相关论文: Integral Quadratic Constraints with Infinite-Dimen…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives trajectories starting in these sets to the target set. The method…
We introduce a Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in two spatial variables. PIEs are an algebraic state-space representation of infinite-dimensional systems and have been used to model 1D…
Finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs) is considered. The discussion is restricted to those that are radial with index $0$; this corresponds to a nilpotency degree of 1. We establish the…
Two inertial DC algorithms for indefinite quadratic programs under linear constraints (IQPs) are considered in this paper. Using a qualification condition related to the normal cones of unbounded pseudo-faces of the polyhedral convex…
This paper develops a robust control synthesis method for uncertain linear systems with input saturation in the framework of integral quadratic constraints (IQCs). The system is reformulated as a linear fractional representation (LFR) that…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed…
In this paper, we analyze the stability of feedback interconnections of a linear time-invariant system with a neural network nonlinearity in discrete time. Our analysis is based on abstracting neural networks using integral quadratic…
Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of solving centralized robust stability analysis techniques, privacy requirements in the network can…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions,…
We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…
We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for…
In a previous report, the second and third authors gave general theorems for unique strong solutions of infinite-dimensional stochastic differential equations (ISDEs) describing the dynamics of infinitely many interacting Brownian…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As…
Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints…
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…