Performance Analysis for Distributed and Multiobjective Model Predictive Control — The role of Pareto fronts, multiobjective dissipativity and multiple equilibria
Final Report Abstract
Model predictive control (MPC) can efficiently solve optimal control problems on large or infinite horizons. Thus, it is a natural extension to consider not only one but multiple objectives in the optimization. This project focused on multiobjective optimal control problems, the analysis of their properties such as strict dissipativity and the design and analysis of algorithms for multiobjective model predictive control (MO MPC). The dissipativity and turnpike-based analysis is a very successful approach for singleobjective optimal control and MPC. This project extended this analysis to the case of multiple equilibria, which appear, e.g., in discounted optimal control problems and for which a local dissipativity and a local turnpike analysis were developed. Another extension pursued in this project was the dissipativity analysis for scalarized multiobjective optimization problems. More precisely, conditions under which the convex combination of strictly dissipative stage cost remains strictly dissipative were derived. To this end, nonlinear programming techniques were used, and the relationship between strict dissipativity and optimal steady-state problems was exploited. Another line of research in this project concerned the development of novel MO MPC schemes. Based on the scheme from the first funding period, a new - less restrictive - scheme, together with milder assumptions on the problem data, was developed. This way, the applicability to a broader class of optimal control problems was provided. For the newly derived scheme, both averaged and non-averaged performance results and trajectory convergence were shown. Inspired by single-objective MPC results for optimal control problems without terminal conditions, performance bounds for all cost criteria were given. Further, a stability analysis was provided by proving that the objective function with strictly dissipative stage cost is a time-varying Lyapunov function. The theoretical analysis served as the foundation for numerical studies examining the impact of selection rules on the solution behavior, highlighting an aspect specific to MO MPC that introduces an additional degree of freedom in the multiobjective setting.
Publications
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Local Turnpike Analysis Using Local Dissipativity for Discrete Time Discounted Optimal Control. Applied Mathematics & Optimization, 84(S2), 1585-1606.
Grüne, Lars & Krügel, Lisa
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Multiobjective strict dissipativity via a weighted sum approach. Systems & Control Letters, 170, 105396.
Grüne, Lars; Krügel, Lisa & Müller, Matthias A.
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Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC. Computational Optimization and Applications, 86(3), 1081-1116.
Eichfelder, Gabriele; Grüne, Lars; Krügel, Lisa & Schießl, Jonas
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Local Turnpike Properties in Finite Horizon Optimal Control. 2023 62nd IEEE Conference on Decision and Control (CDC), 5273–5278.
Krügel, Lisa; Faulwasser, Timm & Grüne, Lars
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Transient Performance of MPC for Tracking. IEEE Control Systems Letters, 7(2023), 2545-2550.
Köhler, Matthias; Krügel, Lisa; Grüne, Lars; Müller, Matthias A. & Allgöwer, Frank
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Dissipativity-Based Analysis of Multiobjective Optimal and Predictive Control. PhD thesis, University of Bayreuth, 2024
Lisa Krügel
