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This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
Coordinating large populations of autonomous agents, such as UAV swarms or satellite constellations, poses significant computational challenges for traditional multi-agent control methods. This paper introduces a new optimization framework…
Observable operator models (OOMs) offer a powerful framework for modelling stochastic processes, surpassing the traditional hidden Markov models (HMMs) in generality and efficiency. However, using OOMs to model infinite-dimensional…
To mitigate dissipative effects from environmental interactions and efficiently stabilize quantum states, time-optimal control has emerged as an effective strategy for open quantum systems. This paper extends the framework by incorporating…
Accurate deformable object manipulation (DOM) is essential for achieving autonomy in robotic surgery, where soft tissues are being displaced, stretched, and dissected. Many DOM methods can be powered by simulation, which ensures realistic…
Optimization Modulo Theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or pseudo-Boolean terms. However, many SMT and OMT…
Prompt learning in pretrained visual-language models has shown remarkable flexibility across various downstream tasks. Leveraging its inherent lightweight nature, recent research attempted to integrate the powerful pretrained models into…
This paper discusses the design of an extremum seeking controller that relies on a monitoring function for a class of SISO uncertain nonlinear systems characterized by arbitrary and uncertain relative degree. Our demonstration illustrates…
In modern robotics, addressing the lack of accurate state space information in real-world scenarios has led to a significant focus on utilizing visuomotor observation to provide safety assurances. Although supervised learning methods, such…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
We develop a new Hamiton-Jacobi (HJ) and differential game approach for exploring the Pareto front of (constrained) multi-objective optimization (MOO) problems. Given a preference function, we embed the scalarized MOO problem into the value…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
Estimating the reachable set of a dynamical system is a fundamental problem in control theory, particularly when control inputs are bounded. Direct simulation using randomly sampled admissible controls often leads to trajectories that…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
Traditional SLAM algorithms are typically based on artificial features, which lack high-level information. By introducing semantic information, SLAM can own higher stability and robustness rather than purely hand-crafted features. However,…
This paper is concerned with numerically finding a global solution of constrained optimal control problems with many local minima. The focus is on the optimal decentralized control (ODC) problem, whose feasible set is recently shown to have…
Retrieval-Augmented Generation (RAG) systems are increasingly deployed on large-scale document collections, often comprising millions of documents and tens of millions of text chunks. In industrial-scale retrieval platforms, scalability is…
In optimal control problems of control-affine systems, whose solutions are bang-bang or singular type, verification of optimality using the Hamilton-Jacobi-Bellman (HJB) equation involves the computation of partial derivatives of switching…
This paper presents a two-stage framework for constrained near-optimal feedback control of input-affine nonlinear systems. An approximate value function for the unconstrained control problem is computed offline by solving the…