This paper investigates the causal rate-distortion function for networked Linear Quadratic Gaussian (LQG) control systems with two encoders and a single decoder, a longstanding open problem in information/control theory. While previous work has explored the causal rate-distortion function for single-encoder and feedback-enabled networked settings, the case of networks without feedback remains unaddressed. We establish a novel directed information lower bound, the first derived for the networked LQG setting. We further demonstrate the optimality of linear, independent encoders and linear decoders for optimizing this lower bound. By reducing the original infinite-dimensional optimization problem to a finite-dimensional one, our approach simplifies the analysis. Additionally, our directed information lower bound provides an alternate proof for the sufficiency of linear encoders in point-to-point settings, both with and without side information, extending prior results in the literature.

Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of efficiently finding optimal and safe control for high-dimensional systems. Specifically, we propose to use dimensionality reduction techniques from a comparison theorem for stochastic differential equations together with a generalizable physics-informed neural network to estimate the optimal value function and the safety probability of the system. The proposed framework results in substantial sample efficiency improvement compared to existing methods. We further develop an autoencoder-like neural network to automatically identify the low-dimensional features in the system to enhance the ease of design for system integration. We also provide experiments and quantitative analysis to validate the efficacy of the proposed method. Source code is available at https://github.com/jacobwang925/path-integral-PINN.

Abstract This study introduces a novel numerical method for identifying and visualizing the terrestrial magnetic field topology in a large‐scale three‐dimensional global MHD (Magneto‐Hydro‐Dynamic) simulation. The (un)stable two‐dimensional manifolds are generated from critical points (CPs) located north and south of the magnetosphere using an improved geodesic level set method. A boundary value problem is solved numerically using a shooting method to forward a new geodesic level set from the previous set. These sets are generated starting from a small circle whose centre is a CP. The level sets are the sets of mesh points that form the magnetic manifold, which determines the magnetic field topology. In this study, a consistent method is proposed to determine the magnetospheric topology. Using this scheme, we successfully visualize a terrestrial magnetospheric field topology and identify its two neutral lines using the global MHD simulation. Our results present a terrestrial topology that agrees well with the recent magnetospheric physics and can help us understand various nonlinear magnetospheric dynamics and phenomena. Our visualization enables us to fill the gaps between current magnetospheric physics that can be observed via satellites and nonlinear dynamics, particularly, the bifurcation theory, in the future.

In this article, we propose a path planning methodology for a mobile robot navigating through an obstacle-filled environment to generate a reference path that is traceable with moderate sensing efforts. The desired reference path is characterized as the shortest path in an obstacle-filled Gaussian belief manifold equipped with a novel information-geometric distance function. The distance function we introduce is shown to be an asymmetric quasi-pseudometric and can be interpreted as the minimum information gain required to steer the Gaussian belief. An RRT*-based numerical solution algorithm is presented to solve the formulated shortest-path problem. To gain insight into the asymptotic optimality of the proposed algorithm, we show that the considered path length function is continuous with respect to the topology of total variation. Simulation results demonstrate that the proposed method is effective in various robot navigation scenarios to reduce sensing costs, such as the required frequency of sensor measurements and the number of sensors that must be operated simultaneously.

We consider a cloud-based control architecture for a linear plant with Gaussian process noise, where the state of the plant contains a client's sensitive information. We assume that the cloud tries to estimate the state while executing a designated control algorithm. The mutual information between the client's actual state and the cloud's estimate is adopted as a measure of privacy loss. We discuss the necessity of uplink and downlink privacy masks. After observing that privacy is not necessarily a monotone function of the noise levels of privacy masks, we discuss the joint design procedure for uplink and downlink privacy masks. Finally, the trade-off between privacy and control performance is explored.

In this paper, we consider a discrete time linear quadratic Gaussian (LQG) control problem in which state information of the plant is encoded in a variable-length binary codeword at every time step, and a control input is determined based on the codewords generated in the past. We derive a lower bound of the rate achievable by the class of prefix-free codes attaining the required LQG control performance. This lower bound coincides with the infimum of a certain directed information expression, and is computable by semidefinite programming (SDP). Based on a technique by Silva et al., we also provide an upper bound of the best achievable rate by constructing a controller equipped with a uniform quantizer with subtractive dither and Shannon-Fano coding. The gap between the obtained lower and upper bounds is less than 0:754r + 1 bits per time step regardless of the required LQG control performance, where r is the rank of a signal-to-noise ratio matrix obtained by SDP, which is no greater than the dimension of the state.

We propose a new blind source separation (BSS) algorithm that is effective when Hankel matrices constructed from individual source signals are near low-rank and satisfy a certain near-orthogonality condition. Source separation is achieved by finding a nonsingular reverse-mixing operation that minimizes nuclear norms of Hankel matrices constructed from estimated source signals. The new formulation results in a non-convex optimization problem involving a reverse-mixing matrix. Preliminary analysis of local recoverability of source signals as well as few numerical simulations are presented in this letter.

We demonstrate the robust execution of two regrasping primitives, rotation and pivoting on a four-fingered hand, based on the real-time sensors data based control. We indicate frequently occurring grasp errors and faults during execution of the two regrasping primitives. The sensors data is obtained from two sources. One is force-torque sensors mounted on the finger tips of the four fingers. The other is a laser range sensor mounted on the palm of the hand. The grasp information acquired through these two sources is useful for both sensing the errors and controlling the fingers. The paper proposes strategies to recover or prevent faulty grasps during manipulation, which may lead to unwanted object movements or grasp failures. The object to be manipulated is a polygonal prism, the model of which is known a priori.

ASURA is a large scale, chwier-based, distributed, shared memory, multiprocessor being developed at Kyoto University and Kubota Corporation.Up to 128 clusters are interconnected to form an ASURA system of up to 102d processors.The basic concept of the ASURA design is to take advantage of the hierarchical structure of the system.Implementing this concept, a large shared cache is piaced between each cluster and the inter-ciuster network.The shared cache and the shared memories distributed among the clusters form part of ASURA's hierarchical memory architecture, providing various unique features to ASURA.In this paper, the hierarchicalmemory architecture of ASURA and its unique cache coherence scheme, including a proposal of a new hierarchical directory scheme, are described wzth some simulation results.Permission tocopy without fes all or pan of Ibis .n81e&al is granted, pmvidd that tbe copies me not made or dishiluted fw dim commenial advantage, the ACMwpyrisbtmalice and tbe title of the F.Iblication and its date appesr, snd notice is given that cqying is by permission of tbe Association forComputing Mschimy.ToCOPY ciherwi%csto republih.requires a fee Snlvcu Specilic pmnissian.