Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics

Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics.Comment: 9 pages, 3 figures; to appear in Scientific Report

Nonlinear model reduction by deep autoencoder of noise response data

In this paper a novel model order reduction method for nonlinear systems is proposed. Differently from existing ones, the proposed method provides a suitable non-linear projection, which we refer to as control-oriented deep autoencoder (CoDA), in an easily implementable manner. This is done by combining noise response data based model reduction, whose control theoretic optimality was recently proven by the author, with stacked autoencoder design via deep learning

Maximum Entropy Density Control of Discrete-Time Linear Systems with Quadratic Cost

This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy (MaxEnt) density control problem. Specifically, the running cost is given by quadratic forms of the state and the control input, and the initial and final distributions are Gaussian. We first reveal that our problem boils down to solving two Riccati difference equations coupled through their boundary values. Based on them, we give the closed-form expression of the unique optimal policy. Next, we show that the optimal policy for the density control of the time-reversed system can be obtained simultaneously with the forward-time optimal policy. Finally, by considering the limit where the entropy regularization vanishes, we derive the optimal policy for the unregularized density control problem.Comment: 16 page

Combinatorial Optimization Approach to Client Scheduling for Federated Learning

For machine learning in situations where data is scattered and cannot be aggregated, federated learning, in which aggregators and agents send and receive model parameters, is one of the most promising methods. The scheduling problem of deciding which agents to communicate with has been studied in various ways, but it is not easy to solve due to its combinatorial optimization nature. In this letter, we attempt to solve this scheduling problem using combinatorial optimization theory. Specifically, we propose an efficient exact solution method based on dynamic programming and a greedy method whose superiority is confirmed by numerical examples. We also discuss the applicability of the proposed methods to a more dynamic and uncertain environment

Entropic Model Predictive Optimal Transport for Underactuated Linear Systems

This letter investigates dynamical optimal transport of underactuated linear systems over an infinite time horizon. In our previous work, we proposed to integrate model predictive control and the celebrated Sinkhorn algorithm to perform efficient dynamical transport of agents. However, the proposed method requires the invertibility of input matrices, which severely limits its applicability. To resolve this issue, we extend the method to (possibly underactuated) controllable linear systems. In addition, we ensure the convergence properties of the method for general controllable linear systems. The effectiveness of the proposed method is demonstrated by a numerical example.Comment: Published in IEEE Control Systems Letter

An LMI Framework for Contraction-based Nonlinear Control Design by Derivatives of Gaussian Process Regression

Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed not on controllers but on their partial derivatives, which makes control design challenging. In this paper, we illustrate this so-called integrability problem can be solved by a non-standard use of Gaussian process regression (GPR) for parameterizing controllers and then establish an LMI framework of contraction-based control design for nonlinear discrete-time systems, as an easy-to-implement tool. Later on, we consider the case where the drift vector fields are unknown and employ GPR for functional fitting as its standard use. GPR describes learning errors in terms of probability, and thus we further discuss how to incorporate stochastic learning errors into the proposed LMI framework

Entropic model predictive optimal transport over dynamical systems

We consider the optimal control problem of steering an agent population to a desired distribution over an infinite horizon. This is an optimal transport problem over dynamical systems, which is challenging due to its high computational cost. In this paper, by using entropy regularization, we propose Sinkhorn MPC, which is a dynamical transport algorithm integrating model predictive control (MPC) and the so-called Sinkhorn algorithm. The notable feature of the proposed method is that it achieves cost-effective transport in real time by performing control and transport planning simultaneously, which is illustrated in numerical examples. Moreover, under some assumption on iterations of the Sinkhorn algorithm integrated in MPC, we reveal the global convergence property for Sinkhorn MPC thanks to the entropy regularization. Furthermore, focusing on a quadratic control cost, without the aforementioned assumption we show the ultimate boundedness and the local asymptotic stability for Sinkhorn MPC

顔面神経麻痺後遺症患者の瞬目反射回復曲線

Postparalytic facial dysfunctions (PPFD) such as associate movements, crocodile tears and facial contracture are well-known sequelae of peripheral facial nerve palsy. The physiological basis for those disturbing conditions are unknown. Peripheral hypothesis such as misdirection theory or ephaptic transmission theory have been widely accepted. On the other hand, some investigators made the hypothesis that hyperexcitability of the facial motoneurons had some contribution to the onset of the PPFD. A few physiological studies indicated the evidence of hyperexcitability of the facial motoneurons, however, there is not enough evidence of physiological changes in the nuclear or supranuclear system in patients with PPFD. Therefore, the blink reflex excitability recovery curves were studied in 10 patients with PPFD and 10 healthy control subjects to detect if physiological changes had occurred in the patients with PPFD. The inhibitory effects of the conditioning stimuli on the ipsilateral R 2 (iR 2) and contralateral R 2 (cR 2) responses observed in normal controls were significantly less in patients with PPFD. The results of this study indicate that patients with PPFD have increased excitability of central interneurons which mediate the R 2 pathway. We suggest that not only changes in the peripheral facial nerve but also changes in the central nervous system may contribute to the onset of PPFD

A Fundamental Performance Limit of Cloud-based Control in Terms of Differential Privacy Level

In this paper, we address a privacy issue raised by cloud based control. In a cloud based control framework, a plant typically has no access to the models of the cloud system and other plants connected via the cloud system. Under restricted information, the plant is required to design its local controller for achieving control objectives. As a control objective, we consider a tracking problem, and for constant reference signals, a class of tracking controllers is identified based on Youla parametrization. More importantly, as local tracking controllers are implemented, there is a possibility that the cloud system or other plants connected via the cloud system may be able to identify private information of the plant by using the collected signal from the plant; for example, the reference signal (say, the target production amount) of the plant can be viewed as a piece of private information. In order to evaluate the privacy level of the reference signal, we employ the concept of differential privacy. For the Laplace mechanism induced by the entire system, we show that the differential privacy level cannot be further improved from a ceiling value for any parameters of the local controller. In other words, there is a performance limit in terms of differential privacy level, which is determined by the plant and cloud system only.</p