Output regulation for 1-D reaction-diffusion equation with a class of time-varying disturbances from exosystem

Jing, Wei; Guo, Bao‐Zhu

doi:10.1016/j.automatica.2022.110274

Cited by 2 publications

(4 citation statements)

References 16 publications

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“…A. HIGH-GAIN OBSERVER USED AS EXOSYSTEM AND THE MODIFIED FRANCIS-ISIDORI-BYRNES EQUATIONS Consider a smooth, unmodelled, and continuously differentiable signal ψ(t) as the output of the nonlinear system (11) and ( 12) with ρ ≥ 1. Therefore, by considering 0 (x) = 0 the High-Gain Observer ( 13) and ( 14) can be rewritten as…”

Section: High-gain Observermentioning

confidence: 99%

“…In [8] is used a fuzzy adaptive output feedback control scheme to approximate unknown functions for a class of nonlinear uncertain strict-feedback systems under the action of nonlinear exosystems. Moreover, in the case of PDE's introducing an adaptive internal model that estimates unknown frequencies, output regulation, and disturbance rejection are achieved, even if the disturbance is generated by an unknown finitedimensional exosystem [9], [10], or the exosystem coefficients are time-varying [11]. Likewise, [12] proposes an event-triggered control based on an adaptive internal model for a class of uncertain linear systems, where the system matrix of the exosystem contains unknown parameters.…”

Section: Introductionmentioning

confidence: 99%

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On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

et al. 2023

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This paper is devoted to solving the output regulation problem on the basis of the new Francis equations for arbitrary reference/disturbance signals, whose model are obtained by High-Gain observers, providing in this way, the regulation of unmodeled but measurable reference signals. The design is given by fixing a steady state globally attractive by means of LMIs which allows controlling the decay rate by considering input bounds; while the regulation problem is solved by computing the steady-state input based on a modified set of the regulation equations, when the exosystem is constructed upon High-Gain observers, extending in this way, the classical output regulation theory for unmodeled reference/disturbance signal. The Furuta pendulum is used to illustrate the viability of the proposed approach.INDEX TERMS Output regulation, high-gain observer, linear matrix inequality.

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Section: High-gain Observermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

et al. 2023

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“…By the semigroup theory, Wei and Guo [30] yield that the exponentially stable C 0 -semigroup e At generated by the operator A defined by (3.13), and the unbounded operator −𝛿(x) is admissible for e At . Then, due to the admissibility of −𝛿(x), it is pointed out that equation (3.10) has a unique solution (ṽ, ε).…”

Section: Proof Define An Operator a ∶ D(a)(⊂ ) →  Similar To (211) ...mentioning

confidence: 99%

“…Proof Define an operator

normal𝔸 : D false(normal𝔸 false) false(\subset scriptH false) \to scriptH

similar to () as follows:

({, \begin{matrix} left \\ array 𝔸 f = f^{''} - λ_{1} f, \forall f \in D (𝔸), \\ array D (𝔸) = {f \in H^{2} (0,1) | f^{'} (0) = 0, f (1) = 0} . \end{matrix})

We write system () to be an abstract form as

\frac{d}{d t} \overset{ε}{true} false(\cdot, t false) = normal𝔸 \overset{ε}{true} false(\cdot, t false) + h false(x, t false) \overset{v}{true} false(t false) - δ false(x false) false(normalΔ false(t false) \overset{v}{true} false(t false) false) .

By the semigroup theory, Wei and Guo [30] yield that the exponentially stable

{C}_0

‐semigroup

e^{normal𝔸 t}

generated by the operator

normal𝔸

defined by (), and the unbounded operator

-\delta (x)

is admissible for

e^{normal𝔸 t}

. Then, due to the admissibility of

-\delta (x)

, it is pointed out that equation () has a unique solution

…”

Section: Observer Designmentioning

confidence: 99%

Output regulation for the reaction‐diffusion equation with time‐varying disturbances and non‐collocated observation

Liu,

2023

Math Methods in App Sciences

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The present article focuses on the output regulation problem for uncertain 1‐d reaction‐diffusion equation(RDE), in which the disturbance inputs are located at both the interior of the equation and uncontrolled end. Both the reference signal and the disturbances signal are specified due to an exosystem of time‐varying coefficients. The difficulty of the problem is that the control end is noncollocated with the regulated output. The so‐called feedforward control is designed by introducing an regulator, which is determined by infinite‐dimensional equation. A state observer is proposed based on the measurement output to recover the original and the external systems. The suitable feedback control has to be integrated by replacing the states in the expression of feedforward control law. As a result, exponential convergence of the error between the reference signal and the output, and the closed‐loop stability are established. Numerical results are performed the effectiveness of the results.

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Output regulation for 1-D reaction-diffusion equation with a class of time-varying disturbances from exosystem

Cited by 2 publications

References 16 publications

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

On the Output Regulation for an Underactuated Inverse Pendulum When the Exosystem Is a High-Gain Observer

Output regulation for the reaction‐diffusion equation with time‐varying disturbances and non‐collocated observation

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