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Summary We present a certainty equivalence‐based adaptive boundary control scheme with a regulation‐triggered batch least‐squares identifier, for a heterodirectional transport partial differential equation‐ordinary differential equation (PDE‐ODE) system where the transport speeds of both transport PDEs are unknown. We use a nominal controller which is fed piecewise‐constant parameter estimates from an event‐triggered parameter update law that applies a least‐squares estimator to data “batches” collected over time intervals between the triggers. A parameter update is triggered by an observed growth in the norm of the PDE state. The proposed triggering‐based adaptive control guarantees: (1) the absence of a Zeno phenomenon; (2) parameter estimates are convergent to the true values in finite time (from most initial conditions); (3) exponential regulation of the plant states to zero. The effectiveness of the proposed design is verified by a numerical example.
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This content will become publicly available on September 25, 2026
Adaptive boundary control of reaction–diffusion PDEs with unknown distributed delay and unknown parameters
Abstract We study a reaction–diffusion partial differential equation (PDE) system with a distributed input, subject to multiple unknown plant parameters with arbitrarily large uncertainties. Using Lyapunov-based techniques, we design a delay-adaptive predictor feedback controller that ensures local boundedness of system trajectories and asymptotic regulation of the closed-loop system in terms of the plant state. Specifically, we model the input delay as a one-dimensional transport PDE with a spatial variable, effectively transforming the time delay into a spatially distributed shift. For the resulting coupled transport and reaction–advection–diffusion PDE system, we employ a PDE backstepping approach combined with the certainty-equivalence principle to derive an adaptive control law that compensates for both the unknown time delay and the unknown functional parameters. Simulation results are provided to illustrate the feasibility of our control design.
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- PAR ID:
- 10657849
- Publisher / Repository:
- IMA Journal of Mathematical Control and Information
- Date Published:
- Journal Name:
- IMA Journal of Mathematical Control and Information
- Volume:
- 42
- Issue:
- 4
- ISSN:
- 0265-0754
- Subject(s) / Keyword(s):
- Delay-adaptive control distributed input delay partial differential equation (PDE) backstepping predictor feedback reaction–advection–diffusion PDE.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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