$\mathcal{W}_\infty$-transport with discrete target as a combinatorial matching problem

时滞满足$\mathcal{H}_\infty$范数界的分布式控制

Distributed Control Subject to Delays Satisfying an $\mathcal{H}_\infty$ Norm Bound

本文提出了一种表征分布式控制器的延迟约束引起的强连通通信图，实现了指定的闭环$\mathcal{H}_\infty$规范。受解决受延迟的$\mathcal{H}_2$问题的启发，我们利用通信图是强连接的这一事实，将控制器分解为局部有限冲激响应分量和全局但延迟的无限冲激响应分量。这使我们能够减少控制综合问题的线性矩阵不等式的可行性测试。

Sparse Sensing and Optimal Precision: An Integrated Framework for $\mathcal{H}_2/\mathcal{H}_{\infty}$ Optimal Observer Design

In this paper, we simultaneously determine the optimal sensor precision and the observer gain, which achieves the specified accuracy in the state estimates. Along with the unknown observer gain, the formulation parameterizes the scaling of the exogenous inputs that correspond to the sensor noise. Reciprocal of this scaling is defined as the sensor precision, and sparseness is achieved by minimizing the $l_1$ norm of the precision vector. The optimization is performed with constraints guaranteeing specified accuracy in state estimates, which are defined in terms of $\mathcal{H}_2$ or $\mathcal{…

Global Convergence of Direct Policy Search for State-Feedback $\mathcal{H}_\infty$ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential

Direct policy search has been widely applied in modern reinforcement learning and continuous control. However, the theoretical properties of direct policy search on nonsmooth robust control synthesis have not been fully understood. The optimal $\mathcal{H}_\infty$ control framework aims at designing a policy to minimize the closed-loop $\mathcal{H}_\infty$ norm, and is arguably the most fundamental robust control paradigm. In this work, we show that direct policy search is guaranteed to find the global solution of the robust $\mathcal{H}_\infty$ state-feedback control design problem. Notice th…

地月空间中的$\mathcal{H}_\infty$最优导航与LFT模型

$\mathcal{H}_\infty$ Optimal Navigation in the Cislunar Space with LFT Models

针对地月空间导航中混沌动力学和传感器误差的挑战，本文提出基于LFT模型和$\mathcal{H}_\infty$综合的鲁棒估计框架，仿真验证了其在监视星座中的有效性。

Minimax Lower Bounds for $\mathcal{H}_\infty$-Norm Estimation

The problem of estimating the $\mathcal{H}_\infty$-norm of an LTI system from noisy input/output measurements has attracted recent attention as an alternative to parameter identification for bounding unmodeled dynamics in robust control. In this paper, we study lower bounds for $\mathcal{H}_\infty$-norm estimation under a query model where at each iteration the algorithm chooses a bounded input signal and receives the response of the chosen signal corrupted by white noise. We prove that when the underlying system is an FIR filter, $\mathcal{H}_\infty$-norm estimation is no more efficient than …

Sparse Sensing and Optimal Precision: Robust $\mathcal{H}_{\infty}$ Optimal Observer Design with Model Uncertainty

We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the $\mathcal{H}_{\infty}$ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and unstructured uncertainties. The objective is to design an observer with a given $\mathcal{H}_{\infty}$ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible …

$\mathcal{H}_\infty$ 二次输出系统的模型降阶

$\mathcal{H}_\infty$ model order reduction for quadratic output systems

针对二次输出系统，定义 $\mathcal{H}_\infty$ 范数并提出优化算法以最小化降阶模型与全阶模型在该范数下的误差，数值实验验证了方法的有效性。

混合 $\mathcal{H}_2/\mathcal{H}_\infty$ 策略学习综合

Mixed $\mathcal{H}_2/\mathcal{H}_\infty$-Policy Learning Synthesis

本文提出一种无模型混合 $\mathcal{H}_2/\mathcal{H}_\infty$ 鲁棒稳定最优控制策略，通过 Itô 随机微分计算在零和微分博弈中迭代求解广义代数 Riccati 方程，以克服传统策略优化收敛慢且不鲁棒的问题。

$\mathcal{H}_2/\mathcal{H}_\infty$ 框架下具有全状态反馈的 LPV 系统的稀疏驱动

Sparse Actuation for LPV Systems with Full-State Feedback in $\mathcal{H}_2/\mathcal{H}_\infty$ Framework

本文首次针对 LPV 非线性系统提出一种凸优化框架，通过在 $l_1$ 意义上最小化驱动器幅度限制来实现稀疏驱动，并在 $\mathcal{H}_2/\mathcal{H}_\infty$ 意义上保证闭环性能，最后在柔性机翼振动控制中验证了该方法。

稀疏传感与执行下的 $\mathcal{H}_2/\mathcal{H}_\infty$ 最优控制

$\mathcal{H}_2/\mathcal{H}_\infty$ Optimal Control with Sparse Sensing and Actuation

本文提出凸优化框架，利用加权 $\ell_1$ 范数联合设计稀疏传感、执行及控制律，保证指定的 $\mathcal{H}_2/\mathcal{H}_\infty$ 性能，并在非线性结构动力学中验证其优势。

Robust output-feedback stabilization for incompressible flows using low-dimensional $\mathcal{H}_{\infty}$-controllers

Output-based controllers are known to be fragile with respect to model uncertainties. The standard $\mathcal{H}_{\infty}$-control theory provides a general approach to robust controller design based on the solution of the $\mathcal{H}_{\infty}$-Riccati equations. In view of stabilizing incompressible flows in simulations, two major challenges have to be addressed: the high-dimensional nature of the spatially discretized model and the differential-algebraic structure that comes with the incompressibility constraint. This work demonstrates the synthesis of low-dimensional robust controllers with…

状态空间解法解决具有嵌套信息约束的最小熵H∞最优控制问题

State-space solution to a minimum-entropy $\mathcal{H}_\infty$-optimal control problem with a nested information constraint

本文提出状态空间解法，解决具有嵌套信息约束的最小熵H∞最优控制问题，推导控制器公式，讨论观察者结构，并提供求解耦合Riccati方程的数值方法。