166 research outputs found
Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance
Issued as Progress report, and Final report, Project no. E-21-67
Robust Output Regulation of the Linearized Boussinesq Equations with Boundary Control and Observation
We study temperature and velocity output tracking problem for a
two-dimensional room model with the fluid dynamics governed by the linearized
translated Boussinesq equations. Additionally, the room model includes
finite-dimensional models for actuation and sensing dynamics, thus the complete
model dynamics are governed by an ODE-PDE-ODE system. As the main result, we
design a low-dimensional internal model based controller for robust output
racking of the room model. Efficiency of the controller is demonstrated through
a numerical example of velocity and temperature tracking.Comment: 26 pages, 9 figures, submitte
Numerical controllability of the wave equation through primal methods and Carleman estimates
This paper deals with the numerical computation of boundary null controls for
the 1D wave equation with a potential. The goal is to compute an approximation
of controls that drive the solution from a prescribed initial state to zero at
a large enough controllability time. We do not use in this work duality
arguments but explore instead a direct approach in the framework of global
Carleman estimates. More precisely, we consider the control that minimizes over
the class of admissible null controls a functional involving weighted integrals
of the state and of the control. The optimality conditions show that both the
optimal control and the associated state are expressed in terms of a new
variable, the solution of a fourth-order elliptic problem defined in the
space-time domain. We first prove that, for some specific weights determined by
the global Carleman inequalities for the wave equation, this problem is
well-posed. Then, in the framework of the finite element method, we introduce a
family of finite-dimensional approximate control problems and we prove a strong
convergence result. Numerical experiments confirm the analysis. We complete our
study with several comments
On the Construction of Safe Controllable Regions for Affine Systems with Applications to Robotics
This paper studies the problem of constructing in-block controllable (IBC)
regions for affine systems. That is, we are concerned with constructing regions
in the state space of affine systems such that all the states in the interior
of the region are mutually accessible through the region's interior by applying
uniformly bounded inputs. We first show that existing results for checking
in-block controllability on given polytopic regions cannot be easily extended
to address the question of constructing IBC regions. We then explore the
geometry of the problem to provide a computationally efficient algorithm for
constructing IBC regions. We also prove the soundness of the algorithm. We then
use the proposed algorithm to construct safe speed profiles for different
robotic systems, including fully-actuated robots, ground robots modeled as
unicycles with acceleration limits, and unmanned aerial vehicles (UAVs).
Finally, we present several experimental results on UAVs to verify the
effectiveness of the proposed algorithm. For instance, we use the proposed
algorithm for real-time collision avoidance for UAVs.Comment: 17 pages, 18 figures, under review for publication in Automatic
Introduction to Online Nonstochastic Control
This text presents an introduction to an emerging paradigm in control of
dynamical systems and differentiable reinforcement learning called online
nonstochastic control. The new approach applies techniques from online convex
optimization and convex relaxations to obtain new methods with provable
guarantees for classical settings in optimal and robust control.
The primary distinction between online nonstochastic control and other
frameworks is the objective. In optimal control, robust control, and other
control methodologies that assume stochastic noise, the goal is to perform
comparably to an offline optimal strategy. In online nonstochastic control,
both the cost functions as well as the perturbations from the assumed dynamical
model are chosen by an adversary. Thus the optimal policy is not defined a
priori. Rather, the target is to attain low regret against the best policy in
hindsight from a benchmark class of policies.
This objective suggests the use of the decision making framework of online
convex optimization as an algorithmic methodology. The resulting methods are
based on iterative mathematical optimization algorithms, and are accompanied by
finite-time regret and computational complexity guarantees.Comment: Draft; comments/suggestions welcome at
[email protected]
Robust Output Tracking for a Room Temperature Model with Distributed Control and Observation
We consider robust output regulation of a partial differential equation model
describing temperature evolution in a room. More precisely, we examine a
two-dimensional room model with the velocity field and temperature evolution
governed by the incompressible steady state Navier-Stokes and
advection-diffusion equations, respectively, which coupled together form a
simplification of the Boussinesq equations. We assume that the control and
observation operators of our system are distributed, whereas the disturbance
acts on a part of the boundary of the system. We solve the robust output
regulation problem using a finite-dimensional low-order controller, which is
constructed using model reduction on a finite element approximation of the
model. Through numerical simulations, we compare performance of the
reduced-order controller to that of the controller without model reduction as
well as to performance of a low-gain robust controller.Comment: 12 pages, 5 figures. Accepted for publication in the Proceedings of
the 24th International Symposium on Mathematical Theory of Networks and
Systems, 23-27 August, 202
A mixed formulation for the direct approximation of -weighted controls for the linear heat equation
This paper deals with the numerical computation of null controls for the linear heat equation. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a given positive time. In [Fernandez-Cara \& MĂĽnch, Strong convergence approximations of null controls for the 1D heat equation, 2013], a so-called primal method is described leading to a strongly convergent approximation of distributed control: the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality conditions. In this work, we adapt the method to approximate the control of minimal square integrable-weighted norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and its adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach covers both the boundary and the inner situation and is valid in any dimension
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