arXiv subjects

Yang Zheng

Publications and source records attributed to Yang Zheng.

157 records · Page 9Linked to original sources

arXiv2018

Cooperative Control of Heterogeneous Connected Vehicles with Directed Acyclic Interactions

Cooperation of multiple connected vehicles has the potential to benefit the road traffic greatly. In this paper, we consider analysis and synthesis problems of the cooperative control of a platoon of heterogeneous connected vehicles with directed acyclic interactions (characterized by directed acyclic graphs). In contrast to previous works that view heterogeneity as a type of uncertainty, this paper directly takes heterogeneity into account in the problem formulation, allowing us to develop a deeper understanding of the influence of heterogeneity on the collective behavior of a platoon of connected vehicles. Our major strategies include an application of the celebrated internal model principle and an exploitation of lower-triangular structures for platoons with directed acyclic interactions. The major findings include: 1) we explicitly highlight the tracking ability of heterogeneous platoons, showing that the followers can only track the leader's spacing and velocity; 2) we analytically derive a stability region of feedback gains for platoons with directed acyclic interactions; 3) and consequently we propose a synthesis method based on the solution to an algebraic Riccati equation that shares the dimension of single vehicle dynamics. Numerical experiments are carried out to validate the effectiveness of our results.

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arXiv2018

Parallel Optimal Control for Cooperative Automation of Large-scale Connected Vehicles via ADMM

This paper proposes a parallel optimization algorithm for cooperative automation of large-scale connected vehicles. The task of cooperative automation is formulated as a centralized optimization problem taking the whole decision space of all vehicles into account. Considering the uncertainty of the environment, the problem is solved in a receding horizon fashion. Then, we employ the alternating direction method of multipliers (ADMM) to solve the centralized optimization in a parallel way, which scales more favorably to large-scale instances. Also, Taylor series is used to linearize nonconvex constraints caused by coupling collision avoidance constraints among interactive vehicles. Simulations with two typical traffic scenes for multiple vehicles demonstrate the effectiveness and efficiency of our method.

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arXiv2018

Sparse sum-of-squares (SOS) optimization: A bridge between DSOS/SDSOS and SOS optimization for sparse polynomials

Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares (SSOS) optimization, diagonally dominant sum-of-squares (DSOS) optimization, and scaled diagonally dominant sum-of-squares (SDSOS) optimization. We prove that the set of SSOS polynomials, an inner approximation of the cone of SOS polynomials, strictly contains the spaces of sparse DSOS/SDSOS polynomials. When applicable, therefore, SSOS optimization is less conservative than its DSOS/SDSOS counterparts. Numerical results for large-scale sparse polynomial optimization problems demonstrate this fact, and also that SSOS optimization can be faster than DSOS/SDSOS methods despite requiring the solution of semidefinite programs instead of less expensive linear/second-order cone programs.

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arXiv2018

Decomposition and Completion of Sum-of-Squares Matrices

This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix. Also, the completion of an SOS matrix is equivalent to a set of SOS conditions on its principal submatrices and a consistency condition on the Gram representation of the principal submatrices. These results are partial extensions of chordal decomposition and completion of scalar matrices to matrices with polynomial entries. We apply the SOS decomposition result to exploit sparsity in matrix-valued SOS programs. Numerical results demonstrate the high potential of this approach for solving large-scale sparse matrix-valued SOS programs.

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arXiv2018

Scalable analysis of linear networked systems via chordal decomposition

This paper introduces a chordal decomposition approach for scalable analysis of linear networked systems, including stability, $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ performance. Our main strategy is to exploit any sparsity within these analysis problems and use chordal decomposition. We first show that Grone's and Agler's theorems can be generalized to block matrices with any partition. This facilitates networked systems analysis, allowing one to solely focus on the physical connections of networked systems to exploit scalability. Then, by choosing Lyapunov functions with appropriate sparsity patterns, we decompose large positive semidefinite constraints in all of the analysis problems into multiple smaller ones depending on the maximal cliques of the system graph. This makes the solutions more computationally efficient via a recent first-order algorithm. Numerical experiments demonstrate the efficiency and scalability of the proposed method.

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arXiv2017

Improving Efficiency and Scalability of Sum of Squares Optimization: Recent Advances and Limitations

It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are large and costly to solve when the polynomials involved in the SOS programs have a large number of variables and degree. In this paper, we review SOS optimization techniques and present two new methods for improving their computational efficiency. The first method leverages the sparsity of the underlying SDP to obtain computational speed-ups. Further improvements can be obtained if the coefficients of the polynomials that describe the problem have a particular sparsity pattern, called chordal sparsity. The second method bypasses semidefinite programming altogether and relies instead on solving a sequence of more tractable convex programs, namely linear and second order cone programs. This opens up the question as to how well one can approximate the cone of SOS polynomials by second order representable cones. In the last part of the paper, we present some recent negative results related to this question.

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arXiv2017

Block-Diagonal Solutions to Lyapunov Inequalities and Generalisations of Diagonal Dominance

Diagonally dominant matrices have many applications in systems and control theory. Linear dynamical systems with scaled diagonally dominant drift matrices, which include stable positive systems, allow for scalable stability analysis. For example, it is known that Lyapunov inequalities for this class of systems admit diagonal solutions. In this paper, we present an extension of scaled diagonally dominance to block partitioned matrices. We show that our definition describes matrices admitting block-diagonal solutions to Lyapunov inequalities and that these solutions can be computed using linear algebraic tools. We also show how in some cases the Lyapunov inequalities can be decoupled into a set of lower dimensional linear matrix inequalities, thus leading to improved scalability. We conclude by illustrating some advantages and limitations of our results with numerical examples.

