pwc-archive/papers-with-abstracts huggingface dataset:
On the complexity of linear systems: an approach via rate distortion theory and emulating systems
Authors: Eric Wendel, John Baillieul, Joseph Hollmann
Date: 2023-06-04 00:00:00
Tasks: Decision Making

We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a Gaussian source of uncertainty in those increments. The complexity of a linear system has relevance in control-communications contexts requiring local and dynamic decision-making based on sampled data representations. We relate this notion of complexity to the design of attention-varying controllers, and demonstrate a novel methodology for constructing source codes via the endpoint maps of so-called emulating systems, with potential for non-parametric, data-based simulation and analysis of unknown dynamical systems.
Hypoxia-resistance heterogeneity in tumours: the impact of geometrical characterization of environmental niches and evolutionary trade-offs. A mathematical approach
Authors: Giulia Chiari, Giada Fiandaca, Marcello Edoardo Delitala
Date: 2023-06-01 00:00:00

In the study of cancer evolution and therapeutic strategies, scientific evidence shows that a key dynamics lies in the tumor-environment interaction. In particular, oxygen concentration plays a central role in the determination of the phenotypic heterogeneity of cancer cell populations, whose qualitative and geometric characteristics are predominant factors in the occurrence of relapses and failure of eradication. We propose a mathematical model able to describe the eco-evolutionary spatial dynamics of tumour cells in their adaptation to hypoxic microenvironments. As a main novelty with respect to the existing literature, we combine a phenotypic indicator reflecting the experimentally-observed metabolic trade-off between the hypoxia-resistance ability and the proliferative potential with a 2d geometric domain, without the constraint of radial symmetry. The model is settled in the mathematical framework of phenotype-structured population dynamics and it is formulated in terms of systems of coupled non-linear integro-differential equations. The computational outcomes demonstrate that hypoxia-induced selection results in a geometric characterization of phenotypic-defined tumour niches that impact on tumour aggressiveness and invasive ability. Furthermore, results show how the knowledge of environmental characteristics provides a predictive advantage on tumour mass development in terms of size, shape, and composition.
Power Control with QoS Guarantees: A Differentiable Projection-based Unsupervised Learning Framework
Authors: Mehrazin Alizadeh, Hina Tabassum
Date: 2023-05-31 00:00:00

Deep neural networks (DNNs) are emerging as a potential solution to solve NP-hard wireless resource allocation problems. However, in the presence of intricate constraints, e.g., users' quality-of-service (QoS) constraints, guaranteeing constraint satisfaction becomes a fundamental challenge. In this paper, we propose a novel unsupervised learning framework to solve the classical power control problem in a multi-user interference channel, where the objective is to maximize the network sumrate under users' minimum data rate or QoS requirements and power budget constraints. Utilizing a differentiable projection function, two novel deep learning (DL) solutions are pursued. The first is called Deep Implicit Projection Network (DIPNet), and the second is called Deep Explicit Projection Network (DEPNet). DIPNet utilizes a differentiable convex optimization layer to implicitly define a projection function. On the other hand, DEPNet uses an explicitly-defined projection function, which has an iterative nature and relies on a differentiable correction process. DIPNet requires convex constraints; whereas, the DEPNet does not require convexity and has a reduced computational complexity. To enhance the sum-rate performance of the proposed models even further, Frank-Wolfe algorithm (FW) has been applied to the output of the proposed models. Extensive simulations depict that the proposed DNN solutions not only improve the achievable data rate but also achieve zero constraint violation probability, compared to the existing DNNs. The proposed solutions outperform the classic optimization methods in terms of computation time complexity.
Edit Distance based RL for RNNT decoding
Authors: Dongseong Hwang, Changwan Ryu, Khe Chai Sim
Date: 2023-05-31 00:00:00

RNN-T is currently considered the industry standard in ASR due to its exceptional WERs in various benchmark tests and its ability to support seamless streaming and longform transcription. However, its biggest drawback lies in the significant discrepancy between its training and inference objectives. During training, RNN-T maximizes all alignment probabilities by teacher forcing, while during inference, it uses beam search which may not necessarily find the maximum probable alignment. Additionally, RNN-T's inability to experience mistakes during teacher forcing training makes it more problematic when a mistake occurs in inference. To address this issue, this paper proposes a Reinforcement Learning method that minimizes the gap between training and inference time. Our Edit Distance based RL (EDRL) approach computes rewards based on the edit distance, and trains the network at every action level. The proposed approach yielded SoTA WERs on LibriSpeech for the 600M Conformer RNN-T model.
Responsible Design Patterns for Machine Learning Pipelines
Authors: Saud Hakem Al Harbi, Lionel Nganyewou Tidjon, Foutse khomh
Date: 2023-05-31 00:00:00
Tasks: Ethics, Management

