arXiv subjects

Yang Zheng

Publications and source records attributed to Yang Zheng.

At least 127 records · Page 7Linked to original sources

arXiv2022

System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation

It is known that the set of internally stabilizing controller $\mathcal{C}_{\text{stab}}$ is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the Youla parameterization, and two recent notions are the system-level parameterization (SLP) and the input-output parameterization (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parametrization in different scenarios. Our main contributions are: 1) We reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of $\mathcal{C}_{\text{stab}}$. 2) We investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating $\mathcal{C}_{\text{stab}}$ given FIR constraints. 3) These four parameterizations require no \emph{a priori} doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in floating-point arithmetic computation and/or implementation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability; but a direct IOP implementation will fail to stabilize open-loop unstable systems in practice. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis even the plant is open-loop stable.

math.OC↗

arXiv2022

Learning 3D Mineral Prospectivity from 3D Geological Models Using Convolutional Neural Networks: Application to a Structure-controlled Hydrothermal Gold Deposit

The three-dimensional (3D) geological models are the typical and key data source in the 3D mineral prospecitivity modeling. Identifying prospectivity-informative predictor variables from the 3D geological models is a challenging and tedious task. Motivated by the ability of convolutional neural networks (CNNs) to learn the intrinsic features, in this paper, we present a novel method that leverages CNNs to learn 3D mineral prospectivity from the 3D geological models. By exploiting the learning ability of CNNs, the presented method allows for disentangling complex correlation to the mineralization and thus opens a door to circumvent the tedious work for designing the predictor variables. Specifically, to explore the unstructured 3D geological models with the CNNs whose input should be structured, we develop a 2D CNN framework in which the geometry of geological boundary is compiled and reorganized into multi-channel images and fed into the CNN. This ensures an effective and efficient training of CNNs while allowing the prospective model to approximate the ore-forming process. The presented method is applied to a typical structure-controlled hydrothermal deposit, the Dayingezhuang gold deposit, eastern China, in which the presented method was compared with the prospectivity modeling methods using hand-designed predictor variables. The results demonstrate the presented method capacitates a performance boost of the 3D prospectivity modeling and empowers us to decrease work-load and prospecting risk in prediction of deep-seated orebodies.

physics.geo-ph↗

arXiv2021

DeepMultiCap: Performance Capture of Multiple Characters Using Sparse Multiview Cameras

We propose DeepMultiCap, a novel method for multi-person performance capture using sparse multi-view cameras. Our method can capture time varying surface details without the need of using pre-scanned template models. To tackle with the serious occlusion challenge for close interacting scenes, we combine a recently proposed pixel-aligned implicit function with parametric model for robust reconstruction of the invisible surface areas. An effective attention-aware module is designed to obtain the fine-grained geometry details from multi-view images, where high-fidelity results can be generated. In addition to the spatial attention method, for video inputs, we further propose a novel temporal fusion method to alleviate the noise and temporal inconsistencies for moving character reconstruction. For quantitative evaluation, we contribute a high quality multi-person dataset, MultiHuman, which consists of 150 static scenes with different levels of occlusions and ground truth 3D human models. Experimental results demonstrate the state-of-the-art performance of our method and the well generalization to real multiview video data, which outperforms the prior works by a large margin.

cs.CV↗

arXiv2021

Decomposed Structured Subsets for Semidefinite and Sum-of-Squares Optimization

Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of matrix variables and the number of constraints increases. To improve scalability, SDPs can be approximated with lower and upper bounds through the use of structured subsets (e.g., diagonally-dominant and scaled-diagonally dominant matrices). Meanwhile, any underlying sparsity or symmetry structure may be leveraged to form an equivalent SDP with smaller positive semidefinite constraints. In this paper, we present a notion of decomposed structured subsets}to approximate an SDP with structured subsets after an equivalent conversion. The lower/upper bounds found by approximation after conversion become tighter than the bounds obtained by approximating the original SDP directly. We apply decomposed structured subsets to semidefinite and sum-of-squares optimization problems with examples of H-infinity norm estimation and constrained polynomial optimization. An existing basis pursuit method is adapted into this framework to iteratively refine bounds.

math.OC↗

arXiv2021

Leading Cruise Control in Mixed Traffic Flow: System Modeling, Controllability, and String Stability

Connected and autonomous vehicles (CAVs) have great potential to improve road transportation systems. Most existing strategies for CAVs' longitudinal control focus on downstream traffic conditions, but neglect the impact of CAVs' behaviors on upstream traffic flow. In this paper, we introduce a notion of Leading Cruise Control (LCC), in which the CAV maintains car-following operations adapting to the states of its preceding vehicles, and also aims to lead the motion of its following vehicles. Specifically, by controlling the CAV, LCC aims to attenuate downstream traffic perturbations and smooth upstream traffic flow actively. We first present the dynamical modeling of LCC, with a focus on three fundamental scenarios: car-following, free-driving, and Connected Cruise Control. Then, the analysis of controllability, observability, and head-to-tail string stability reveals the feasibility and potential of LCC in improving mixed traffic flow performance. Extensive numerical studies validate that the capability of CAVs in dissipating traffic perturbations is further strengthened when incorporating the information of the vehicles behind into the CAV's control.

