Ballard Seminar: Distributed Optimal Control Synthesis and Reducing Nonlinear Disturbance Vulnerability for Complex Systems

Abstract: Complex systems consist of a collection of components with local dynamics and control that are coupled by physical or cyber networks. Examples include the electrical power grid, mobile robots, and autonomous vehicles. Such systems provide essential services to society but are notoriously challenging to analyze or control due to their large scale and complexity. The first part of the talk focuses on distributed optimal control synthesis in complex systems. In many systems it is important for linear feedback controllers to provide desired performance while satisfying saturation limits and preserving model privacy. For example, renewable generation will have to provide necessary control services with limited power and proprietary manufacturer models. The design is formulated as an optimal control problem where the objective is to minimize the mixed H2/H∞ norm of the closed-loop transfer function subject to input and output constraints. To solve this challenging optimization problem, novel control design techniques are developed which use convex reparameterization and approximation by simple poles to transform the original problem into a tractable convex optimization. The approximation is shown to converge to the Hardy space of stable transfer functions, resulting in a design method with bounded suboptimality. Novel distributed optimization methods are developed to solve the design problem while preserving model privacy. The method is applied for control design of distributed energy resources. The second part of the talk focuses on reducing vulnerability to nonlinear disturbances in complex systems. Complex systems naturally experience disturbances that disrupt normal operation and can lead to instability. For instance, a sudden gust of wind can cause a quadcopter to lose stability in flight. Therefore, it is valuable to tune controllers so as to enlarge the region of safe operation near the current operating point. A theoretical framework based on modern dynamical systems theory is developed which leads to the transformation of this abstract problem into a class of concrete numerical optimization algorithms which can be solved efficiently. These algorithms exploit properties of the region of attraction boundary of a stable equilibrium point in order to vary controller parameter values so as to enlarge the region of attraction near the current state. The resulting methods are applied to improve robustness of a quadcopter to unexpected gusts of wind during flight.

Bio: Michael W. Fisher is an Assistant Professor in the Department of Electrical and Computer Engineering at the University of Waterloo, Canada. He was a postdoctoral researcher with the Automatic Control and Power System Laboratories at ETH Zurich from 2020-2022. He received his Ph.D. in Electrical Engineering: Systems at the University of Michigan, Ann Arbor in 2020, and a M.Sc. in Mathematics from the same institution in 2017. He received his B.A. in Mathematics and Physics from Swarthmore College in 2014. His research interests are in dynamics, control, and optimization of complex systems. Dr. Fisher was a finalist for the 2017 Conference on Decision and Control (CDC) Best Student Paper Award and a recipient of the 2019 CDC Outstanding Student Paper Award.