Integrating ethical practices into the AI development process for artificial intelligence (AI) is essential to ensure safe, fair, and responsible operation. AI ethics involves applying ethical principles to the entire life cycle of AI systems. This is essential to mitigate potential risks and harms associated with AI, such as algorithm biases. To achieve this goal, responsible design patterns (RDPs) are critical for Machine Learning (ML) pipelines to guarantee ethical and fair outcomes. In this paper, we propose a comprehensive framework incorporating RDPs into ML pipelines to mitigate risks and ensure the ethical development of AI systems. Our framework comprises new responsible AI design patterns for ML pipelines identified through a survey of AI ethics and data management experts and validated through real-world scenarios with expert feedback. The framework guides AI developers, data scientists, and policy-makers to implement ethical practices in AI development and deploy responsible AI systems in production.
Evaluating GPT's Programming Capability through CodeWars' Katas
Authors: Zizhuo Zhang, Lian Wen, Shaoyang Zhang, David Chen, Yanfei Jiang
Date: 2023-05-31 00:00:00

In the burgeoning field of artificial intelligence (AI), understanding the capabilities and limitations of programming-oriented models is crucial. This paper presents a novel evaluation of the programming proficiency of Generative Pretrained Transformer (GPT) models, specifically GPT-3.5 and GPT-4, against coding problems of varying difficulty levels drawn from Codewars. The experiments reveal a distinct boundary at the 3kyu level, beyond which these GPT models struggle to provide solutions. These findings led to the proposal of a measure for coding problem complexity that incorporates both problem difficulty and the time required for solution. The research emphasizes the need for validation and creative thinking capabilities in AI models to better emulate human problem-solving techniques. Future work aims to refine this proposed complexity measure, enhance AI models with these suggested capabilities, and develop an objective measure for programming problem difficulty. The results of this research offer invaluable insights for improving AI programming capabilities and advancing the frontier of AI problem-solving abilities.
Learning the effective order of a hypergraph dynamical system
Authors: Leonie Neuhäuser, Michael Scholkemper, Francesco Tudisco, Michael T. Schaub
Date: 2023-06-02 00:00:00

Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much of this hypergraph structure is actually necessary to faithfully replicate the observed dynamical behaviour. To answer this question, we propose a method to determine the minimum order of a hypergraph necessary to approximate the corresponding dynamics accurately. Specifically, we develop an analytical framework that allows us to determine this order when the type of dynamics is known. We utilize these ideas in conjunction with a hypergraph neural network to directly learn the dynamics itself and the resulting order of the hypergraph from both synthetic and real data sets consisting of observed system trajectories.
Beyond Nyquist in Frequency Response Function Identification: Applied to Slow-Sampled Systems
Authors: Max van Haren, Leonid Mirkin, Lennart Blanken, Tom Oomen
Date: 2023-06-05 00:00:00

Fast-sampled models are essential for control design, e.g., to address intersample behavior. The aim of this paper is to develop a non-parametric identification technique for fast-sampled models of systems that have relevant dynamics and actuation above the Nyquist frequency of the sensor, such as vision-in-the-loop systems. The developed method assumes smoothness of the frequency response function, which allows to disentangle aliased components through local models over multiple frequency bands. The method identifies fast-sampled models of slowly-sampled systems accurately in a single identification experiment. Finally, an experimental example demonstrates the effectiveness of the technique.
Time Dependent Inverse Optimal Control using Trigonometric Basis Functions
Authors: Rahel Rickenbach, Elena Arcari, Melanie N. Zeilinger
Date: 2023-06-05 00:00:00

The choice of objective is critical for the performance of an optimal controller. When control requirements vary during operation, e.g. due to changes in the environment with which the system is interacting, these variations should be reflected in the cost function. In this paper we consider the problem of identifying a time dependent cost function from given trajectories. We propose a strategy for explicitly representing time dependency in the cost function, i.e. decomposing it into the product of an unknown time dependent parameter vector and a known state and input dependent vector, modelling the former via a linear combination of trigonometric basis functions. These are incorporated within an inverse optimal control framework that uses the Karush-Kuhn-Tucker (KKT) conditions for ensuring optimality, and allows for formulating an optimization problem with respect to a finite set of basis function hyperparameters. Results are shown for two systems in simulation and evaluated against state-of-the-art approaches.
Quantification of Residential Flexibility Potential using Global Forecasting Models
Authors: Lorenzo Nespoli, Vasco Medici
Date: 2023-06-05 00:00:00

