arXiv subjects

Hai Lin

Publications and source records attributed to Hai Lin.

At least 91 records · Page 5Linked to original sources

arXiv2022

Coherent state operators, giant gravitons, and gauge-gravity correspondence

We generalize a construction of coherent state operators describing various giant graviton branes. We enlarge the coherent state parameters, by including complementary coherent state parameters, to describe a system of dual giants and giants. One of the advantages of using complementary coherent state parameters is that they have rich sub-block structures that record different type of giant gravitons or wrapped branes. The coherent state parameters are further packaged into supermatrix, to construct special coherent states, which encode information of both giants and dual giants. We add strings onto the coherent state operators. The string-added states capture near-BPS states. Hence the constructions of BPS coherent state operators are also useful for analyzing near-BPS states. The coherent state representation, auxiliary integrals, as well as auxiliary susy integrals, facilitate the computations efficiently. We describe multi-matrix operators and BPS states, and unify some classes of operators. Finally, reduced coherent states as well as their fermionic counterparts are discussed.

hep-th↗

arXiv2022

Distributed Adaptive Backstepping Control for Vehicular Platoons with Mismatched Disturbances Using Vector String Lyapunov Functions

In this paper, we consider the problem of platooning control with mismatched disturbances using the distributed adaptive backstepping method. The main challenges are: (1) maintaining the compositionality and the distributed nature of the controller, and (2) ensuring the robustness of the controller with respect to general types of disturbances. To address these challenges, we first propose a novel notion that we named "Vector String Lyapunov Function", whose existence implies l2 weak string stability. This notion is based on the vector Lyapunov function-based stability analysis, which depends on the input-to-state-stability of a comparison system. Using this notion, we propose an adaptive backstepping controller for the platoon such that the compositionality and the distributed nature of the controller can be ensured while the internal stability and string stability of the closed-loop system are formally guaranteed. Finally, simulation examples are provided to illustrate the effectiveness of the proposed control algorithm. In particular, we provide simulation results comparing our proposed control algorithm with a recently proposed control algorithm from the literature, under two types of information flow topologies and disturbances.

eess.SY↗

arXiv2022

Error Performance of Rectangular Pulse-shaped OTFS with Practical Receivers

In this letter, we investigate error performance of rectangular pulse-shaped orthogonal time frequency space (OTFS) modulation with a practical receiver. Specifically, we consider an essential bandpass filter at receiver RF front-end, which has been ignored in existing works. We analyse the effect of rectangular pulses on practical OTFS receiver performance, and derive the exact forms of interference in delay-Doppler (DD) domain. We demonstrate that the transmitted information symbols in certain regions of the DD domain are severely contaminated. As a result, there is an error floor in the receiver error performance, which needs to be addressed for such OTFS waveform in practical systems.

eess.SP↗

arXiv2022

Task Space Tracking of Soft Manipulators: Inner-Outer Loop Control Based on Cosserat-Rod Models

Soft robots are robotic systems made of deformable materials and exhibit unique flexibility that can be exploited for complex environments and tasks. However, their control problem has been considered a challenging subject because they are of infinite degrees of freedom and highly under-actuated. Existing studies have mainly relied on simplified and approximated finite-dimensional models. In this work, we exploit infinite-dimensional nonlinear control for soft robots. We adopt the Cosserat-rod theory and employ nonlinear partial differential equations (PDEs) to model the kinematics and dynamics of soft manipulators, including their translational motions (for shear and elongation) and rotational motions (for bending and torsion). The objective is to achieve position tracking of the whole manipulator in a planar task space by controlling the moments (generated by actuators). The control design is inspired by the energy decay property of damped wave equations and has an inner-outer loop structure. In the outer loop, we design desired rotational motions that rotate the translational component into a direction that asymptotically dissipates the energy associated with position tracking errors. In the inner loop, we design inputs for the rotational components to track their desired motions, again by dissipating the rotational energy. We prove that the closed-loop system is exponentially stable and evaluate its performance through simulations.

cs.RO↗

arXiv2022

Centralized and Decentralized Techniques for Analysis and Synthesis of Non-Linear Networked Systems

In this paper, we develop centralized and decentralized techniques for analyzing and synthesizing networked systems comprised of interconnected sets of non-linear subsystems - only using the subsystem dissipativity properties. In particular, this paper extends a recent work that proposed dissipativity based centralized analysis techniques for non-linear networked systems as linear matrix inequality (LMI) problems. First, we consider four networked system configurations (NSCs) of interest and provide centralized stability/dissipativity \emph{analysis} techniques for them as LMI problems. Second, we show that the centralized interconnection topology \emph{synthesis} techniques for these NSCs can also be developed as LMI problems. This enables synthesizing the interconnection topology among the subsystems so that specific stability/dissipativity measures of the networked system are optimized. Next, we show that the proposed analysis and synthesis techniques can be implemented in a decentralized and compositional manner (i.e., subsystems can be added/removed conveniently). Finally, we include several numerical results to demonstrate our contributions.

