Certainty-equivalent adaptive MPC for uncertain nonlinear systems
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915872611762176 |
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| author | Köhler, Johannes |
| author_facet | Köhler, Johannes |
| contents | We provide a method to design adaptive controllers for nonlinear systems using model predictive control (MPC). By combining a certainty-equivalent MPC formulation with least-mean-square parameter adaptation, we obtain an adaptive controller with strong robust performance guarantees: The cumulative tracking error and violation of state constraints scale linearly with noise energy, disturbance energy, and path length of parameter variation. A key technical contribution is developing the underlying certainty-equivalent MPC that tracks output references, accounts for actuator limitations and desired state constraints, requires no system-specific offline design, and provides strong inherent robustness properties. This is achieved by leveraging finite-horizon rollouts, artificial references, recent analysis techniques for optimization-based controllers, and soft state constraints. For open-loop stable systems, we derive a semi-global result that applies to arbitrarily large measurement noise, disturbances, and parametric uncertainty. For stabilizable systems, we derive a regional result that is valid within a given region of attraction and for sufficiently small uncertainty. Applicability and benefits are demonstrated with numerical simulations involving systems with large parametric uncertainty: a linear stable chain of mass-spring-dampers and a nonlinear unstable quadrotor navigating obstacles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17843 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Certainty-equivalent adaptive MPC for uncertain nonlinear systems Köhler, Johannes Optimization and Control Systems and Control We provide a method to design adaptive controllers for nonlinear systems using model predictive control (MPC). By combining a certainty-equivalent MPC formulation with least-mean-square parameter adaptation, we obtain an adaptive controller with strong robust performance guarantees: The cumulative tracking error and violation of state constraints scale linearly with noise energy, disturbance energy, and path length of parameter variation. A key technical contribution is developing the underlying certainty-equivalent MPC that tracks output references, accounts for actuator limitations and desired state constraints, requires no system-specific offline design, and provides strong inherent robustness properties. This is achieved by leveraging finite-horizon rollouts, artificial references, recent analysis techniques for optimization-based controllers, and soft state constraints. For open-loop stable systems, we derive a semi-global result that applies to arbitrarily large measurement noise, disturbances, and parametric uncertainty. For stabilizable systems, we derive a regional result that is valid within a given region of attraction and for sufficiently small uncertainty. Applicability and benefits are demonstrated with numerical simulations involving systems with large parametric uncertainty: a linear stable chain of mass-spring-dampers and a nonlinear unstable quadrotor navigating obstacles. |
| title | Certainty-equivalent adaptive MPC for uncertain nonlinear systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.17843 |