相关论文: Mesh Refinement Method for Solving Bang-Bang Optim…

In this paper, we present an advanced approach to solving the inverse rig problem in blendshape animation, using high-quality corrective blendshapes. Our algorithm introduces novel enhancements in three key areas: ensuring high data…

This work studies a class of optimal control problems with scalar inputs and general constraints, whose solutions follow a bang-ride pattern that always activates a constraint and enables efficient numerical computation. As a motivating…

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…

We analyse the role of the bang-bang property in affine optimal control problems. We show that many essential stability properties of affine problems are only satisfied when minimizers are bang-bang. Moreover, we prove that almost any…

We present a novel way of deciding when and where to refine a mesh in probability space in order to facilitate the uncertainty quantification in the presence of discontinuities in random space. A discontinuity in random space makes the…

We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…

In this paper, we propose a monotone mixed finite difference scheme for solving the two-dimensional Monge-Amp\`ere equation. In order to accomplish this, we convert the Monge-Amp\`ere equation to an equivalent Hamilton-Jacobi-Bellman (HJB)…

In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in…

Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or…

We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee…

The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear…

An optimal guidance method is developed that reduces sensitivity to parameters in the dynamic model. The method combines a previously developed method for guidance and control using adaptive Legendre-Gauss-Radau (LGR) collocation and a…

This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small correlation lengths. The presented method is based on a…

We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the…

This paper focuses on the application of the variance-based global sensitivity analysis for a topology derivative method in order to solve a stochastic nonlinear time-dependent magnetoquasistatic interface problem. To illustrate the…

Many expensive black-box optimisation problems are sensitive to their inputs. In these problems it makes more sense to locate a region of good designs, than a single-possibly fragile-optimal design. Expensive black-box functions can be…

We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…

The application of systems and control theory to membrane physiology is presented here. Modeling efforts have focused on describing those physiologically realistic mechanisms which govern the regulation of membrane permeability in nerve.…

This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…

We consider the effect of using approximate system predictions in event-triggered control schemes. Such approximations may result from using numerical transcription methods for solving continuous-time optimal control problems. Mesh…