This paper proposes a general and practical approach to estimate the economic benefits of optimally controlling deferrable loads in a Distribution System Operator's (DSO) grid, without relying on historical observations. We achieve this by learning the simulated response of flexible loads to random control signals, using a non-parametric global forecasting model. An optimal control policy is found by including the latter in an optimization problem. We apply this method to electric water heaters and heat pumps operated through ripple control and show how flexibility, including rebound effects, can be characterized and controlled. Finally, we show that the forecaster's accuracy is sufficient to completely bypass the simulations and directly use the forecaster to estimate the economic benefit of flexibility control.
Aerial Swarm Defense using Interception and Herding Strategies
Authors: Vishnu S. Chipade, Dimitra Panagou
Date: 2023-06-04 00:00:00

This paper presents a multi-mode solution to the problem of defending a circular protected area (target) from a wide range of attacks by swarms of risk-taking and/or risk-averse attacking agents (attackers). The proposed multi-mode solution combines two defense strategies, namely: 1) an interception strategy for a team of defenders to intercept multiple risk-taking attackers while ensuring that the defenders do not collide with each other, 2) a herding strategy to herd a swarm of risk-averse attackers to a safe area. In particular, we develop mixed integer programs (MIPs) and geometry-inspired heuristics to distribute and assign and/or reassign the defenders to interception and herding tasks under different spatiotemporal behaviors by the attackers such as splitting into smaller swarms to evade defenders easily or high-speed maneuvers by some risk-taking attackers to maximize damage to the protected area. We provide theoretical as well as numerical comparisons of the computational costs of these MIPs and the heuristics, and demonstrate the overall approach in simulations.
Distributionally robust uncertainty quantification via data-driven stochastic optimal control
Authors: Guanru Pan, Timm Faulwasser
Date: 2023-06-04 00:00:00
Tasks: LEMMA, Uncertainty Quantification

This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability measures or distributions. Typically, stochastic optimal control requires knowledge of underlying dynamics and is as such challenging. Relying on a stochastic fundamental lemma from data-driven control and on the framework of polynomial chaos expansions, we propose an approach to reformulate distributionally robust optimal control problems with ambiguity sets as uncertain conic programs in a finite-dimensional vector space. We show how to construct these programs from previously recorded data and how to relax the uncertain conic program to numerically tractable convex programs via appropriate sampling of the underlying distributions. The efficacy of our method is illustrated via a numerical example.
Synchronization of multiple rigid body systems: a survey
Authors: X. Jin, Daniel W. C. Ho, Y. Tang
Date: 2023-06-04 00:00:00
Tasks: Survey

The multi-agent system has been a hot topic in the past few decades owing to its lower cost, higher robustness, and higher flexibility. As a particular multi-agent system, the multiple rigid body system received a growing interest for its wide applications in transportation, aerospace, and ocean exploration. Due to the non-Euclidean configuration space of attitudes and the inherent nonlinearity of the dynamics of rigid body systems, synchronization of multiple rigid body systems is quite challenging. This paper aims to present an overview of the recent progress in synchronization of multiple rigid body systems from the view of two fundamental problems. The first problem focuses on attitude synchronization, while the second one focuses on cooperative motion control in that rotation and translation dynamics are coupled. Finally, a summary and future directions are given in the conclusion.
Payoff Mechanism Design for Coordination in Multi-Agent Task Allocation Games
Authors: Shinkyu Park, Julian Barreiro-Gomez
Date: 2023-06-04 00:00:00
Tasks: Decision Making

We investigate a multi-agent decision-making problem where a large population of agents is responsible for carrying out a set of assigned tasks. The amount of jobs in each task varies over time governed by a dynamical system model. Each agent needs to select one of the available strategies to take on one or more tasks. Since each strategy allows an agent to perform multiple tasks at a time, possibly at distinct rates, the strategy selection of the agents needs to be coordinated. We formulate the problem using the population game formalism and refer to it as the task allocation game. We discuss the design of a decision-making model that incentivizes the agents to coordinate in the strategy selection process. As key contributions, we propose a method to find a payoff-driven decision-making model, and discuss how the model allows the strategy selection of the agents to be responsive to the amount of remaining jobs in each task while asymptotically attaining the optimal strategies. Leveraging analytical tools from feedback control theory, we derive technical conditions that the model needs to satisfy, which are used to construct a numerical approach to compute the model. We validate our solution through simulations to highlight how the proposed approach coordinates the agents in task allocation games.
Decompositions of Nonlinear Input-Output Systems to Zero the Output
Authors: W. Steven Gray, Kurusch Ebrahimi-Fard, Alexander Schmeding
Date: 2023-06-03 00:00:00

