Applied Math Colloquium | Michael Fisher, Optimal Constrained Control and Nonlinear Stability Analysis for Complex Systems

MC 5501 

Speaker

Michael Fisher, Department of Electrical and Computer Engineering, University of Waterloo

Title

Optimal Constrained Control and Nonlinear Stability Analysis for Complex Systems

Abstract

Complex systems consist of a collection of devices with local dynamics and control that are coupled by physical or cyber networks. Examples include the electrical power grid, communication systems, and networks of 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 talk will discuss new methods to enable safe, reliable, and desired operation of complex systems.

The first part of the talk focuses on optimal constrained control in complex systems. In many systems it is important for linear feedback controllers to provide desired performance while simultaneously satisfying saturation and resource limits non­-conservatively. The design is formulated as an optimal control problem where the objective is to minimize the mismatch between actual and desired behavior subject to state, input, and output constraints. To solve this challenging, nonconvex optimization problem, a novel control design technique is developed which transforms the original problem into a convex optimization that can be solved efficiently using a suitable approximation. This approximation is shown to converge to the Hardy space of stable transfer functions, resulting in a design method with bounded suboptimality. The method is applied for control design of a dynamic virtual power plant of distributed energy resources.

The second part of the talk focuses on stability analysis in complex systems. Complex systems naturally experience disturbances that disrupt normal operation and can lead to instability. Whether a system is able to recover from a particular nonlinear disturbance depends on the values of system parameters, which are typically uncertain and time-varying. Therefore, it is valuable to compute the margins for safe operation: the smallest change in system parameter values from an initial operating point that would make the system vulnerable to a particular disturbance. 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 by exploiting properties of the region of attraction boundary of a stable equilibrium point. The resulting methods are applied to assess fault vulnerability in power systems.