Fuzzy Output Regulation of Nonlinear Time-Delay Distributed Parameter Systems With Quantization and Actuator Failures: Application to Hot Strip Mill Cooling Process

This work develops a network of adaptive boundary observers and studies the agreement between state and parameter estimates for a single target parabolic partial differential equation (PDE) system in the presence of structured and unstructured uncertainties. It is assumed that the unknown parameters take the form of either a structured uncertainty with unknown constant parameters or an unstructured uncertainty that can be neutralized by a radial basis function neural networks with unknown weights. The proposed adaptive observers consisting of agents in the network follow the structure of adaptive identifiers for the considered target PDE systems with the insertion of a penalty term in both the state and parameter estimates. Different from earlier efforts, the proposed adaptive laws include a penalty term of the mismatch between the parameter and state estimates generated by the other adjacent agents, which helps to accelerate the estimation of uncertainties. Additionally, the effects of these modifications on the agreement amongst the state and parameter estimates are investigated. Theoretical proofs are provided to show that the proposed approach guarantees the exponential convergence of estimation errors in the case of structured uncertainties and the ultimate boundedness of estimation errors in the case of unstructured uncertainties. Finally, numerical simulations are carried out to verify the effectiveness of the design methods.

Section: Stability Analysismentioning

confidence: 75%

“…To illustrate the design of consensus observer network in Section 3, we consider the following system

\begin{align} \partial_{t} v ((), x, t) = \partial_{x x} v ((), x, t) + b e^{x} c o s ((), 𝒰 false(t false)) + 5 s i n ((), 𝒴 false(t false)), \end{align}

\begin{align} \partial_{x} v ((), 0, t) = prefix- μ 𝒴 false(t false), \end{align}

with the input

\begin{align} 𝒰 false(t false) = \cos ((), \frac{π}{2} t), \end{align}

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

Section: System With Structured Uncertaintymentioning

confidence: 99%

See 3 more Smart Citations

Adaptive boundary observer network design for the consensus on the estimation of a class of parabolic partial differential equation systems

Cai,

Yuan,

Luo

et al. 2023

Finite‐time dissipative control of fuzzy distributed parameter CPSs with quantization under cyber attacks

Ding

Chang

et al. 2023

Self Cite

The finite‐time dissipative control for a class of nonlinear distributed parameter Cyber‐Physical Systems (CPSs) is studied in this article. By replacing the nonlinear term with the Takagi‐Sugeno (T‐S) fuzzy model, the nonlinear distributed parameter CPSs are represented by a fuzzy parabolic partial differential equation (PDE). To reduce the transmission burden of communication channels, the state information is considered to be dynamically quantized before transmission. Then, a fuzzy state feedback controller under cyber attacks is designed. Sufficient design criteria for the fuzzy controller and the adjusting parameters of dynamic quantizer are developed to obtain the finite‐time dissipative performance of the fuzzy closed‐loop system by the free‐matrix inequality approach. Finally, a simulation study in a cascaded of two cylindrical lithium batteries is explored to validate the efficiency of the control strategy.

Interval observer design for unobservable switched nonlinear partial differential equation systems and its application

Song,

Peng,

Song

et al. 2024

SummaryThis paper designs an interval observer for switched nonlinear partial differential equation (PDE) systems. Initially, persistent dwell‐time switching rules are used to model switched PDE systems with fast and slow switching phenomena. Next, for unobservable systems caused by uncertainties, the interval observer for the target PDE systems is proposed by utilizing unknown but bounded information of the initial states, boundary conditions, external disturbances, and measurement noises. Subsequently, by utilizing the estimated state's upper and lower bounds, an interval observer‐based control strategy is devised to stabilize the studied systems, and sufficient conditions to ensure the stability of the target systems and the observation error dynamics are provided. Furthermore, the designed interval observer is employed to detect sensor failures in the presence of various uncertainties. Finally, two examples, including the lithium‐ion battery's temperature estimation and fault detection, are utilized to demonstrate the effectiveness of the obtained methods.