Francesco Sorrentino

Isaac S. Klickstein, Afroza Shirin, Francesco Sorrentino

Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.

Afroza Shirin, Isaac Klickstein, Song Feng et al.

The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.

Afroza Shirin, Fabio Della Rossa, Isaac Klickstein et al.

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.

Joseph D. Hart, Francesco Sorrentino, Thomas L. Carroll

Reservoir computing, a recurrent neural network paradigm in which only the output layer is trained, has demonstrated remarkable performance on tasks such as prediction and control of nonlinear systems. Recently, it was demonstrated that adding time-shifts to the signals generated by a reservoir can provide large improvements in performance accuracy. In this work, we present a technique to choose the time-shifts by maximizing the rank of the reservoir matrix using a rank-revealing QR algorithm. This technique, which is not task dependent, does not require a model of the system, and therefore is directly applicable to analog hardware reservoir computers. We demonstrate our time-shift selection technique on two types of reservoir computer: one based on an opto-electronic oscillator and the traditional recurrent network with a $tanh$ activation function. We find that our technique provides improved accuracy over random time-shift selection in essentially all cases.

Isaac Klickstein, Francesco Sorrentino

The control of complex networks has generated a lot of interest in a variety of fields from traffic management to neural systems. A commonly used metric to compare two particular control strategies that accomplish the same task is the control energy, the integral of the sum of squares of all control inputs. The minimum control energy problem determines the control input that lower bounds all other control inputs with respect to their control energies. Here, we focus on the infinite lattice graph with linear dynamics and analytically derive the expression for the minimum control energy in terms of the modified Bessel function. We then demonstrate that the control energy of the infinite lattice graph accurately predicts the control energy of finite lattice graphs.

Ishan Kafle, Sudarshan Bartaula, Afroza Shirin et al.

We consider the problem of a dynamical network whose dynamics is subject to external perturbations (`attacks') locally applied at a subset of the network nodes. We assume that the network has an ability to defend itself against attacks with appropriate countermeasures, which we model as actuators located at (another) subset of the network nodes. We derive the optimal defense strategy as an optimal control problem. We see that the network topology, as well as the distribution of attackers and defenders over the network affect the optimal control solution and the minimum control energy. We study the optimal control defense strategy for several network topologies, including chain networks, star networks, ring networks, and scale free networks.

Isaac Klickstein, Francesco Sorrentino

The control of dynamical, networked systems continues to receive much attention across the engineering and scientific research fields. Of particular interest is the proper way to determine which nodes of the network should receive external control inputs in order to effectively and efficiently control portions of the network. Published methods to accomplish this task either find a minimal set of driver nodes to guarantee controllability or a larger set of driver nodes which optimizes some control metric. Here, we investigate the control of lattice systems which provides analytical insight into the relationship between network structure and controllability. First we derive a closed form expression for the individual elements of the controllability Gramian of infinite lattice systems. Second, we focus on nearest neighbor lattices for which the distance between nodes appears in the expression for the controllability Gramian. We show that common control energy metrics scale exponentially with respect to the maximum distance between a driver node and a target node.

Sahand Tangerami, Nicholas A. Mecholsky, Francesco Sorrentino

Machine learning has become a fundamental approach for modeling, prediction, and control, enabling systems to learn from data and perform complex tasks. Reservoir computing is a machine learning tool that leverages high-dimensional dynamical systems to efficiently process temporal data for prediction and observation tasks. Traditionally, the connectivity of a reservoir computer (RC) is generated at random, lacking a principled design. Here, we focus on optimizing the topology of a linear RC to improve its performance and interpretability, which we achieve by decoupling the RC dynamics into a number of independent modes. We then proceed to optimize each one of these modes to perform a given task, which corresponds to selecting an optimal RC connectivity in terms of a given set of eigenvalues of the RC adjacency matrix. Simulations on networks of varying sizes show that the optimized RC significantly outperforms randomly constructed reservoirs in both the training and testing phases and also often surpasses nonlinear reservoirs of comparable size. This approach provides both practical performance advantages and theoretical guidelines for designing efficient, task-specific, and analytically transparent RC architectures.

Kumar Anurag, Kasra Azizi, Francesco Sorrentino et al.

Accurate modeling is crucial in many engineering and scientific applications, yet obtaining a reliable process model for complex systems is often challenging. To address this challenge, we propose a novel framework, reservoir computing with unscented Kalman filtering (RCUKF), which integrates data-driven modeling via reservoir computing (RC) with Bayesian estimation through the unscented Kalman filter (UKF). The RC component learns the nonlinear system dynamics directly from data, serving as a surrogate process model in the UKF prediction step to generate state estimates in high-dimensional or chaotic regimes where nominal mathematical models may fail. Meanwhile, the UKF measurement update integrates real-time sensor data to correct potential drift in the data-driven model. We demonstrate RCUKF effectiveness on well-known benchmark problems and a real-time vehicle trajectory estimation task in a high-fidelity simulation environment.

Chad Nathe, Enrico Del Frate, Thomas Carroll et al.

The topology of a network associated with a reservoir computer is often taken so that the connectivity and the weights are chosen randomly. Optimization is hardly considered as the parameter space is typically too large. Here we investigate this problem for a class of reservoir computers for which we obtain a decomposition of the reservoir dynamics into modes, which can be computed independently of one another. Each mode depends on an eigenvalue of the network adjacency matrix. We then take a parametric approach in which the eigenvalues are parameters that can be appropriately designed and optimized. In addition, we introduce the application of a time shift to each individual mode. We show that manipulations of the individual modes, either in terms of the eigenvalues or the time shifts, can lead to dramatic reductions in the training error.

Nicola Bezzo, Patricio J. Cruz Davalos, Francesco Sorrentino et al.

In this paper we propose an application of adaptive synchronization of chaos to detect changes in the topology of a mobile robotic network. We assume that the network may evolve in time due to the relative motion of the mobile robots and due to unknown environmental conditions, such as the presence of obstacles in the environment. We consider that each robotic agent is equipped with a chaotic oscillator whose state is propagated to the other robots through wireless communication, with the goal of synchronizing the oscillators. We introduce an adaptive strategy that each agent independently implements to: (i) estimate the net coupling of all the oscillators in its neighborhood and (ii) synchronize the state of the oscillators onto the same time evolution. We show that by using this strategy, synchronization can be attained and changes in the network topology can be detected. We go one step forward and consider the possibility of using this information to control the mobile network. We show the potential applicability of our technique to the problem of maintaining a formation between a set of mobile platforms, which operate in an inhomogeneous and uncertain environment. We discuss the importance of using chaotic oscillators and validate our methodology by numerical simulations.