Related papers: Optimal Control Of Surface Shape
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Designing a freeform surface to reflect or refract light to achieve a target distribution is a challenging inverse problem. In this paper, we propose an end-to-end optimization strategy for an optical surface mesh. Our formulation leverages…
The robotic manipulation of compliant objects is currently one of the most active problems in robotics due to its potential to automate many important applications. Despite the progress achieved by the robotics community in recent years,…
We consider an optimal control problem subject to the thin-film equation which is deduced from the Navier--Stokes equation. The PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints…
We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase variable, incorporating curvature effects in the free…
We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
A flat plate can bend into a curved surface if it experiences an inhomogeneous growth field. In this article a method is described that numerically determines the optimal growth field giving rise to an arbitrary target shape, optimizing for…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a…
In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that…
In this paper, we give a simple control on how an optimal shape can be characterized. The framework of Riemannian manifold of infinite dimension is essential. And the covariant derivative plays a key role in the computation and in the…
We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…
Bearing-based distributed formation control is attractive because it can be implemented using vision-based measurements to achieve a desired formation. Gradient-descent-based controllers using bearing measurements have been shown to have…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…