Adaptive boundary observer for parabolic PDEs subject to domain and boundary parameter uncertainties

Abstract

We are considering the problem of state observation for a class of infinite dimensional systems modeled by parabolic type PDEs. The model is subject to parametric uncertainty entering in both the domain equation and the boundary condition. An adaptive boundary observer, providing online estimates of the system state and parameters, is designed using finite-and infinite-dimensional backsteppinglike transformations. The observer is exponentially convergent under an ad hoc persistent excitation condition.

Battery Adaptive Observer for a Single-Particle Model With Intercalation-Induced Stress

“…Nonetheless, this approach does not directly extend to this paper as the SPM-Stress model contains highly nonlinear components. Ahmed-Ali et al [34] developed an adaptive boundary observer for parabolic PDEs with both domain and boundary parameter uncertainties, with convergence results, where the PDE is linear in the states and parameters, making it more tractable for the backstepping technique. In the context of battery applications, Ascencio derives an adaptive PDE observer for the SPM, including a parameter estimate for the diffusion coefficient [35].…”

Model‐based vs data‐driven adaptive control: An overview

“…To conclude this section about fully model‐based adaptation, we can cite other recent works, ie, post the latest general survey paper, which can be classified under the model‐based paradigm: for nonlinear models,) for models with time delay,) with parameter‐independent realization controllers, with input/output quantization,) under state constraints,) under inputs and actuator‐bandwidth constraints,) for Markovian jump systems,) for switched systems,) for partial differential equation (PDE)–based models,) for nonminimum/minimum‐phase systems,) to achieve adaptive regulation and disturbance rejection,) multiple‐model and switching adaptive control,) linear quadratic regulator (LQR)–based adaptive control, model predictive control–based adaptive control,) applications of model‐based adaptive control,) for sensor/actuator fault mitigation,) for rapidly time‐varying uncertainties, nonquadratic Lyapunov function–based MRAC, for stochastic systems,) retrospective cost adaptive control, persistent excitation–free/data accumulation–based control or concurrent adaptive control, sliding mode–based adaptive control,) set‐theoretic–based adaptive controller with performance guarantees, sampled data systems, and robust adaptive control …”

“…We want to summarize in this section some of the open problems in model‐based adaptive control. For instance, in PDE‐based adaptive control, some of the most recent available results deal only with linear or semilinear PDEs with linear uncertainty parameterization (see, eg, the works of Ahmed‐Ali et al,) Anfinsen et al, and Anfinsen and Aamo). The extension of these results to more general nonlinear PDEs or to nonlinear uncertainty parameterization remains an open problem.…”

Observer‐based output feedback control for a boundary controlled fractional reaction diffusion system with spatially‐varying diffusivity

“…Later on, a lot of related works have been arisen with the aid of this method, such as adaptive observer design for the ordinary differential equation‐PDE (ODE–PDE) systems and parabolic PDEs with domain and boundary parameter uncertainties in [7, 8], and output feedback control of parabolic PDEs with moving boundary in [9]. Note that these works are related to the constant diffusivity.…”