conference
- Volume:
- 1
- Issue:
- 1
- Page Range / eLocation ID:
- 2055 to 2060
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC45564.2020.9147394