eess.SY↗

arXiv2022

CryptoSolve: Towards a Tool for the Symbolic Analysis of Cryptographic Algorithms

Recently, interest has been emerging in the application of symbolic techniques to the specification and analysis of cryptosystems. These techniques, when accompanied by suitable proofs of soundness/completeness, can be used both to identify insecure cryptosystems and prove sound ones secure. But although a number of such symbolic algorithms have been developed and implemented, they remain scattered throughout the literature. In this paper, we present a tool, CryptoSolve, which provides a common basis for specification and implementation of these algorithms, CryptoSolve includes libraries that provide the term algebras used to express symbolic cryptographic systems, as well as implementations of useful algorithms, such as unification and variant generation. In its current initial iteration, it features several algorithms for the generation and analysis of cryptographic modes of operation, which allow one to use block ciphers to encrypt messages more than one block long. The goal of our work is to continue expanding the tool in order to consider additional cryptosystems and security questions, as well as extend the symbolic libraries to increase their applicability.

cs.LO↗

arXiv2022

PDE-based Dynamic Control and Estimation of Soft Robotic Arms

Compared with traditional rigid-body robots, soft robots not only exhibit unprecedented adaptation and flexibility but also present novel challenges in their modeling and control because of their infinite degrees of freedom. Most of the existing approaches have mainly relied on approximated models so that the well-developed finite-dimensional control theory can be exploited. However, this may bring in modeling uncertainty and performance degradation. Hence, we propose to exploit infinite-dimensional analysis for soft robotic systems. Our control design is based on the increasingly adopted Cosserat rod model, which describes the kinematics and dynamics of soft robotic arms using nonlinear partial differential equations (PDE). We design infinite-dimensional state feedback control laws for the Cosserat PDE model to achieve trajectory tracking (consisting of position, rotation, linear and angular velocities) and prove their uniform tracking convergence. We also design an infinite-dimensional extended Kalman filter on Lie groups for the PDE system to estimate all the state variables (including position, rotation, strains, curvature, linear and angular velocities) using only position measurements. The proposed algorithms are evaluated using simulations.

cs.RO↗

arXiv2022

Multi-Robot-Assisted Human Crowd Evacuation using Navigation Velocity Fields

This work studies a robot-assisted crowd evacuation problem where we control a small group of robots to guide a large human crowd to safe locations. The challenge lies in how to model human-robot interactions and design robot controls to indirectly control a human population that significantly outnumbers the robots. To address the challenge, we treat the crowd as a continuum and formulate the evacuation objective as driving the crowd density to target locations. We propose a novel mean-field model which consists of a family of microscopic equations that explicitly model how human motions are locally guided by the robots and an associated macroscopic equation that describes how the crowd density is controlled by the navigation velocity fields generated by all robots. Then, we design density feedback controllers for the robots to dynamically adjust their states such that the generated navigation velocity fields drive the crowd density to a target density. Stability guarantees of the proposed controllers are proven. Agent-based simulations are included to evaluate the proposed evacuation algorithms.

cs.RO↗

arXiv2022

A Decentralized Analysis and Control Synthesis Approach for Networked Systems with Arbitrary Interconnections

This paper considers the problem of decentralized analysis and control synthesis to verify and ensure properties like stability and dissipativity of a large-scale networked system comprised of linear subsystems interconnected in an arbitrary topology. In particular, we design systematic networked system analysis and control synthesis processes that can be executed in a decentralized manner at the subsystem level with minimal information sharing among the subsystems. Compared to our most recent work on the same topic, we consider a substantially more generalized problem setup in this paper and develop decentralized processes to verify and ensure a broader range of networked system properties. We show that for such decentralized processes: optimizing the used subsystem indexing scheme can substantially reduce the required inter-subsystem information-sharing sessions, and in some network topologies, information sharing among only neighboring subsystems is sufficient (distributed!). Moreover, the proposed networked system analysis and control synthesis processes are compositional/resilient to subsystem removals, which enable them to conveniently and efficiently handle situations where new subsystems are being added/removed to/from an existing network. We also provide significant insights into our decentralized approach so that it can be quickly adopted to verify and ensure properties beyond the stability and dissipativity of networked systems. Towards developing such decentralized techniques, we have also derived new centralized solutions for dissipative observer and dynamic output feedback controller design problems. Subsequently, we also specialize all the derived results for discrete-time networked systems. We conclude this paper by providing several simulation results demonstrating the proposed novel decentralized analysis and control synthesis processes and dissipativity-based results.

