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Analysis of Controlled Biological Switches via Stochastic Motion Planning


P. Mohajerin Esfahani, A. Milias, D. Chatterjee

European Control Conference (ECC), Zurich, Switzerland

We consider the problem of regulating a genetic toggle switch by means of an in silico feedback control loop. To achieve this, we first introduce two basic notions of motion planning, and then establish a connection to a class of stochastic optimal control problems concerned with sequential stopping-times. To characterize the desired set of initial conditions, in the context of controlled diffusion processes, we propose a sequence of partial differential equations for which the first one has a known boundary condition, while the boundary conditions of the subsequent ones are determined by the solutions to the preceding steps. We then formulate the control of a bistable system as stochastic motion planning problem, and derive the closed-loop control law that maintains the system inside a prespecified region of its state space. Finally, to provide an autonomous feedback policy, we establish a connection to an eigenvalue problem that describes the asymptotic exit-time of the diffusion process.


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% Autogenerated BibTeX entry
@InProceedings { EsfMil:2013:IFA_4382,
    author={P. Mohajerin Esfahani and A. Milias and D. Chatterjee},
    title={{Analysis of Controlled Biological Switches via Stochastic
	  Motion Planning}},
    booktitle={European Control Conference (ECC)},
    address={Zurich, Switzerland},
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