A robust adaptive model predictive control framework for nonlinear uncertain systems

Abstract

In this paper, we present a tube-based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set-membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared to robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean-squared point estimate in the objective function the framework ensures finite-gain ${\mathcal{L}}_2$ stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and non-increasing properties on general parameter estimation algorithms and tube/set based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this paper, we provide similar conditions for a tube based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared to state of the art approaches.

arXiv commentExtended version of accepted paper in the International Journal of Robust and Nonlinear Control. Contains additional details regarding an alternative design of the terminal ingredients and the numerical example

References in corpus (5)

• Cautious Model Predictive Control using Gaussian Process Regression
• Stochastic data-driven model predictive control using Gaussian processes
• A robust adaptive model predictive control framework for nonlinear uncertain systems
• A nonlinear tracking model predictive control scheme for dynamic target signals
• Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

Cited by in corpus (10)

• A robust adaptive model predictive control framework for nonlinear uncertain systems
• Robust adaptive MPC using control contraction metrics
• The Implicit Rigid Tube Model Predictive Control
• A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version
• A Constraint-Tightening Approach to Nonlinear Stochastic Model Predictive Control for Systems under General Disturbances
• Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version
• Stability and Performance Analysis of Model Predictive Control of Uncertain Linear Systems
• A robust and adaptive MPC formulation for Gaussian process models
• Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version
• Exploiting Model Sparsity in Adaptive MPC: A Compressed Sensing Viewpoint