eess.SY↗

arXiv2022

Contact-Implicit Trajectory Optimization with Hydroelastic Contact and iLQR

Contact-implicit trajectory optimization offers an appealing method of automatically generating complex and contact-rich behaviors for robot manipulation and locomotion. The scalability of such techniques has been limited, however, by the challenge of ensuring both numerical reliability and physical realism. In this paper, we present preliminary results suggesting that the Iterative Linear Quadratic Regulator (iLQR) algorithm together with the recently proposed pressure-field-based hydroelastic contact model enables reliable and physically realistic trajectory optimization through contact. We use this approach to synthesize contact-rich behaviors like quadruped locomotion and whole-arm manipulation. Furthermore, open-loop playback on a Kinova Gen3 robot arm demonstrates the physical accuracy of the whole-arm manipulation trajectories. Code is available at https://bit.ly/ilqr_hc and videos can be found at https://youtu.be/IqxJKbM8_ms.

cs.RO↗

arXiv2022

voxel2vec: A Natural Language Processing Approach to Learning Distributed Representations for Scientific Data

Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and ensemble data, are intricate and complex. This paper presents voxel2vec, a novel unsupervised representation learning model, which is used to learn distributed representations of scalar values/scalar-value combinations in a low-dimensional vector space. Its basic assumption is that if two scalar values/scalar-value combinations have similar contexts, they usually have high similarity in terms of features. By representing scalar values/scalar-value combinations as symbols, voxel2vec learns the similarity between them in the context of spatial distribution and then allows us to explore the overall association between volumes by transfer prediction. We demonstrate the usefulness and effectiveness of voxel2vec by comparing it with the isosurface similarity map of univariate data and applying the learned distributed representations to feature classification for multivariate data and to association analysis for time-varying and ensemble data.

cs.LG↗

arXiv2022

Multicarrier Modulation on Delay-Doppler Plane: Achieving Orthogonality with Fine Resolutions

In this paper, we investigate the design of a novel multicarrier (MC) modulation on delay-Doppler (DD) plane, to couple the modulated signal with a doubly-selective channel having DD resolutions. A key challenge for the design of DD plane MC modulation is to find a realizable pulse orthogonal with respect to the DD plane's fine resolutions. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse. Most importantly, we prove that the proposed transmit pulse is orthogonal with respect to the DD plane's resolutions and therefore a realizable DD plane orthogonal pulse does exist. Finally, we demonstrate the superior performance of the proposed ODDM modulation in terms of out-of-band radiation and bit error rate.

cs.IT↗

arXiv2022

Coherent state excitations and string-added coherent states in gauge-gravity correspondence

We analyze detailed properties of BPS coherent states and their connection to gravity. We interpret the group integral coherent state as a path integral over auxiliary variables coupled to the elementary letters of the theory. The eigenvalues of coherent state amplitudes can be viewed as collective coordinates of giant gravitons. Inspired by the above coherent states and by the integrability, we construct a new type of coherent states in the SL(2) sectors and their cousin PSU(1,1|2) sectors, analogous to the aforementioned coherent states. The large spin and small spin limits can be obtained by varying coherent state amplitudes. We add string words onto the BPS coherent states, and this gives rise to string-added coherent states. The insertions of string multi-words can be viewed as operator-insertions in this path integral. We describe BPS states and near BPS states building upon these coherent states in gauge-gravity correspondence. For example, string-added coherent states and their near BPS spectra are analyzed. This approach is particularly convenient for heavy excited states.

hep-th↗

arXiv2022

PSL is Dead. Long Live PSL

Property Specification Language (PSL) is a form of temporal logic that has been mainly used in discrete domains (e.g. formal hardware verification). In this paper, we show that by merging machine learning techniques with PSL monitors, we can extend PSL to work on continuous domains. We apply this technique in machine learning-based anomaly detection to analyze scenarios of real-time streaming events from continuous variables in order to detect abnormal behaviors of a system. By using machine learning with formal models, we leverage the strengths of both machine learning methods and formal semantics of time. On one hand, machine learning techniques can produce distributions on continuous variables, where abnormalities can be captured as deviations from the distributions. On the other hand, formal methods can characterize discrete temporal behaviors and relations that cannot be easily learned by machine learning techniques. Interestingly, the anomalies detected by machine learning and the underlying time representation used are discrete events. We implemented a temporal monitoring package (TEF) that operates in conjunction with normal data science packages for anomaly detection machine learning systems, and we show that TEF can be used to perform accurate interpretation of temporal correlation between events.