Consider an input-output system where the output is the tracking error given some desired reference signal. It is natural to consider under what conditions the problem has an exact solution, that is, the tracking error is exactly the zero function. If the system has a well defined relative degree and the zero function is in the range of the input-output map, then it is well known that the system is locally left invertible, and thus, the problem has a unique exact solution. A system will fail to have relative degree when more than one exact solution exists. The general goal of this paper is to describe a decomposition of an input-output system having a Chen-Fliess series representation into a parallel product of subsystems in order to identify possible solutions to the problem of zeroing the output. For computational purposes, the focus is on systems whose generating series are polynomials. It is shown that the shuffle algebra on the set of generating polynomials is a unique factorization domain so that any polynomial can be uniquely factored modulo a permutation into its irreducible elements for the purpose of identifying the subsystems in a parallel product decomposition. This is achieved using the fact that this shuffle algebra is isomorphic to the symmetric algebra over the vector space spanned by Lyndon words. A specific algorithm for factoring generating polynomials into its irreducible factors is presented based on the Chen-Fox-Lyndon factorization of words.
Adaptive Approximation-Based Control for Nonlinear Systems: A Unified Solution with Accurate and Inaccurate Measurements
Authors: Dong Zhao
Date: 2023-06-03 00:00:00

A unified solution to adaptive approximation-based control for nonlinear systems with accurate and inaccurate state measurement is synthesized in this study. Starting from the standard adaptive approximation-based controller with accurate state measurement, its corresponding physical interpretation, stability conclusion, and learning ability are rigorously addressed when facing additive measurement inaccuracy, and explicit answers are obtained in the framework of both controller matching and system matching. Finally, it proves that, with a certain condition, the standard adaptive approximation-based controller works as a unified solution for the cases with accurate and inaccurate measurement, and the solution can be extended to the nonlinear system control problems with extra unknown dynamics or faults in actuator and/or process dynamics. A single-link robot arm example is used for the simulation demonstration of the unified solution.
Replay Attack Detection Based on Parity Space Method for Cyber-Physical Systems
Authors: Dong Zhao, Yang Shi, Steven X. Ding, Yueyang Li, Fangzhou Fu
Date: 2023-06-03 00:00:00

The replay attack detection problem is studied from a new perspective based on parity space method in this paper. The proposed detection methods have the ability to distinguish system fault and replay attack, handle both input and output data replay, maintain certain control performance, and can be implemented conveniently and efficiently. First, the replay attack effect on the residual is derived and analyzed. The residual change induced by replay attack is characterized explicitly and the detection performance analysis based on two different test statistics are given. Second, based on the replay attack effect characterization, targeted passive and active design for detection performance enhancement are proposed. Regarding the passive design, four optimization schemes regarding different cost functions are proposed with optimal parity matrix solutions, and the unified solution to the passive optimization schemes is obtained; the active design is enabled by a marginally stable filter so as to enlarge the replay attack effect on the residual for detection. Simulations and comparison studies are given to show the effectiveness of the proposed methods.
Resilient Distributed Parameter Estimation in Sensor Networks
Authors: Jiaqi Yan, Kuo Li, Hideaki Ishii
Date: 2023-06-03 00:00:00
Tasks: parameter estimation

In this paper, we study the problem of parameter estimation in a sensor network, where the measurements and updates of some sensors might be arbitrarily manipulated by adversaries. Despite the presence of such misbehaviors, normally behaving sensors make successive observations of an unknown $d$-dimensional vector parameter and aim to infer its true value by cooperating with their neighbors over a directed communication graph. To this end, by leveraging the so-called dynamic regressor extension and mixing procedure, we transform the problem of estimating the vector parameter to that of estimating $d$ scalar ones. For each of the scalar problem, we propose a resilient combine-then-adapt diffusion algorithm, where each normal sensor performs a resilient combination to discard the suspicious estimates in its neighborhood and to fuse the remaining values, alongside an adaptation step to process its streaming observations. With a low computational cost, this estimator guarantees that each normal sensor exponentially infers the true parameter even if some of them are not sufficiently excited.
Converse negative imaginary theorems
Authors: Sei Zhen Khong, Di Zhao, Alexander Lanzon
Date: 2023-06-03 00:00:00

Converse negative imaginary theorems for linear time-invariant systems are derived. In particular, we provide necessary and sufficient conditions for a feedback system to be robustly stable against various types of negative imaginary (NI) uncertainty. Uncertainty classes of marginally stable NI systems and stable strictly NI systems with restrictions on their static or instantaneous gains are considered. It is shown that robust stability against the former class entails the strictly NI property, whereas the latter class entails the NI property. We also establish a non-existence result that no stable system can robustly stabilise all marginally stable NI uncertainty, thereby showing that the uncertainty class of NI systems is too large as far as robust feedback stability is concerned, thus justifying the consideration of subclasses of NI systems with constrained static or instantaneous gains.