Heterogeneously parameterized tube model predictive control for LPV systems

TL;DR

This paper introduces a flexible heterogeneously parameterized tube MPC framework for LPV systems, enabling a balance between computational complexity and domain of attraction by combining different parameterizations within a single tube.

Contribution

It develops a novel heterogeneously parameterized tube MPC approach that unifies scenario and homothetic tube methods, offering improved flexibility and performance trade-offs.

Findings

Framework allows combining different parameterizations within one tube

Proposed conditions ensure recursive feasibility and stability

Numerical examples demonstrate improved complexity/performance trade-offs

Abstract

This paper presents a heterogeneously parameterized tube-based model predictive control (MPC) design applicable to linear parameter-varying (LPV) systems. In a heterogeneous tube, the parameterizations of the tube cross sections and the associated control laws are allowed to vary along the prediction horizon. Two extreme cases that can be described in this framework are scenario MPC (high complexity, larger domain of attraction) and homothetic tube MPC with a simple time-invariant control parameterization (low complexity, smaller domain of attraction). In the proposed framework, these extreme parameterizations, as well as other parameterizations of intermediate complexity, can be combined within a single tube. By allowing for more flexibility in the parameterization design, one can influence the trade-off between computational cost and the size of the domain of attraction. Sufficient conditions on the parameterization structure are developed under which recursive feasibility and closed-loop stability are guaranteed. A specific parameterization that combines the principles of scenario and homothetic tube MPC is proposed and it is shown to satisfy the required conditions. The properties of the approach, including its capability of achieving improved complexity/performance trade-offs, are demonstrated using two numerical examples.