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Nan Bai

Publications and source records attributed to Nan Bai.

At least 19 recordsLinked to original sources
arXiv2026

Distributed Robust Model Predictive Control for Optimal Consensus of Unknown Multiagent Systems with Event-Triggered Communication

In this paper, we study the optimal consensus problem for multiagent systems with unknown dynamics. We propose a robust model predictive control (MPC) framework that jointly optimizes the control input and consensus sequences while enforcing state and input constraints. Within this framework, noisy offline data are used to construct nominal prediction models and quantify the associated uncertainty, which is explicitly incorporated into the robust MPC design. To solve the resulting optimization problem at each MPC update with reduced inter-agent communication, we develop a distributed gradient-projection alternating direction method of multipliers (ADMM) algorithm with an event-triggered information exchange mechanism and establish its convergence to the optimal solution. Furthermore, sufficient conditions are established to guarantee robust constraint satisfaction and practical consensus of the closed-loop multiagent system. Numerical simulations demonstrate the effectiveness of the proposed framework.

eess.SY↗
arXiv2026

A Unified Framework for Robust Data-Driven Model Predictive Control with Terminal Ingredients

This paper proposes a unified framework for robust data-driven model predictive control (MPC) with terminal ingredients for unknown linear time-invariant systems. Based on Willems' fundamental lemma, a single offline input-output trajectory is used as an implicit model, while online implementation only requires past input-output measurements. Bounded measurement noise is considered in both offline and online output data. The framework consists of an offline stage, where robust terminal ingredients are designed directly from noisy data, and an online stage, where these ingredients are incorporated into a one-step MPC scheme. Recursive feasibility of the proposed framework and practical exponential stability of the closed-loop system are established. Numerical results illustrate the performance tuning capability of the terminal set, with particularly pronounced benefits for short prediction horizons, and show that the proposed framework achieves performance comparable to data-driven MPC without terminal ingredients while requiring a reduced prediction horizon and less online computation.

eess.SY↗
arXiv2026

Distributed Model Predictive Control for Optimal Consensus of Constrained Heterogeneous Multi-agent Systems

This paper investigates the distributed optimal consensus control problem of constrained heterogeneous multi-agent systems within a model predictive control (MPC) scheme. Both the control input sequence and the dynamically feasible consensus equilibrium are optimized simultaneously within the proposed MPC framework to improve consensus performance, yielding a coupled constrained optimization problem at each prediction time. A distributed primal--dual algorithm is developed to solve the resulting optimization problem, and locally verifiable conditions are derived to guarantee its convergence. Furthermore, sufficient terminal conditions are established for the proposed MPC framework to guarantee the recursive feasibility and asymptotic consensus of the closed-loop heterogeneous multi-agent systems. Finally, numerical simulations verify the effectiveness of the proposed approach.

eess.SY↗
arXiv2026

Characterizing Robustness in Nonlinear Optimal Control: From Stability to Optimality

In nonlinear optimal control, uncertainties in system dynamics may affect not only closed-loop stability but also the achieved optimality properties of the resulting solutions. This paper develops a systematic robustness analysis for nonlinear optimal control beyond the conventional focus on stability in robust control theory. First, we demonstrate that the optimal value function retains its Lyapunov property under a quantifiable criterion, thereby guaranteeing the preservation of closed-loop stability. Building upon this foundation, we establish explicit characterizations for optimality deviations induced by model mismatch in both closed-loop performance and optimal controllers, and further reveal their consistency with classical linear-quadratic regulator (LQR) results. In addition, the robustness analysis admits a unified computational formulation that gives rise to an iterative scheme with guaranteed convergence, enabling quantitative assessment of optimality robustness in nonlinear control systems. Numerical examples validate the theoretical analysis.

math.OC↗
arXiv2026

Optimality Robustness in Koopman-Based Control

The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This naturally raises the question of how such uncertainty-induced optimality deviation can be quantified and mitigated. To address this problem, we adopt a unified analysis-to-design perspective that connects the characterization of optimality robustness with its improvement through controller design. At the analysis level, we establish a unified treatment of multiple uncertainty sources in Koopman-based control, where approximation error and noisy data are incorporated into a common robustness analysis through a norm-bounded representation. At the design level, we develop a robustness-aware optimal control methodology that provably reduces such optimality deviations, thereby enhancing robustness while explicitly revealing a quantitative trade-off between nominal optimality and robustness. As for practical implementation aspect, we further propose a tractable policy iteration algorithm, whose well-posedness and convergence are established via vanishing viscosity regularization and elliptic partial differential equation (PDE) techniques. Numerical examples validate the theoretical findings and demonstrate the effectiveness of proposed methodology.

