2,339 research outputs found
Concurrent Learning Adaptive Model Predictive Control with Pseudospectral Implementation
This paper presents a control architecture in which a direct adaptive control
technique is used within the model predictive control framework, using the
concurrent learning based approach, to compensate for model uncertainties. At
each time step, the control sequences and the parameter estimates are both used
as the optimization arguments, thereby undermining the need for switching
between the learning phase and the control phase, as is the case with
hybrid-direct-indirect control architectures. The state derivatives are
approximated using pseudospectral methods, which are vastly used for numerical
optimal control problems. Theoretical results and numerical simulation examples
are used to establish the effectiveness of the architecture.Comment: 21 pages, 13 figure
Constrained optimal control theory for differential linear repetitive processes
Differential repetitive processes are a distinct class of continuous-discrete two-dimensional linear systems of both systems theoretic and applications interest. These processes complete a series of sweeps termed passes through a set of dynamics defined over a finite duration known as the pass length, and once the end is reached the process is reset to its starting position before the next pass begins. Moreover the output or pass profile produced on each pass explicitly contributes to the dynamics of the next one. Applications areas include iterative learning control and iterative solution algorithms, for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modeling of numerous industrial processes such as metal rolling, long-wall cutting, etc. In this paper we develop substantial new results on optimal control of these processes in the presence of constraints where the cost function and constraints are motivated by practical application of iterative learning control to robotic manipulators and other electromechanical systems. The analysis is based on generalizing the well-known maximum and -maximum principles to the
Data-driven discovery of the heat equation in an induction machine via sparse regression
Discovery of natural laws through input-output data analysis has been of considerable interest during the past decade. Various approach among which the increasingly growing body of sparsity-based algorithms have been recently proposed for the purpose of free-form system identification. There has however been limited discussion on the performance of these approaches when applied on experimental datasets. The aim of this paper is to study the capability of this technique for identifying the heat equation as the natural law of heat distribution from experimental data, obtained using a Totally-Enclosed-Fan-Cooled (TEFC) induction machine, with and without active cooling. The results confirm the usefulness of the algorithm as a method to identify the underlying natural law in a physical system in the form of a Partial Differential Equation (PDE)
Data-Driven Estimation in Equilibrium Using Inverse Optimization
Equilibrium modeling is common in a variety of fields such as game theory and
transportation science. The inputs for these models, however, are often
difficult to estimate, while their outputs, i.e., the equilibria they are meant
to describe, are often directly observable. By combining ideas from inverse
optimization with the theory of variational inequalities, we develop an
efficient, data-driven technique for estimating the parameters of these models
from observed equilibria. We use this technique to estimate the utility
functions of players in a game from their observed actions and to estimate the
congestion function on a road network from traffic count data. A distinguishing
feature of our approach is that it supports both parametric and
\emph{nonparametric} estimation by leveraging ideas from statistical learning
(kernel methods and regularization operators). In computational experiments
involving Nash and Wardrop equilibria in a nonparametric setting, we find that
a) we effectively estimate the unknown demand or congestion function,
respectively, and b) our proposed regularization technique substantially
improves the out-of-sample performance of our estimators.Comment: 36 pages, 5 figures Additional theorems for generalization guarantees
and statistical analysis adde
Parameterized Wasserstein Hamiltonian Flow
In this work, we propose a numerical method to compute the Wasserstein
Hamiltonian flow (WHF), which is a Hamiltonian system on the probability
density manifold. Many well-known PDE systems can be reformulated as WHFs. We
use parameterized function as push-forward map to characterize the solution of
WHF, and convert the PDE to a finite-dimensional ODE system, which is a
Hamiltonian system in the phase space of the parameter manifold. We establish
error analysis results for the continuous time approximation scheme in
Wasserstein metric. For the numerical implementation, we use neural networks as
push-forward maps. We apply an effective symplectic scheme to solve the derived
Hamiltonian ODE system so that the method preserves some important quantities
such as total energy. The computation is done by fully deterministic symplectic
integrator without any neural network training. Thus, our method does not
involve direct optimization over network parameters and hence can avoid the
error introduced by stochastic gradient descent (SGD) methods, which is usually
hard to quantify and measure. The proposed algorithm is a sampling-based
approach that scales well to higher dimensional problems. In addition, the
method also provides an alternative connection between the Lagrangian and
Eulerian perspectives of the original WHF through the parameterized ODE
dynamics.Comment: We welcome any comments and suggestion
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