相关论文: Unbiased Extremum Seeking for PDEs

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…

Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…

We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…

This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…

We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

This paper proposes an event-triggered control scheme for multivariable extremum seeking of static maps. Both static and dynamic triggering conditions are developed. Integrating Lyapunov and averaging theories for discontinuous systems, a…

This work concerns the evolutionary approaches to distributed stochastic black-box optimization, in which each worker can individually solve an approximation of the problem with nature-inspired algorithms. We propose a distributed evolution…

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal, then, is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for…

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by…

The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the…

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…

This paper presents novel methods for achieving stable and efficient convergence in multivariable extremum seeking control (ESC) using sliding mode techniques. Drawing inspiration from both classical sliding mode control and more recent…

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized PDE systems are expensive due to the high computational cost of high-fidelity simulations. Reduced/Latent state…

Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain…

This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…

A compact version of the variation evolving method (VEM) is developed in the primal variable space for optimal control computation. Following the idea that originates from the Lyapunov continuous-time dynamics stability theory in the…

In this work, we introduce the Equivariance Seeker Model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances…