Non-asymptotic State Estimation of Linear Reaction Diffusion Equation using Modulating Functions

Ghaffour, Lilia; Noack, Matti; Reger, Johann; Laleg‐Kirati, Taous‐Meriem

doi:10.1016/j.ifacol.2020.12.2570

Cited by 12 publications

(11 citation statements)

References 19 publications

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“…Similar to the strategy in [23], a series expansion of the solution of system (1) is utilized for extracting the unknown state information. In the present work, it is assumed that the subsystem states w l (x, t), l ∈ {1, .…”

Section: Function Basis Expansionmentioning

confidence: 99%

“…The major research goal of the contribution is related to the extension of the nonasymptotic observer design approach for PDEs by using modulating functions from [23] towards coupled PDE systems. In order to construct a relationship between the known measurements and the parameterization of the unmeasured state variable, the modulation functional is applied to the dynamics of the system and suitable conditions for neglecting unknown terms are formulated.…”

Section: Non-asymptotic Observer Design For Coupled Pde Systemmentioning

confidence: 99%

“…For the derivation of the auxiliary system, the modulation functional ( 6) is applied to the dynamics of the system (1). The following calculations are performed in a similar fashion as in [23]. First, the modulation functional is applied to the second spatial derivative of the state with ϕ as the modulation function defined in (6).…”

Section: Derivation Of the Auxiliary Systemmentioning

confidence: 99%

“…Up to this part, the procedure is applied along [23]. It is worth noticing that for eliminating the part of the inner product brackets multiplied with the unknown state w j , n auxiliary PDE equations would have to be solved for ϕ m i with only one solution.…”

Section: Derivation Of the Auxiliary Systemmentioning

confidence: 99%

“…The most recent result [23] is related to the state estimation for reaction-diffusion PDE with constant parameters. There the whole state is estimated from a measurement on the boundary.…”

Section: Introductionmentioning

confidence: 99%

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State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions

Rojas

Noack

Reger

et al. 2022

Sensors

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Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary systems are generated from the original system by applying modulating functions and formulating annihilation conditions. It is extended by a decoupling matrix step. The calculated kernels are utilized for modulating the input and output signals over a receding time window to obtain the coefficients for the basis expansion for the desired state estimation. The developed algorithm and its real-time functionality are verified via simulation of an example system related to the dynamics of chemical tubular reactors and compared to the conventional backstepping observer. The method achieves a successful state reconstruction of the system while mitigating white noise induced by the sensor. Ultimately, the modulating function approach represents a solution for the distributed state estimation problem without solving a PDE online.

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Section: Function Basis Expansionmentioning

confidence: 99%

Section: Non-asymptotic Observer Design For Coupled Pde Systemmentioning

confidence: 99%

Section: Derivation Of the Auxiliary Systemmentioning

confidence: 99%

Section: Derivation Of the Auxiliary Systemmentioning

confidence: 99%

“…The most recent result [23] is related to the state estimation for reaction-diffusion PDE with constant parameters. There the whole state is estimated from a measurement on the boundary.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations