Incremental Dissipativity based Control of Discrete-Time Nonlinear Systems via the LPV Framework
arXiv:2110.00290 · doi:10.1109/CDC45484.2021.9682893
Abstract
Unlike for Linear Time-Invariant (LTI) systems, for nonlinear systems, there exists no general framework for systematic convex controller design which incorporates performance shaping. The Linear Parameter-Varying (LPV) framework sought to bridge this gap by extending convex LTI synthesis results such that they could be applied to nonlinear systems. However, recent literature has shown that naive application of the LPV framework can fail to guarantee the desired asymptotic stability guarantees for nonlinear systems. Incremental dissipativity theory has been successfully used in the literature to overcome these issues for Continuous-Time (CT) systems. However, so far no solution has been proposed for output-feedback based incremental control for the Discrete-Time (DT) case. Using recent results on convex analysis of incremental dissipativity for DT nonlinear systems, in this paper, we propose a convex output-feedback controller synthesis method to ensure closed-loop incremental dissipativity of DT nonlinear systems via the LPV framework. The proposed method is applied on a simulation example, demonstrating improved stability and performance properties compared to a standard LPV controller design.
arXiv commentAccepted to 60th Conference on Decision and Control, Austin, 2021
References in corpus (6)
- Convex Incremental Dissipativity Analysis of Nonlinear Systems - Extended version
- Pitfalls of Guaranteeing Asymptotic Stability in LPV Control of Nonlinear Systems
- Incremental Stability and Performance Analysis of Discrete-Time Nonlinear Systems using the LPV Framework
- Linear Parameter-Varying Control of Nonlinear Systems based on Incremental Stability
- Virtual Control Contraction Metrics: Convex Nonlinear Feedback Design via Behavioral Embedding
- Nonlinear Tracking and Rejection using Linear Parameter-Varying Control