eess.SY↗

arXiv2021

Chordal and factor-width decompositions for scalable semidefinite and polynomial optimization

Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems and medium-scale nonlinear systems. Chordal decomposition exploits the sparsity of semidefinite matrices in a semidefinite program (SDP), in order to formulate an equivalent SDP with smaller semidefinite constraints that can be solved more efficiently. Factor-width decompositions, instead, relax or strengthen SDPs with dense semidefinite matrices into more tractable problems, trading feasibility or optimality for lower computational complexity. This article reviews recent advances in large-scale semidefinite and polynomial optimization enabled by these two types of decomposition, highlighting connections and differences between them. We also demonstrate that chordal and factor-width decompositions allow for significant computational savings on a range of classical problems from control theory, and on more recent problems from machine learning. Finally, we outline possible directions for future research that have the potential to facilitate the efficient optimization-based study of increasingly complex large-scale dynamical systems.

math.OC↗

arXiv2021

Sum-of-squares chordal decomposition of polynomial matrix inequalities

We prove decomposition theorems for sparse positive (semi)definite polynomial matrices that can be viewed as sparsity-exploiting versions of the Hilbert--Artin, Reznick, Putinar, and Putinar--Vasilescu Positivstellensätze. First, we establish that a polynomial matrix $P(x)$ with chordal sparsity is positive semidefinite for all $x\in \mathbb{R}^n$ if and only if there exists a sum-of-squares (SOS) polynomial $σ(x)$ such that $σP$ is a sum of sparse SOS matrices. Second, we show that setting $σ(x)=(x_1^2 + \cdots + x_n^2)^ν$ for some integer $ν$ suffices if $P$ is homogeneous and positive definite globally. Third, we prove that if $P$ is positive definite on a compact semialgebraic set $\mathcal{K}=\{x:g_1(x)\geq 0,\ldots,g_m(x)\geq 0\}$ satisfying the Archimedean condition, then $P(x) = S_0(x) + g_1(x)S_1(x) + \cdots + g_m(x)S_m(x)$ for matrices $S_i(x)$ that are sums of sparse SOS matrices. Finally, if $\mathcal{K}$ is not compact or does not satisfy the Archimedean condition, we obtain a similar decomposition for $(x_1^2 + \ldots + x_n^2)^νP(x)$ with some integer $ν\geq 0$ when $P$ and $g_1,\ldots,g_m$ are homogeneous of even degree. Using these results, we find sparse SOS representation theorems for polynomials that are quadratic and correlatively sparse in a subset of variables, and we construct new convergent hierarchies of sparsity-exploiting SOS reformulations for convex optimization problems with large and sparse polynomial matrix inequalities. Numerical examples demonstrate that these hierarchies can have a significantly lower computational complexity than traditional ones.

math.OC↗

arXiv2021

Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems

This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.

math.OC↗

arXiv2021

Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control

This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers $\mathcal{C}_n$; and 2) structure of stationary points. It is known that similarity transformations do not change the input-output behavior of a dynamical controller or LQG cost. This inherent symmetry by similarity transformations makes the landscape of LQG very rich. We show that 1) the set of stabilizing controllers $\mathcal{C}_n$ has at most two path-connected components and they are diffeomorphic under a mapping defined by a similarity transformation; 2) there might exist many \emph{strictly suboptimal stationary points} of the LQG cost function over $\mathcal{C}_n$ and these stationary points are always \emph{non-minimal}; 3) all \emph{minimal} stationary points are globally optimal and they are identical up to a similarity transformation. These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem.

math.OC↗

arXiv2020

Probing blood pressure and arterial stiffness noninvasively by guided axial waves

The clinical and economic burden of cardiovascular diseases (CVDs) poses a global challenge. Growing evidence suggests an early assessment of arterial stiffness can provide insights into the pathogenesis of CVDs. However, it remains difficult to quantitatively characterize the arterial stiffness in vivo. Here we utilize the guided elastic waves continuously excited and detected by ultrasound as a tool to probe the blood pressure (BP) and mechanical properties of the common carotid artery (CCA) simultaneously. In a pilot study of 17 healthy volunteers, we obverse a ~20% variation in the group velocity (5.16 m/s in systole and 4.31 m/s in diastole) induced by variation of the BP. A linear relationship between the square of the group velocity and the BP is revealed by our experimental data and finite element analysis, which enables us to measure the waveform of the BP. Furthermore, we propose to use the wavelet analysis to extract the dispersion relation of the guided waves, which provides a quantitative measurement of the arterial stiffness. The results and methods reported in this study show the group velocity and dispersion relation of the guided waves can be adopted to probe BP and arterial stiffness noninvasively and thus promising for early diagnosis of the CVDs.