eess.SY↗
arXiv2026

Optimality Deviation using the Koopman Operator

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics through a lifted state space, the presence of approximation error inevitably leads to deviations in the computed optimal controller and the resulting value function. We derive explicit upper bounds for these optimality deviations, which characterize the worst-case effect of approximation error. Supported by numerical examples, these theoretical findings provide a quantitative foundation for improving the robustness of data-driven optimal controller design.

math.OC↗
arXiv2026

Solving for the integrable boundary states of the ABJM spin chain from $KT$-relations

We study integrable boundary states of the alternating SU(4) spin chain arising in ABJM theory. Starting from the $KT$-relation, we directly solve the integrability constraints for states with $n$-site translational invariance. For odd and even $n$, these constraints are reduced respectively to state equations and operator equations for the elementary $n$-site block and the matrix $K(u)$. We analyze chiral and achiral cases for $n\leq4$. In the 1-site case we allow general operator-valued integrable pairs with an internal space, while in the remaining cases we focus on $c$-number solutions.

hep-th↗
arXiv2026

Chiral Integrable Boundary States of ABJM Spin Chain from Reflection Equations

We develop a general framework for constructing $2n$-site chiral integrable matrix product states in Aharony-Bergman-Jafferis-Maldacena spin chain, based on reflection equations and the fusion procedure. For four-site chiral integrable product states, we propose their exact overlap formulas with Bethe states. We also investigate the chiral integrable subspaces numerically.

hep-th↗
arXiv2025

A general fusion procedure for open $\mathfrak{gl}(N)$ spin chains: Application to the ABJM spin chain

We formulate a general fusion procedure for open $\mathfrak{gl}(N)$ spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of $\mathfrak{gl}(N)$. We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of $\mathfrak{su}(4)$.

hep-th↗
arXiv2025

Integrating Uncertainties for Koopman-Based Stabilization

Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in data-driven control via the Koopman operator, fully accounting for three uncertainties: projection error, estimation error, and process disturbance. It comprehensively investigates both direct and indirect data-driven control approaches, facilitating flexible methodology selection for analysis and control. For the direct approach, considering process disturbances, the lifted-state feedback controller, designed via a linear matrix inequality (LMI), robustly stabilizes all lifted bilinear systems consistent with noisy data. For the indirect approach requiring system identification, the feedback controller, designed using a nonlinear matrix inequality convertible to an LMI, ensures closed-loop stability under worst-case process disturbances. Numerical simulations via cross-validation validate the effectiveness of both approaches, highlighting their theoretical significance and practical utility.

eess.SY↗
arXiv2025

Information Retrieval for Climate Impact

The purpose of the MANILA24 Workshop on information retrieval for climate impact was to bring together researchers from academia, industry, governments, and NGOs to identify and discuss core research problems in information retrieval to assess climate change impacts. The workshop aimed to foster collaboration by bringing communities together that have so far not been very well connected -- information retrieval, natural language processing, systematic reviews, impact assessments, and climate science. The workshop brought together a diverse set of researchers and practitioners interested in contributing to the development of a technical research agenda for information retrieval to assess climate change impacts.

cs.IR↗
arXiv2024

MentalGLM Series: Explainable Large Language Models for Mental Health Analysis on Chinese Social Media

As the prevalence of mental health challenges, social media has emerged as a key platform for individuals to express their emotions.Deep learning tends to be a promising solution for analyzing mental health on social media. However, black box models are often inflexible when switching between tasks, and their results typically lack explanations. With the rise of large language models (LLMs), their flexibility has introduced new approaches to the field. Also due to the generative nature, they can be prompted to explain decision-making processes. However, their performance on complex psychological analysis still lags behind deep learning. In this paper, we introduce the first multi-task Chinese Social Media Interpretable Mental Health Instructions (C-IMHI) dataset, consisting of 9K samples, which has been quality-controlled and manually validated. We also propose MentalGLM series models, the first open-source LLMs designed for explainable mental health analysis targeting Chinese social media, trained on a corpus of 50K instructions. The proposed models were evaluated on three downstream tasks and achieved better or comparable performance compared to deep learning models, generalized LLMs, and task fine-tuned LLMs. We validated a portion of the generated decision explanations with experts, showing promising results. We also evaluated the proposed models on a clinical dataset, where they outperformed other LLMs, indicating their potential applicability in the clinical field. Our models show strong performance, validated across tasks and perspectives. The decision explanations enhance usability and facilitate better understanding and practical application of the models. Both the constructed dataset and the models are publicly available via: https://github.com/zwzzzQAQ/MentalGLM.

cs.CL↗
arXiv2024

The Fused Model of Alternating Spin Chain from ABJM Theory

In this paper we give an algebraic construction of the fused model for ABJM spin chain and find the corresponding boost operator. We also investigate the open spin Hamiltonian for fused model and point out the general common structures of the boundary terms.

