The talk focuses on the synthesis of online algorithms to optimize the behavior of dynamical systems operating in uncertain, dynamically changing environments. Departing from traditional decision-making architectures grounded on explicit spatio-temporal boundaries between model-based optimization and local closed-loop control, the main strategy revolves around the synthesis of online optimization algorithms that effectively act as feedback controllers to drive dynamical systems towards well-defined operational points. In particular, the desired equilibrium points coincide with optimal solution trajectories of time-varying optimization problems formalizing performance metrics and operational constraints that may evolve over time. The first part of the talk considers the case where the dynamics of the plant are fast and algorithms are synthetized based on the algebraic representation of the system; the design of the algorithms capitalizes on an online implementation of first-order methods, suitably modified to accommodate actionable feedback in the form of measurements from the systems and functional evaluations of the cost. Leveraging contraction arguments, the performance of the closed-loop online algorithm is analyzed in terms of tracking of an optimal solution trajectory implicitly defined by the time-varying optimization problem; in particular, results in terms of convergence in expectation and in high-probability are presented. The talk then considers the case where the time scales of online algorithms and dynamical systems are comparable; in this case, sufficient conditions on the tunable parameters of the online algorithm are presented to guarantee exponential and input-to-state stability of the interconnection between the online algorithm and the dynamical system. The theoretical endeavors are motivated by problems arising in power system, transportation, and control of epidemics.
Emiliano Dall’Anese is an Assistant Professor in the Department of Electrical, Computer, and Energy Engineering at the University of Colorado Boulder, where he is also an affiliate faculty with the Department of Applied Mathematics. He received the Ph.D. degree from the Department of Information Engineering, University of Padova, Italy, in 2011. His research interests span the areas of optimization, control, and learning, with current emphasis on online optimization and learning, and optimization of dynamical systems; tools and methods are applied to problems in energy, transportation, and healthcare. He received the National Science Foundation CAREER Award in 2020.