Linking Approximate Dynamic Programming, Predictive Control, and Dissipativity: Novel Adaptive Control Approaches for Nonlinear Systems

• Applicants: Professor Dr.-Ing. Timm Faulwasser; Professor Dr.-Ing. Stefan Streif
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 566009879

Approximate Dynamic Programming (ADP), Model Predictive Control (MPC), and dissipativity are established concepts, which are closely related through optimality considerations. Indeed, there is mature understanding of many aspects of MPC such as, e.g., nominal stability and performance. Beyond nominal considerations, robust designs are often intrinsically conservative and stochastic methods tend to induce a substantial mathematical overhead. Hence, in the face of uncertainty, control approaches for nonlinear systems which allow for online adaptation of models, feedback laws, or both are of growing interest. In the context of MPC, ADP concepts are promising guiding principles for online adaptation due to their close mutual relation. Yet, established analysis techniques for MPC often use upper-bounds on the cost-to-go (e.g. in tracking MPC with terminal ingredients) or they rely on lower-bounds on the cost-to-go (e.g. in dissipativity-based designs). Conceptually, we aim to broaden the scope, i.e., we consider terminal penalties that are mere approximations of the cost-to-go. Specifically, this project explores new approaches to adaptive control of nonlinear systems linking ADP, MPC, and dissipativity. We focus on two fundamental research questions: i) How to leverage ADP for the design of MPC controllers for nonlinear systems subject to model uncertainty? ii) How to exploit dissipativity concepts in ADP? The investigations with respect to i) target the understanding of model uncertainty in ADP and the analysis of approximations errors of ADP. For this, we investigate the interplay of closed-loop stability and approximation errors and the effect of model errors on ADP control policies. In turn, these considerations provide the basis to analyze the robustness of MPC wherein the terminal penalty is not an upper-bound on the cost-to-go but a mere approximation of it. Moreover, we are interested in analyzing the closed-loop performance of MPC with approximated cost-to-go. At the core of our investigations of ii) is the deep relation between optimal control and the dissipativity notion of open systems. Specifically, we leverage the links between storage functions needed for dissipativity and infinite-horizon value functions of optimal control problems to develop novel schemes for dissipativity-informed online ADP. The helpful relations between storage and value functions include gradient approximation properties and the fact that the storage provides a lower bound on the value function. Moreover, we combine the insights of our investigations on i) with the above towards dissipativity-informed online adaptation in MPC. Our findings are validated on case studies from biogas reactors, which is subject to growing research attention due to the increasing need for renewable energy sources.

• DFG Programme: Research Grants