Related papers: From Control to Mathematics-Part I: Controllabilit…
Nonlinear optimal control problems are often solved with numerical methods that require knowledge of system's dynamics which may be difficult to infer, and that carry a large computational cost associated with iterative calculations. We…
Multi-task learning (MTL) has been widely adopted for its ability to simultaneously learn multiple tasks. While existing gradient manipulation methods often yield more balanced solutions than simple scalarization-based approaches, they…
This tutorial consists of a brief introduction to the modern control approach called model predictive control (MPC) and its numerical implementation using MATLAB. We discuss the basic concepts and numerical implementation of the two major…
Human demonstration data is often ambiguous and incomplete, motivating imitation learning approaches that also exhibit reliable planning behavior. A common paradigm to perform planning-from-demonstration involves learning a reward function…
Ensemble control, an emerging research field focusing on the study of large populations of dynamical systems, has demonstrated great potential in numerous scientific and practical applications. Striking examples include pulse design for…
Manufacturing processes are often perturbed by drifts in the environment and wear in the system, requiring control re-tuning even in the presence of repetitive operations. This paper presents an iterative learning framework for automatic…
This paper presents a novel methodology to develop scheduling algorithms. The scheduling problem is phrased as a control problem, and control-theoretical techniques are used to design a scheduling algorithm that meets specific requirements.…
Including Model Predictive Control (MPC) in the undergraduate/graduate control curriculum is becoming vitally important due to the growing adoption of MPC in many industrial areas. In this paper, we present an overview of the predictive…
Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
Learning from data of past tasks can substantially improve the accuracy of mechatronic systems. Often, for fast and safe learning a model of the system is required. The aim of this paper is to develop a model-free approach for fast and safe…
In-Context Learning (ICL) enables pretrained LLMs to adapt to downstream tasks by conditioning on a small set of input-output demonstrations, without any parameter updates. Although there have been many theoretical efforts to explain how…
The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear…
This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bi-level…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
Composite adaptive control (CAC) that integrates direct and indirect adaptive control techniques can achieve smaller tracking errors and faster parameter convergence compared with direct and indirect adaptive control techniques. However,…
One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…
Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address…