physics.med-ph↗

arXiv2020

Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories

This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is only suitable for stable systems. We provide finite-time analysis for learning Markov parameters based on the ordinary least-squares (OLS) estimator using multiple trajectories, which covers both stable and unstable systems. For unstable systems, our results suggest that the Markov parameters are harder to estimate in the presence of process noise. Without process noise, our upper bound on the estimation error is independent of the spectral radius of system dynamics with high probability. These two features are different from fully observed LTI systems for which recent work has shown that unstable systems with a bigger spectral radius are easier to estimate. Extensive numerical experiments demonstrate the performance of our OLS estimator.

math.OC↗

arXiv2020

Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method

A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non=invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.

cond-mat.soft↗

arXiv2020

Impact of Disturbances on Mixed Traffic Control with Autonomous Vehicles

This paper investigates the impact of disturbances on controlling an autonomous vehicle to smooth mixed traffic flow in a ring road setup. By exploiting the ring structure of this system, it is shown that velocity perturbations impacting any vehicle on the ring enter an uncontrollable and marginally stable mode defined by the sum of relative vehicle spacings. These disturbances are then integrated up by the system and cannot be unwound via controlling the autonomous vehicle. In particular, if the velocity disturbances are zero-mean Gaussians, then the traffic flow on the ring will undergo a random walk with the variance growing indefinitely and independently of the control policy applied. In contrast, the impact of acceleration disturbances is benign as these disturbances do no enter the uncontrollable mode, meaning that they can be easily regulated using the autonomous vehicle. Our results support and complement the existing theoretic analysis and field experiments.

eess.SY↗

arXiv2020

Leading Cruise Control in Mixed Traffic Flow

Vehicle-to-vehicle (V2V) communications have a great potential to improve traffic system performance. Most existing work of connected and autonomous vehicles (CAVs) focused on adaptation to downstream traffic conditions, neglecting the impact of CAVs' behaviors on upstream traffic flow. In this paper, we introduce a notion of Leading Cruise Control (LCC) that retains the basic car-following operation and explicitly considers the influence of the CAV's actions on the vehicles behind. We first present a detailed modeling process for LCC. Then, rigorous controllability analysis verifies the feasibility of exploiting the CAV as a leader to actively lead the motion of its following vehicles. Besides, the head-to-tail transfer function is derived for LCC under adequate employment of V2V connectivity. Numerical studies confirm the potential of LCC to strengthen the capability of CAVs in suppressing traffic instabilities and smoothing traffic flow.

eess.SY↗

arXiv2020

An Input-Output Parametrization of Stabilizing Controllers: amidst Youla and System Level Synthesis

This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time-invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.

eess.SY↗

arXiv2020

Sparsity Invariance for Convex Design of Distributed Controllers

We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure. This problem is NP-hard in general and motivates the development of tractable approximations. We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI). The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity pattern. For sparsity constraints, the approach of SI goes beyond the notion of Quadratic Invariance (QI): 1) the SI approach always yields a convex restriction; 2) the solution via the SI approach is guaranteed to be globally optimal when QI holds and performs at least as well as considering a nearest QI subset. Moreover, the notion of SI naturally applies to designing structured static controllers, while QI is not utilizable. Numerical examples show that even for non-QI cases, SI can recover solutions that are 1) globally optimal and 2) strictly more performing than previous methods.

eess.SY↗

arXiv2020

BI-MAML: Balanced Incremental Approach for Meta Learning

We present a novel Balanced Incremental Model Agnostic Meta Learning system (BI-MAML) for learning multiple tasks. Our method implements a meta-update rule to incrementally adapt its model to new tasks without forgetting old tasks. Such a capability is not possible in current state-of-the-art MAML approaches. These methods effectively adapt to new tasks, however, suffer from 'catastrophic forgetting' phenomena, in which new tasks that are streamed into the model degrade the performance of the model on previously learned tasks. Our system performs the meta-updates with only a few-shots and can successfully accomplish them. Our key idea for achieving this is the design of balanced learning strategy for the baseline model. The strategy sets the baseline model to perform equally well on various tasks and incorporates time efficiency. The balanced learning strategy enables BI-MAML to both outperform other state-of-the-art models in terms of classification accuracy for existing tasks and also accomplish efficient adaption to similar new tasks with less required shots. We evaluate BI-MAML by conducting comparisons on two common benchmark datasets with multiple number of image classification tasks. BI-MAML performance demonstrates advantages in both accuracy and efficiency.

cs.LG↗

arXiv2020

Learning the Globally Optimal Distributed LQ Regulator

We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed control and present a significant challenge in the sense that standard model-based optimization and learning leads to intractable numerical programs in general. Building upon recent results in zeroth-order optimization, we establish model-free sample-complexity bounds for the class of distributed LQ problems where a local gradient dominance constant exists on any sublevel set of the cost function. %which admit a local gradient dominance constant valid on the sublevel set of the cost function. We prove that a fundamental class of distributed control problems - commonly referred to as Quadratically Invariant (QI) problems - as well as others possess this property. To the best of our knowledge, our result is the first sample-complexity bound guarantee on learning globally optimal distributed output-feedback control policies.

eess.SY↗