Control of transport PDE/nonlinear ODE cascades with state-dependent propagation speed
Abstract
In this paper, we deal with the control of a transport partial differential equation/ nonlinear ordinary differential equation (PDE/nonlinear ODE) cascade system in which the transport coefficient depends on the ODE state. We develop a PDE-based predictor-feedback boundary control law, which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed-loop system. The stability proof is based on an infinite-dimensional backstepping transformation and a Lyapunov-like argument. The relation of the PDE-ODE cascade with a state-dependent propagation speed to an ODE system with a state-dependent input delay, which is defined implicitly via an integral of past values of the ODE state, is also highlighted and the corresponding equivalent predictor-feedback design is presented together with an alternative proof of global asymptotic stability of the closed-loop system based on the construction of a Lyapunov functional. The practical relevance of our control framework is illustrated in an example that is concerned with the control of a metal rolling process.
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System (1)-(3) is no longer equivalent to the classical time-delay system in [5,6,14-17].
“Equation (31) indicates that system (1)-(3) is no longer equivalent to the following classical time-delay system in [5,6,14-17]”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [16]
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- Authors
- Diagne, M., Bekiaris-Liberis, N., Otto, A., & Krstic, M.
- Affiliations
- Rensselaer Polytechnic Institute (US)
- Technical University of Crete (GR)
- Chemnitz University of Technology (DE)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2017-12
- Volume
- 62
- Issue
- 12
- Pages
- 6278-6293
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2612370936
- Cited by
- 52
- References
- 48
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 5 · 2023: 4 · 2022: 4 · 2021: 11 · 2020: 10 · 2019: 6 · 2018: 1
- FWCI
- 2.92
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Differential Equations Analysis
- Keywords
- predictor feedback, boundary control, global asymptotic stability, backstepping transformation, input delay, Lyapunov functional
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