171 research outputs found
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
Modular control under privacy protection:Fundamental trade-offs
In privacy-preserving controller design, there is usually a trade-off between the privacy level and control performances, and we show in this paper that this trade-off in particular determines a lower bound on the differential privacy level of the closed-loop system. The control task we consider is reference tracking in a plug-and-play setting, and the plant under control is a networked system of modules, each of which has no access to the models of the others. For a module, we first identify the whole set of tracking local controllers based on the Youla parametrization. At the same time, each module, to protect its own privacy, tries to prevent the other interconnected modules to identify its private information; in this context, for example, the tracking reference signal (say, the target production amount if each module is a workshop in a factory) can be viewed as a piece of private information. Each module can tune the parameters of its local controller to increase the privacy level of its reference signal. However, if the distribution of Laplace (resp. uniform) noise is fixed, the differential privacy level of a Laplace (resp. uniform) mechanism cannot be further improved from a ceiling value no matter how one tunes parameters. In other words, for modular systems under local reference tracking control, there is a lower bound on the differential privacy level
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