A Learning- and Scenario-based MPC Design for Nonlinear Systems in LPV Framework with Safety and Stability Guarantees

TL;DR

This paper introduces a novel learning- and scenario-based MPC method for nonlinear systems within the LPV framework, ensuring safety and stability through probabilistic modeling and scenario generation.

Contribution

It develops a probabilistic LPV model using variational Bayesian neural networks and integrates it into a scenario-based MPC with stability guarantees.

Findings

Ensures safety with high probability using scenario-based MPC.

Guarantees stability via parameter-dependent terminal costs and invariant sets.

Demonstrates effectiveness through numerical examples.

Abstract

This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modeled in 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 used to generate scenarios which ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance 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.