Optimization algorithms for sequential decision-making

Many modern control problems require sequential optimization algorithms running in real-time and directly connected with the system, in order to cope with highly dynamic environments and enable adaptive mechanisms. We call this control architecture algorithm-based control.

Conventional approaches often treat the optimization algorithm as an idealized block inserted into the closed-loop, neglecting the dynamics that arise from the interconnection of plant and algorithm. By viewing algorithms themselves as dynamical systems, our research develops new frameworks for analyzing and designing methods that interact with the plant dynamically, rather than solving the optimization problem in isolation. For this, we study optimization algorithms solving time-varying and uncertain problems. This in turn allows us to consider control problem where decisions must be made sequentially with incomplete knowledge, requiring guarantees that go beyond what classical analyses can provide.

We combine techniques from modern optimization, such as operator splitting methods and online convex optimization, with tools from control theory. For example, Linear Parameter-Varying allow us to capture algorithms that adapt to changing environments. The Internal Model Principle reveals necessary dynamics that the algorithm has to incorporate. Integral Quadratic Constraints let us analyze convergence and performance of algorithms that use complex operators. In addition to classical measures like convergence rates and stability, we work with metrics tailored to uncertain, non-stationary environments, such as dynamic regret.

Systems theory of optimization algorithms

• Tavakoli, M., Jakob, F., Carnevale, G., Notarstefano, G., Iannelli, A. - "Accelerated ADMM: Automated Parameter Tuning and Improved Linear Convergence"  - arXiv 2511.21210 Link
• Miller, J., Jakob, F., Scherer, C., Iannelli, A. - "Analysis and Synthesis of Switched Optimization Algorithms"  - arXiv 2510.21490. Link
• Jakob F., Iannelli A. - "Online Convex Optimization and Integral Quadratic Constraints: An automated appraoch to regret analysis." - IEEE Conference on Decision and Control 2025. Link
• Jakob F., Iannelli A. - "A Linear Parameter Varying Framework for the Analysis of  Time-Varying Optimization Algorithms" - arXiv 2501.07461. Link

Regret-based control

• Karapetyan A., Tsiamis A., Balta E.C., Iannelli A., Lygeros J. - "Implications of Regret on Stability of Linear Dynamical Systems" - IFAC World Congress 2023. Link
• Karapetyan A., Iannelli A., Lygeros J. - "On the Regret of H∞ control"  - IEEE Conference on Decision and Control 2022. Link
• Karapetyan A., Balta E.C., Iannelli A., Lygeros J. - "Closed-Loop Finite-Time Analysis of Suboptimal Online Control" - IEEE Transactions on Automatic Control, 2025. Link

J. Miller, C. Scherer (University of Stuttgart), G. Notarstefano (University of Bologna), A. Karapetyan, A. Tsiamis, E.C. Balta, J. Lygeros (ETH Zürich).