8,439 research outputs found
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Sequential Quadratic Programming-based Iterative Learning Control for Nonlinear Systems
Learning-based control methods for industrial processes leverage the
repetitive nature of the underlying process to learn optimal inputs for the
system. While many works focus on linear systems, real-world problems involve
nonlinear dynamics. In this work, we propose an algorithm for the nonlinear
iterative learning control problem based on sequential quadratic programming, a
well-studied method for nonconvex optimization. We repeatedly solve quadratic
subproblems built using approximate nonlinear models and process measurements,
to find an optimal input for the original system. We demonstrate our method in
a trajectory optimization problem for a precision motion system. We present
simulations to illustrate the performance of the proposed method for linear and
nonlinear dynamics models
Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies
Gradient-based methods have been widely used for system design and
optimization in diverse application domains. Recently, there has been a renewed
interest in studying theoretical properties of these methods in the context of
control and reinforcement learning. This article surveys some of the recent
developments on policy optimization, a gradient-based iterative approach for
feedback control synthesis, popularized by successes of reinforcement learning.
We take an interdisciplinary perspective in our exposition that connects
control theory, reinforcement learning, and large-scale optimization. We review
a number of recently-developed theoretical results on the optimization
landscape, global convergence, and sample complexity of gradient-based methods
for various continuous control problems such as the linear quadratic regulator
(LQR), control, risk-sensitive control, linear quadratic
Gaussian (LQG) control, and output feedback synthesis. In conjunction with
these optimization results, we also discuss how direct policy optimization
handles stability and robustness concerns in learning-based control, two main
desiderata in control engineering. We conclude the survey by pointing out
several challenges and opportunities at the intersection of learning and
control.Comment: To Appear in Annual Review of Control, Robotics, and Autonomous
System
A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics
We propose in this paper an adaptive reduced order modelling technique based
on domain partitioning for parametric problems of fracture. We show that
coupling domain decomposition and projection-based model order reduction
permits to focus the numerical effort where it is most needed: around the zones
where damage propagates. No \textit{a priori} knowledge of the damage pattern
is required, the extraction of the corresponding spatial regions being based
solely on algebra. The efficiency of the proposed approach is demonstrated
numerically with an example relevant to engineering fracture.Comment: Submitted for publication in CMAM
- …