Isaac Klickstein

Isaac Klickstein

Engineering PhD applying numerical methods to solve controls and optimization problems

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portfolio

publications

Optimal control of complex networks: Balancing accuracy and energy of the control action

Afroza Shirin, Isaac Klickstein, and Francesco Sorrentino

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017

We hypothesized that the large control energy that arises when applying the minimum energy control to a complex network is due to the implicit requirement of perfect accuracy. By relaxing this requirement, we show there is an exponential reduction in control energy.

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Locally optimal control of complex networks

Isaac Klickstein, Afroza Shirin, and Francesco Sorrentino

Published in Physical Review Letters, 2017

We use the solution of the minimum energy control problem for linear systems to derive a piece-wise controller to overcome the limitations of the nonlocality introduced by linearization.

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Generating graphs with symmetry

Isaac Klickstein and Francesco Sorrentino

Published in IEEE Transactions on Network Science and Engineering, 2018

This is an improved version of the algorithm to generate graphs with symmetry that we previously published.

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Generating symmetric graphs

Isaac Klickstein and Francesco Sorrentino

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018

This is an improved version of the algorithm to generate graphs with symmetry that we previously published.

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Energy scaling with control distance in complex networks

Isaac Klickstein, Ishan Kafle, Sudarshan Bartaula, and Francesco Sorrentino

Published in 2018 IEEE International Symposium on Circuits and Systems (ISCAS), 2018

This was my first attempt at using simple graph models to explain the enormous variance of control energy when holding the number of driver nodes and the number of target nodes constant even over the same graph.

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Control distance and energy scaling of complex networks

Isaac Klickstein and Francesco Sorrentino

Published in IEEE Transactions on Network Science and Engineering, 2018

To investigate the single driver single target control problem on a network, the exact solution of the differential Lyapunov equation is derived for an infinite path graph which is shown to be a good approximate value for sparse networks. We also introduce a corrective factor by computing the controllability Gramian of a model to represent the role of redunant paths.<div style='text-align:center'></div>

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Control energy of lattice graphs

Isaac Klickstein and Francesco Sorrentino

Published in 2018 IEEE Conference on Decision and Control (CDC), 2018

The controllability Gramian of hyper-cubic graphs is derived analytically to investigate the role of graph density in the reduction of control energy.

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Prediction of optimal drug schedules for controlling autophagy

Afroza Shirin, Isaac Klickstein, Song Fend, Yen Ting Lin, William Hlavacek, and Francesco Sorrentino

Published in Scientific Reports, 2019

Numerical optimal control techniques are applied to a recently developed model of cellular autophagy to determine promising multi-drug therapies. We found surprising drug combinations capable of up-regulating or down-regulating autophagy where each drug alone was unable to perform the task.

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Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon

Afroza Shirin, Fabio Della Rossa, Isaac Klickstein, John Russell, and Francesco Sorrentino

Published in PLoS ONE, 2019

Numerical optimal control techniques are applied to the FDA approved model for in silico diabetes treatment testing. We both recover the pulsatile solution representing the well-known treatment of injecting a shot of insulin roughly 30 minutes before eating as well as develop potential treatment schedules when both insulin and glucagon are available.

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Symmetry induced group consensus

Isaac Klickstein, Louis Pecora, and Francesco Sorrentino

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019

The consensus problem is investigated for networked systems which exhibit graph symmetries. By using a block diagonalizing transformation that makes explicit symmetric and non-symmetric motion, we show that consensus is possible even when the entire system is unstable.

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Stability analysis of reservoir computers dynamics via Lyapunov functions

Afroza Shirin, Isaac Klickstein, and Francesco Sorrentino

Published in Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019

Reservoir computers are a type of learning algorithm designed to learn dynamical systems. We derive a class of Lyapunov functions to ensure the reservoir computer remains stable while also demonstrating that reservoir computers which are barely stable are the best at representing unknown dynamical systems.

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The controllability gramian of lattice graphs

Isaac Klickstein and Francesco Sorrentino

Published in Automatica, 2020

This was the culmination of the analytic solution of lattice networks. The solution is derived in terms of integrals whose expression in terms of elementary functions is unlikely though.

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