cs.LG↗

arXiv2022

Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables

Signal Temporal Logic (STL) provides a convenient way of encoding complex control objectives for robotic and cyber-physical systems. The state-of-the-art in trajectory synthesis for STL is based on Mixed-Integer Convex Programming (MICP). The MICP approach is sound and complete, but has limited scalability due to exponential complexity in the number of binary variables. In this letter, we propose a more efficient MICP encoding for STL. Our new encoding is based on the insight that disjunction can be encoded using a logarithmic number of binary variables and conjunction can be encoded without binary variables. We demonstrate in simulation examples that our proposed approach significantly outperforms the state-of-the-art for long and complex specifications. Open-source software is available at https://stlpy.readthedocs.io.

eess.SY↗

arXiv2022

On-line Estimation of Stability and Passivity Metrics

We consider the problem of on-line evaluation of critical characteristic parameters such as the L_2-gain (L2G), input feedforward passivity index (IFP) and output feedback passivity index (OFP) of non-linear systems using their input-output data. Typically, having an accurate measure of such "system indices" enables the application of systematic control design techniques. Moreover, if such system indices can efficiently be evaluated on-line, they can be exploited to device intelligent controller reconfiguration and fault-tolerant control techniques. However, the existing estimation methods of such system indices (i.e., L2G, IFP and OFP) are predominantly off-line, computationally inefficient, and require a large amount of actual or synthetically generated input-output trajectory data under some specific initial/terminal conditions. On the other hand, the existing on-line estimation methods take an averaging-based approach, which may be sub-optimal, computationally inefficient and susceptible to estimate saturation. In this paper, to overcome these challenges (in the on-line estimation of system indices), we establish and exploit several interesting theoretical results on a particular class of fractional function optimization problems. For comparison purposes, the details of an existing averaging-based approach are provided for the same on-line estimation problem. Finally, several numerical examples are discussed to demonstrate the proposed on-line estimation approach and to highlight our contributions.

eess.SY↗

arXiv2022

Backstepping Mean-Field Density Control for Large-Scale Heterogeneous Nonlinear Stochastic Systems

This work studies the problem of controlling the mean-field density of large-scale stochastic systems, which has applications in various fields such as swarm robotics. Recently, there is a growing amount of literature that employs mean-field partial differential equations (PDEs) to model the density evolution and uses density feedback to design control laws which, by acting on individual systems, stabilize their density towards a target profile. In spite of its stability property and computational efficiency, the success of density feedback relies on assuming the systems to be homogeneous first-order integrators (plus white noise) and ignores higher-order dynamics, making it less applicable in practice. In this work, we present a backstepping design algorithm that extends density control to heterogeneous and higher-order stochastic systems in strict-feedback forms. We show that the strict-feedback form in the individual level corresponds to, in the collective level, a PDE (of densities) distributedly driven by a collection of heterogeneous stochastic systems. The presented backstepping design then starts with a density feedback design for the PDE, followed by a sequence of stabilizing design for the remaining stochastic systems. We present a candidate control law with stability proof and apply it to nonholonomic mobile robots. A simulation is included to verify the effectiveness of the algorithm.

eess.SY↗

arXiv2022

Feedback Interconnected Mean-Field Density Estimation and Control

Swarm robotic systems have foreseeable applications in the near future. Recently, there has been an increasing amount of literature that employs mean-field partial differential equations (PDEs) to model the time-evolution of the probability density of swarm robotic systems and uses density feedback to design stabilizing control laws that act on individuals such that their density converges to a target profile. However, it remains largely unexplored considering problems of how to estimate the mean-field density, how the density estimation algorithms affect the control performance, and whether the estimation performance in turn depends on the control algorithms. In this work, we focus on studying the interplay of these algorithms. Specifically, we propose new density control laws which use the mean-field density and its gradient as feedback, and prove that they are globally input-to-state stable (ISS) with respect to estimation errors. Then, we design filtering algorithms to estimate the density and its gradient separately, and prove that these estimates are convergent assuming the control laws are known. Finally, we show that the feedback interconnection of these estimation and control algorithms is still globally ISS, which is attributed to the bilinearity of the PDE system. An agent-based simulation is included to verify the stability of these algorithms and their feedback interconnection.

eess.SY↗