Research

Robust Control Reading List

• A course in H-infinity control theory by Bruce Francis

• Feedback control theory by Sigurd Skogestas, Ian Postethwaite

• Multivariable feedback control by John Doyle, Bruce Francis, and Allen Tannenbaum

• Robust and optimal control by Kemin Zhou, John Doyle, Keith Glover

• A course in robust control: A convex approach by Geir Dullerad and Fernando Paganini

• Dynamics system and control by Munther Dahleh

• Theory of robust control by Carsten Scherer

• Linear matrix inequalities in system and control theory by Stephen Boyd, Laurent El Ghaoui, Eric Feron, and Venkataramanan Balakrishnan

Networked Control Systems

Networked Control System

Networked Control Systems (NCS) are control systems where sensors, controllers, and actuators communicate over a shared network instead of direct, dedicated connections. This setup offers flexibility, scalability, and easier maintenance, making NCS popular in applications like industrial automation, robotics, and smart grids. However, it also introduces challenges such as communication delays, packet loss, bandwidth limitations, and synchronization issues, which can affect the system's stability and performance. We address these networked uncertainties in a unified framework.

Phase Theory over Large-Scale Networks

Complex Electrical Networks

The small gain theorem, introduced in the 1960s, heralded a long-lasting prosperity of gain-based analysis and synthesis theory, particularly within the H-infinity framework. In contrast, the exploration of a phase-based counterpart began in the 1970s but saw limited development compared to the gain theory for many years. During this same period, energy-related concepts in engineering and physics, such as passivity and dissipativity, were integrated into control systems studies, leading to the flourishing development of dissipativity theory. Rather than acting as independent concepts, gain, phase, and dissipativity exhibit intricate yet intrinsic connections. Notably, a recent surge in phase-based research provides researchers with opportunities to reconsider the foundations of control analysis and synthesis, uncovering new connections among these essential concepts. Our study focuses on the phase properties of large-scale N-port networks, quantifying and extending the notion of passivity, which originated from the same theoretical platform.

Stability Margins Achievable by PID Control

Robust Feedback Digraph

Proportional-Integral-Derivative (PID) control has been the workhorse of control technology for about a century. Yet to this day, designing and tuning PID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on classical graphical techniques (Bode). Our goal is to take a fresh look on PID control in the context of optimizing stability margins for low-order (first- and second-order) linear time-invariant systems. Specifically, we seek to derive explicit expressions for gain, phase, and delay margins that are achievable using PID control, and thereby gain insights into the role of unstable poles and nonminimum-phase zeros in attaining robust stability.

Sensor Placement against Cyber Attacks

Distributed System under Cyber Attacks

Undetectable attacks are a significant class of malicious threats to the security of cyber-physical systems. These attacks can alter a system's state without affecting the output measurements, making them invisible through standard output monitoring. This project focuses on undetectable attacks in cone-invariant systems and multi-agent systems. We begin by providing a general characterization of zero-dynamics attacks, which are fully undetectable attacks targeting a system's nonminimum phase zeros. This geometric characterization enables the development of a defense strategy that aims to place a minimal number of sensors to detect and counter zero-dynamics attacks on the system's actuators. By leveraging these geometrical insights, the strategy enhances the system's resilience against undetectable attacks by strategically positioning sensors to cover the most critical points of vulnerability.

Machine Learning and Robust Control: Regret Minimization

Regret-based Robust and Optimal Control

Regret minimization, originating from online learning and game theory, focuses on the difference between the performance of the chosen strategy and the best possible strategy in hindsight. The goal is to minimize this regret over time. The interplay between regret minimization and robust control becomes evident in scenarios where decisions need to be made in uncertain and dynamic environments. Key points of their interplay include: 1) Focusing on minimizing regret as a robust performance metric, rather than using classical H_infty and H_2 metrics. 2) Designing online robust controllers through online learning algorithms.