不确定性线性方程描述的动力系统的状态估计

An MCMC Method for Uncertainty Set Generation via Operator-Theoretic Metrics

Model uncertainty sets are required in many robust optimization problems, such as robust control and prediction with uncertainty, but there is no definite methodology to generate uncertainty sets for nonlinear dynamical systems. In this paper, we propose a method for model uncertainty set generation via Markov chain Monte Carlo. The proposed method samples from distributions over dynamical systems via metrics over transfer operators and is applicable to general nonlinear systems. We adapt Hamiltonian Monte Carlo for sampling high-dimensional transfer operators in a computationally efficient ma…

Convex Relaxations for Global Optimization Under Uncertainty Described by Continuous Random Variables

This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control, etc. Here, we restrict our attention to problems with expected-value objectives and no recourse decisions. In principle, such problems can be solved globally using spatial branch-and-bound (B&B). However, B&B requires the ability to bound the optimal objective value on subintervals of the search space, and existing techniques are not generally applicable bec…

A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in functional analysis and wide applicability as demonstrated in distinct numerical examples. The implication of this new concept is a new mode of thinking about the statistical nature of uncertainty in dynamical systems.

Maximum principle for stochastic recursive optimal control problem under model uncertainty

In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of the linearization techniques and weak convergence methods, we derive the corresponding stochastic maximum principle. Moreover, a linear quadratic robust control problem is also studied.

Asymptotic forecast uncertainty and the unstable subspace in the presence of additive model error

It is well understood that dynamic instability is among the primary drivers of forecast uncertainty in chaotic, physical systems. Data assimilation techniques have been designed to exploit this phenomena, reducing the effective dimension of the data assimilation problem to the directions of rapidly growing errors. Recent mathematical work has, moreover, provided formal proofs of the central hypothesis of the Assimilation in the Unstable Subspace methodology of Anna Trevisan and her collaborators: for filters and smoothers in perfect, linear, Gaussian models, the distribution of forecast errors…

自适应动力系统基本极限的发散性刻画

Divergence-based characterization of fundamental limitations of adaptive dynamical systems

自适应动态系统出现在多种环境中，例如，优化、控制、通信、信号处理和机器学习。因此，准确描述其基本局限性至关重要。在本文中，我们考虑自适应控制和/或识别随机动力系统的一般问题，我们的{ \em先验}知识允许我们将系统的度量空间（不确定性集）的一个子集。我们提出了一个信息理论的元定理，捕捉度量的复杂性（或丰富性）的不确定性集，在控制和观察系统的过程中在线获取的信息量之间的权衡，和剩余的不确定性后，观察已经收集。遵循Zames的方法，我们通过不确定性集合的Kolmogorov（度量）熵来量化{ \em a priori}信息，而在线获取的信息被表示为信息分歧之和。一般的理论是用来推导新的极小极大下界的度量识别误差，以及给一个简单的推导所需的最小时间来稳定一个不确定的随机线性系统。