hep-th↗
arXiv2023

Augmented Computational Design: Methodical Application of Artificial Intelligence in Generative Design

This chapter presents methodological reflections on the necessity and utility of artificial intelligence in generative design. Specifically, the chapter discusses how generative design processes can be augmented by AI to deliver in terms of a few outcomes of interest or performance indicators while dealing with hundreds or thousands of small decisions. The core of the performance-based generative design paradigm is about making statistical or simulation-driven associations between these choices and consequences for mapping and navigating such a complex decision space. This chapter will discuss promising directions in Artificial Intelligence for augmenting decision-making processes in architectural design for mapping and navigating complex design spaces.

cs.AI↗
arXiv2023

EquiCity Game: A mathematical serious game for participatory design of spatial configurations

We propose mechanisms for a mathematical social-choice game that is designed to mediate decision-making processes for city planning, urban area redevelopment, and architectural design (massing) of urban housing complexes. The proposed game is effectively a multi-player generative configurator equipped with automated appraisal/scoring mechanisms for revealing the aggregate impact of alternatives; featuring a participatory digital process to support transparent and inclusive decision-making processes in spatial design for ensuring an equitable balance of sustainable development goals. As such, the game effectively empowers a group of decision-makers to reach a fair consensus by mathematically simulating many rounds of trade-offs between their decisions, with different levels of interest or control over various types of investments. Our proposed gamified design process encompasses decision-making about the most idiosyncratic aspects of a site related to its heritage status and cultural significance to the physical aspects such as balancing access to sunlight and the right to sunlight of the neighbours of the site, ensuring coherence of the entire configuration with regards to a network of desired closeness ratings, the satisfaction of a programme of requirements, and intricately balancing individual development goals in conjunction with communal goals and environmental design codes. The game is developed fully based on an algebraic computational process on our own digital twinning platform, using open geospatial data and open-source computational tools such as NumPy. The mathematical process consists of a Markovian design machine for balancing the decisions of actors, a massing configurator equipped with Fuzzy Logic and Multi-Criteria Decision Analysis, algebraic graph-theoretical accessibility evaluators, and automated solar-climatic evaluators using geospatial computational geometry.

cs.CY↗
arXiv2022

Heri-Graphs: A Workflow of Creating Datasets for Multi-modal Machine Learning on Graphs of Heritage Values and Attributes with Social Media

Values (why to conserve) and Attributes (what to conserve) are essential concepts of cultural heritage. Recent studies have been using social media to map values and attributes conveyed by public to cultural heritage. However, it is rare to connect heterogeneous modalities of images, texts, geo-locations, timestamps, and social network structures to mine the semantic and structural characteristics therein. This study presents a methodological workflow for constructing such multi-modal datasets using posts and images on Flickr for graph-based machine learning (ML) tasks concerning heritage values and attributes. After data pre-processing using state-of-the-art ML models, the multi-modal information of visual contents and textual semantics are modelled as node features and labels, while their social relationships and spatiotemporal contexts are modelled as links in Multi-Graphs. The workflow is tested in three cities containing UNESCO World Heritage properties - Amsterdam, Suzhou, and Venice, which yielded datasets with high consistency for semi-supervised learning tasks. The entire process is formally described with mathematical notations, ready to be applied in provisional tasks both as ML problems with technical relevance and as urban/heritage study questions with societal interests. This study could also benefit the understanding and mapping of heritage values and attributes for future research in global cases, aiming at inclusive heritage management practices.

cs.SI↗
arXiv2021

WHOSe Heritage: Classification of UNESCO World Heritage "Outstanding Universal Value" Documents with Soft Labels

The UNESCO World Heritage List (WHL) includes the exceptionally valuable cultural and natural heritage to be preserved for mankind. Evaluating and justifying the Outstanding Universal Value (OUV) is essential for each site inscribed in the WHL, and yet a complex task, even for experts, since the selection criteria of OUV are not mutually exclusive. Furthermore, manual annotation of heritage values and attributes from multi-source textual data, which is currently dominant in heritage studies, is knowledge-demanding and time-consuming, impeding systematic analysis of such authoritative documents in terms of their implications on heritage management. This study applies state-of-the-art NLP models to build a classifier on a new dataset containing Statements of OUV, seeking an explainable and scalable automation tool to facilitate the nomination, evaluation, research, and monitoring processes of World Heritage sites. Label smoothing is innovatively adapted to improve the model performance by adding prior inter-class relationship knowledge to generate soft labels. The study shows that the best models fine-tuned from BERT and ULMFiT can reach 94.3% top-3 accuracy. A human study with expert evaluation on the model prediction shows that the models are sufficiently generalizable. The study is promising to be further developed and applied in heritage research and practice.

cs.CL↗