How scaling of the disturbance set affects robust positively invariant sets for linear systems

System Level Disturbance Reachable Sets and their Application to Tube-based MPC

Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube-based MPC formulation based on system level disturbance reachable sets (SL-DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL-DRS. This allows us to formulate a system level tube-MPC (SLTMPC) method using the SL-DRS…

Transient Stability Analysis of Power Grids with Admissible and Maximal Robust Positively Invariant Sets

The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a set-based approach is presented to assess the transient stability of power systems. The approach is based on the theory of barriers, to obtain an exact description of the boundaries of admissible sets and maximal robust positively invariant sets, respectively. We decompose a power system into generator and load components, replace couplings with bounded disturbanc…

Robust Control Policies given Formal Specifications in Uncertain Environments

We consider robust control synthesis for linear systems with complex specifications that are affected by uncertain disturbances. This work is motivated by autonomous systems interacting with partially known, time-varying environments. Given a specification in bounded linear temporal logic, we propose a method to synthesize control policies that fulfill the specification for all considered disturbances, where the disturbances affect the atomic propositions of the specification. Our approach relies on introducing affine disturbance feedback policies and casting the problem as a bilinear optimiza…

具有加性不确定性的鲁棒滚动时域博弈

Robust Receding Horizon Games with Additive Uncertainty

研究多智能体驱动线性系统的滚动时域博弈，提出结合基于管的约束收紧与有限时域广义纳什均衡问题的鲁棒控制框架，保证递归可行性，利用潜在博弈结构证明状态收敛。

受扰动非线性动力系统的预测安全滤波器

Predictive stability filters for nonlinear dynamical systems affected by disturbances

本文扩展预测安全滤波器框架，通过利用预测轨迹构造的隐式 Lyapunov 函数保证受扰非线性闭环系统的鲁棒渐近稳定性，并在汽车车道保持仿真中验证了所提策略。

状态依赖动态管模型预测控制：一种带有扰动模糊模型的新型管模型预测控制方法

State-Dependent Dynamic Tube MPC: A Novel Tube MPC Method with a Fuzzy Model of Disturbances

本文提出状态依赖动态管模型预测控制（SDD-TMPC），通过模糊模型学习随状态变化的扰动动态并纳入鲁棒TMPC决策，在保持鲁棒稳定性的同时降低保守性并提高可行性。

耦合线性常微分方程和双曲型偏微分方程的H$_1$-ISS分析与边界控制设计

H$_1$-ISS Analysis and Boundary Control Design for Coupled Linear ODEs and Hyperbolic PDEs

研究耦合线性ODEs和双曲型PDEs系统的边界控制设计，将基于李雅普诺夫的ISS条件扩展到H$_1$设置，推导稳定性分析和控制设计条件，通过数值例子验证所提方法的有效性和潜力。

A Decoding Approach to Fault Tolerant Control of Linear Systems with Quantized Disturbance Input

The aim of this paper is to propose an alternative method to solve a Fault Tolerant Control problem. The model is a linear system affected by a disturbance term: this represents a large class of technological faulty processes. The goal is to make the system able to tolerate the undesired perturbation, i.e., to remove or at least reduce its negative effects; such a task is performed in three steps: the detection of the fault, its identification and the consequent process recovery. When the disturbance function is known to be \emph{quantized} over a finite number of levels, the detection can be …

A set-theoretic generalization of dissipativity with applications in Tube MPC

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept of dissipativity of systems that are affected by external disturbances. The corresponding theoretical developments build upon set based analysis methods and lay a general theoretical foundation for a rigorous stability analysis of economic tube model predictive controllers. Besides, we discuss practical prodecures for verifying set-dissipativity of constraine…

PWM DC-DC Buck变换器中的鲁棒负载扰动抑制

Robust Load Disturbance Rejection in PWM DC-DC Buck Converters

针对PWM DC-DC Buck变换器的负载扰动问题，提出H∞外环与新型LEC内环嵌套控制方案，通过mu分析保证参数不确定下的鲁棒稳定性，并经仿真与实验验证其性能优势。

通过凸优化综合离散时间不确定系统的安全证书

Synthesis of safety certificates for discrete-time uncertain systems via convex optimization

本文针对受加性扰动的离散时间线性系统，提出两类半定规划以协同设计控制障碍函数和线性反馈控制器，分别给出最坏情形无限时域安全与有限时域概率安全保证，并扩展至输入约束、分布模糊、安全滤波和避障。

Computationally efficient robust MPC using optimized constraint tightening

A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the resulting constraint tightening is minimized. This is achieved by formulating the constraint tightening problem as a convex optimization problem with the feedback term as a variable. The resulting MPC controller has the computational complexity of nominal MPC, and guarantees recursive feasibility, stability and constraint satisfaction. The advantages of the proposed…