A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

ABSTRACT

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance.

KEYWORDS:

• Safe scenario-based model predictive control
• learning-based control design
• linear parameter-varying framework
• Bayesian neural networks

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was financially supported by National Science Foundation under award #1912757. The second author's work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project #419290163.