Periodic Reporting for period 4 - CORNEA (Controlling evolutionary dynamics of networked autonomous agents)
Berichtszeitraum: 2022-11-01 bis 2023-04-30
The wide spectrum of the research theme from theory to experimentation and the multi-disciplinary nature of the research approach lead to exciting advances in control science and engineering bringing scientific, technological and economic benefits. In engineering, the improved control of man-made autonomous robotic systems leads to new applications of environmental sampling and monitoring tasks. The control of large-scale, distributed engineering networks such as traffic networks and smart energy grids, once cast as a large number of coupled agents with autonomous decision-making capabilities, can also benefit from the control algorithms developed in this project. The overall objective of this project is to develop a rigorous theory for the control of evolutionary dynamics so that interacting autonomous agents can be guided to solve group tasks through the pursuit of individual goals in an evolutionary dynamical process. The theory is then tested, validated and improved against experimental results using autonomous robots.
We have also further developed the concept of accessibility and controllability for nonlinear complex networked systems. For example, we examined how structural properties can be utilized for nonlinear balanced equations, and make a new insightful connection between observability and privacy. With this new understanding of dynamics of agents in networks, we naturally introduce control input into the systems. We found that incentives are effective in guiding the behavior of large networks of agents. We have shown how to design incentives for binary decision networks and in the follow-up works, we will look into other types of decision-making dynamics. Although stochastic stability has been a classic topic studied in the past decades, we have shown that we can relax the technical requirement for being monotonic and obtained new Lyapunov criteria. The Lyapunov approach is particularly suitable for studying networks, when the dynamics at the nodes can be modeled by oscillators; we have published several papers on oscillator networks.
Because games are a central part in the decision-making models that we study, we have looked into various Nash equilibrium seeking algorithms in games. We have also studied how one or a few game players might be able to manipulate the outcome of the games, which has led to exciting new manipulation strategies. The game play can be further embedded into a changing environment, and thus the game play and the environment become a closed-loop system, whose stable equilibria or oscillatory trajectories may be directly interpreted by looking into the phase portraits of these dynamical systems. It is even more exciting to combine learning algorithms with game plays, and examine how historical data on game plays can help to choose the current decision-making strategies. We have shown that indeed learning can help players to be more cooperative, which discloses great potential to use learning to resolve challenging social dilemmas.
We have identified a surprising relationship between observability and privacy. As a quantitative criterion for privacy of “mechanisms” in the form of data-generating processes, the concept of differential privacy was first proposed in computer science and has later been applied to linear dynamical systems. However, differential privacy has not been studied in depth together with other properties of dynamical systems, and it has not been fully utilized for controller design. We have clarified that a classical concept in systems and control, input observability (sometimes referred to as left invertibility) has a strong connection with differential privacy. In particular, we have shown that the Gaussian mechanism can be made highly differentially private by adding small noise if the corresponding system is less input observable. In addition, enabled by our new insight into privacy, we have developed a method to design dynamic controllers for the classic tracking control problem while addressing privacy concerns. We call the obtained controller through our design method the privacy preserving controller.