Robust LQR for Uncertain Discrete-Time Systems using Polynomial Chaos

使用含噪测量的直接数据驱动控制

Direct Data Driven Control Using Noisy Measurements

针对未知动态且状态含噪的LQR问题，提出仅用单条含噪轨迹、基于LMI与SDP直接综合控制器的框架，保证均方稳定与最优性能。

Stochastic Optimization using Polynomial Chaos Expansions

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety of physical systems. These methods have also been employed to build surrogate models for accelerating inverse uncertainty quantification (infer model parameters from data) and construct transport maps. In this work, we explore the use of polynomial chaos based approaches for optimizing functions in the presence of uncertainty. These methods enable the fast pr…

基于多项式混沌理论的连续冷冻干燥概率鲁棒不确定性分析与最优控制

Probabilistically Robust Uncertainty Analysis and Optimal Control of Continuous Lyophilization via Polynomial Chaos Theory

本文针对连续冷冻干燥两次干燥阶段的概率不确定性，提出基于多项式混沌理论的机理建模、随机优化与控制框架，以量化不确定性并指导工艺设计。

Polynomial Chaos-Based Flight Control Optimization with Guaranteed Probabilistic Performance

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed method aims at propagating uncertainties effectively and optimizing control parameters to satisfy the probabilistic requirements directly. To achieve this, the sensitivities of violation probabilities are evaluated by the expansion coefficients and the fourth moment method for reliability analysis, after which an optimization that minimizes failur…

Robust Learning-Based Control via Bootstrapped Multiplicative Noise

Despite decades of research and recent progress in adaptive control and reinforcement learning, there remains a fundamental lack of understanding in designing controllers that provide robustness to inherent non-asymptotic uncertainties arising from models estimated with finite, noisy data. We propose a robust adaptive control algorithm that explicitly incorporates such non-asymptotic uncertainties into the control design. The algorithm has three components: (1) a least-squares nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal mode…

PolyChaos.jl -- A Julia Package for Polynomial Chaos in Systems and Control

Polynomial chaos expansion (PCE) is an increasingly popular technique for uncertainty propagation and quantification in systems and control. Based on the theory of Hilbert spaces and orthogonal polynomials, PCE allows for a unifying mathematical framework to study systems under arbitrary uncertainties of finite variance; we introduce this problem as a so-called mapping under uncertainty. For practical PCE-based applications we require orthogonal polynomials relative to given probability densities, and their quadrature rules. With PolyChaos we provide a Julia software package that delivers the …

关于多项式混沌展开截断误差的评论

Comments on Truncation Errors for Polynomial Chaos Expansions

本文研究多项式混沌展开中截断误差的量化与界定，探讨零截断误差的实现条件及所需展开阶数，并通过仿真例验证结果。

Non-intrusive polynomial chaos expansion for topology optimization using polygonal meshes

This paper deals with the applications of stochastic spectral methods for structural topology optimization in the presence of uncertainties. A non-intrusive polynomial chaos expansion is integrated into a topology optimization algorithm to calculate low-order statistical moments of the mechanical-mathematical model response. This procedure, known as robust topology optimization, can optimize the mean of the compliance while simultaneously minimizing its standard deviation. In order to address possible variabilities in the loads applied to the mechanical system of interest, magnitude and direct…

随机最优控制的路径积分理论前沿进展

Advancing Frontiers of Path Integral Theory for Stochastic Optimal Control

本文研究随机最优控制问题，提出路径积分控制框架作为可扩展的采样替代方案，应用于六类SOC问题并提供样本复杂度分析，为复杂环境下的自主决策奠定基础。

电子与光子集成电路中非高斯相关过程变化的不确定性量化

Uncertainty Quantification of Electronic and Photonic ICs with Non-Gaussian Correlated Process Variations

本文提出一种高效方法处理非高斯相关参数，通过扩展多项式混沌并开发张量方法和稀疏求解器，提升了电子和光子集成电路的不确定性量化效率和准确性。