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arXiv2017

Platooning of Connected Vehicles with Undirected Topologies: Robustness Analysis and Distributed H-infinity Controller Synthesis

This paper considers the robustness analysis and distributed $\mathcal{H}_{\infty}$ (H-infinity) controller synthesis for a platoon of connected vehicles with undirected topologies. We first formulate a unified model to describe the collective behavior of homogeneous platoons with external disturbances using graph theory. By exploiting the spectral decomposition of a symmetric matrix, the collective dynamics of a platoon is equivalently decomposed into a set of subsystems sharing the same size with one single vehicle. Then, we provide an explicit scaling trend of robustness measure $γ$-gain, and introduce a scalable multi-step procedure to synthesize a distributed $\mathcal{H}_{\infty}$ controller for large-scale platoons. It is shown that communication topology, especially the leader's information, exerts great influence on both robustness performance and controller synthesis. Further, an intuitive optimization problem is formulated to optimize an undirected topology for a platoon system, and the upper and lower bounds of the objective are explicitly analyzed, which hints us that coordination of multiple mini-platoons is one reasonable architecture to control large-scale platoons. Numerical simulations are conducted to illustrate our findings.

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arXiv2017

Fast ADMM for homogeneous self-dual embedding of sparse SDPs

We propose an efficient first-order method, based on the alternating direction method of multipliers (ADMM), to solve the homogeneous self-dual embedding problem for a primal-dual pair of semidefinite programs (SDPs) with chordal sparsity. Using a series of block eliminations, the per-iteration cost of our method is the same as applying a splitting method to the primal or dual alone. Moreover, our approach is more efficient than other first-order methods for generic sparse conic programs since we work with smaller semidefinite cones. In contrast to previous first-order methods that exploit chordal sparsity, our algorithm returns both primal and dual solutions when available, and a certificate of infeasibility otherwise. Our techniques are implemented in the open-source MATLAB solver CDCS. Numerical experiments on three sets of benchmark problems from the library SDPLIB show speed-ups compared to some common state-of-the-art software packages.

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arXiv2017

Fast ADMM for Semidefinite Programs with Chordal Sparsity

Many problems in control theory can be formulated as semidefinite programs (SDPs). For large-scale SDPs, it is important to exploit the inherent sparsity to improve the scalability. This paper develops efficient first-order methods to solve SDPs with chordal sparsity based on the alternating direction method of multipliers (ADMM). We show that chordal decomposition can be applied to either the primal or the dual standard form of a sparse SDP, resulting in scaled versions of ADMM algorithms with the same computational cost. Each iteration of our algorithms consists of a projection on the product of small positive semidefinite cones, followed by a projection on an affine set, both of which can be carried out efficiently. Our techniques are implemented in CDCS, an open source add-on to MATLAB. Numerical experiments on large-scale sparse problems in SDPLIB and random SDPs with block-arrow sparse patterns show speedups compared to some common state-of-the-art software packages.

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arXiv2017

Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programming using ADMM

This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squares (SOS) programming. We exploit the sparsity of the \emph{coefficient matching conditions} when SOS programs are formulated in the usual monomial basis to reduce the computational cost of the ADMM algorithm. Each iteration of our algorithm requires one projection onto the positive semidefinite cone and the solution of multiple quadratic programs with closed-form solutions free of any matrix inversion. Our techniques are implemented in the open-source MATLAB solver SOSADMM. Numerical experiments on SOS problems arising from unconstrained polynomial minimization and from Lyapunov stability analysis for polynomial systems show speed-ups compared to the interior-point solver SeDuMi, and the first-order solver CDCS.

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arXiv2016

Distributed Model Predictive Control for Heterogeneous Vehicle Platoons under Unidirectional Topologies

This paper presents a distributed model predictive control (DMPC) algorithm for heterogeneous vehicle platoons with unidirectional topologies and a priori unknown desired set point. The vehicles (or nodes) in a platoon are dynamically decoupled but constrained by spatial geometry. Each node is assigned a local open-loop optimal control problem only relying on the information of neighboring nodes, in which the cost function is designed by penalizing on the errors between predicted and assumed trajectories. Together with this penalization, an equality based terminal constraint is proposed to ensure stability, which enforces the terminal states of each node in the predictive horizon equal to the average of its neighboring states. By using the sum of local cost functions as a Lyapunov candidate, it is proved that asymptotic stability of such a DMPC can be achieved through an explicit sufficient condition on the weights of the cost functions. Simulations with passenger cars demonstrate the effectiveness of proposed DMPC.

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arXiv2013

Study on collimation and shielding of the back-streaming neutrons at the CSNS target

The back-streaming neutrons from the spallation target at CSNS are very intense, and can pose serious damage problems for the devices in the accelerator-target interface region. To tackle the problems, a possible scheme for this region was studied, namely a specially designed optics for the proton beam line produces two beam waists, and two collimators are placed at the two waist positions to maximize the collimation effect of the back-streaming neutrons. Detailed Monte Carlo simulations with the beams in the two different CSNS phases show the effectiveness of the collimation system, and the radiation dose rate decreases largely in the interface section. This can ensure the use of epoxy coils for the last magnets and other devices in the beam transport line with reasonable lifetimes, e.g. thirty years. The design philosophy for such an accelerator-target interface region can also be applicable to other high-power proton beam applications.

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