arXiv subjects

Siji Chen

Publications and source records attributed to Siji Chen.

4 recordsLinked to original sources

arXiv2026

Beyond Invariant Dictionary: Data-Driven Koopman Spectral Recovery with Filtered Extended Dynamic Mode Decomposition

The Koopman operator provides a linear framework for analyzing nonlinear dynamical systems through spectral properties. Extended Dynamic Mode Decomposition (EDMD) approximates this operator from data, but non-invariant dictionaries can introduce spurious eigenvalues. We introduce the Projected Koopman Operator Approximation framework for constructing Filtered EDMD operators. The framework projects the Koopman action onto admissible dictionary subspaces that need not be invariant, while exactly preserving every represented Koopman eigenpair with nonzero eigenvalue. A forward--intersection chain provides a canonical hierarchy of compatible subspaces, connecting the full dictionary to its maximal invariant core while retaining useful intermediate models. We analyze two projection geometries: a coordinate-orthogonal projector, which requires no function-space Gram-matrix estimate but is basis-dependent, and a function-space orthogonal projector, which recovers population EDMD at the unfiltered level. We characterize their relationship to EDMD and existing subspace-selection methods. We also develop SVD-based algorithms for constructing sampled forward--intersection spaces and implementing the coordinate projector. Under independent noiseless sampling and exact-rank identifiability, the resulting empirical operators converge almost surely to their population counterparts. Experiments on a Kronecker flow, a polynomial system, and the Van~der~Pol oscillator demonstrate reduced spectral pollution. For Van~der~Pol, the coordinate projector recovers the local equilibrium spectrum independently of the sampling measure, whereas the $L^2(\mu)$ projector approximates the limit-cycle spectrum on the same certified subspace.

math.NA↗

arXiv2026

RSC: Decentralized Rigid Formation Flocking for Large-Scale Swarms via Hybrid Predictive Control and Online Reconfiguration

Decentralized rigid formation flocking requires a swarm of autonomous agents to maintain a predetermined geometric configuration while moving, relying solely on local sensing and communication. However, existing decentralized control methods struggle to maintain strict inter-agent distance constraints in cluttered environments, often suffering from local minima deadlocks, high frequency control oscillations, or limited flexibility during obstacle navigation, resulting in low success rate. To address these limitations, we propose Rigid Swarm Control (RSC), a decentralized control framework for large-scale rigid formation flocking. To escape local minima via robust long-term planning while ensuring short-term safety, RSC integrates finite-horizon trajectory predictions with a reactive artificial potential field (APF) safety controller within a hybrid architecture. Furthermore, to accelerate formation reassembly after obstacle traversal without interrupting task execution, RSC introduces an online leader-follower reconfiguration mechanism based on stable role exchange. Extensive evaluations in challenging cluttered environments with 25 UAVs demonstrate that RSC reliably unifies rigid formation maintenance, obstacle avoidance, and target tracking. Under strict success criteria - collision-free operation with a maximum relative edge-length error below 10%, RSC achieves an 83% success rate, significantly outperforming existing heuristic and learning-based baselines that fall below 5%.

cs.RO↗

arXiv2024

Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothing

Randomized Smoothing (RS) is currently a scalable certified defense method providing robustness certification against adversarial examples. Although significant progress has been achieved in providing defenses against $\ell_p$ adversaries, the interaction between the smoothing distribution and the robustness certification still remains vague. In this work, we comprehensively study the effect of two families of distributions, named Exponential Standard Gaussian (ESG) and Exponential General Gaussian (EGG) distributions, on Randomized Smoothing and Double Sampling Randomized Smoothing (DSRS). We derive an analytic formula for ESG's certified radius, which converges to the origin formula of RS as the dimension $d$ increases. Additionally, we prove that EGG can provide tighter constant factors than DSRS in providing $Ω(\sqrt{d})$ lower bounds of $\ell_2$ certified radius, and thus further addresses the curse of dimensionality in RS. Our experiments on real-world datasets confirm our theoretical analysis of the ESG distributions, that they provide almost the same certification under different exponents $η$ for both RS and DSRS. In addition, EGG brings a significant improvement to the DSRS certification, but the mechanism can be different when the classifier properties are different. Compared to the primitive DSRS, the increase in certified accuracy provided by EGG is prominent, up to 6.4% on ImageNet.

cs.LG↗

arXiv2023

Learning Decentralized Flocking Controllers with Spatio-Temporal Graph Neural Network

Recently a line of researches has delved the use of graph neural networks (GNNs) for decentralized control in swarm robotics. However, it has been observed that relying solely on the states of immediate neighbors is insufficient to imitate a centralized control policy. To address this limitation, prior studies proposed incorporating $L$-hop delayed states into the computation. While this approach shows promise, it can lead to a lack of consensus among distant flock members and the formation of small clusters, consequently resulting in the failure of cohesive flocking behaviors. Instead, our approach leverages spatiotemporal GNN, named STGNN that encompasses both spatial and temporal expansions. The spatial expansion collects delayed states from distant neighbors, while the temporal expansion incorporates previous states from immediate neighbors. The broader and more comprehensive information gathered from both expansions results in more effective and accurate predictions. We develop an expert algorithm for controlling a swarm of robots and employ imitation learning to train our decentralized STGNN model based on the expert algorithm. We simulate the proposed STGNN approach in various settings, demonstrating its decentralized capacity to emulate the global expert algorithm. Further, we implemented our approach to achieve cohesive flocking, leader following and obstacle avoidance by a group of Crazyflie drones. The performance of STGNN underscores its potential as an effective and reliable approach for achieving cohesive flocking, leader following and obstacle avoidance tasks.

cs.RO↗