Output feedback control of dissipative PDE systems with partial sensor information based on adaptive model reduction

Pitchaiah, Sivakumar; Armaou, Antonios

doi:10.1002/aic.13854

Cited by 22 publications

(12 citation statements)

References 28 publications

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“…The accuracy of the ROM based on fewer eigenfunctions computed from an ensemble of small size is usually worse than that of the ROM constructed by adopting more eigenfunctions from a large ensemble of snapshots. However, as pointed out in [18], eigenfunctions that have high frequency spatial profiles (corresponding to small empirical eigenvalues) should be discarded because of potentially significant round-off errors. In this situation, only a single or a few eigenfunctions can be adopted from APOD keeping the dimension of the reduced-order model low.…”

Section: Empc Scheme Of Integrating Apod and Finite-difference Methodmentioning

confidence: 99%

Handling state constraints and economics in feedback control of transport-reaction processes

Lao

Ellis

Christofides

2015

Journal of Process Control

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a b s t r a c tTransport-reaction processes, which are typically described by parabolic partial differential equations (PDEs), play an important role within the chemical process industries. Therefore, it is important to develop feedback control techniques that operate transport-reaction processes in an economically optimal fashion in the presence of constraints in the process states and manipulated inputs. Economic model predictive control (EMPC) is a predictive control scheme that combines process economics and feedback control into an integrated framework with the potential of improving the closed-loop process economic performance compared to traditional control methodologies. In this work, we focus on systems of nonlinear parabolic PDEs and propose a novel EMPC design integrating adaptive proper orthogonal decomposition (APOD) method with a high-order finite-difference method to handle state constraints. The computational efficiency and constraint handling properties of this design are evaluated using a tubular reactor example modeled by two nonlinear parabolic PDEs.

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Section: Empc Scheme Of Integrating Apod and Finite-difference Methodmentioning

confidence: 99%

Handling state constraints and economics in feedback control of transport-reaction processes

Lao

Ellis

Christofides

2015

Journal of Process Control

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“…KLD has already been applied to compute orthogonal EEFs for PDE systems [8], [17], [45], [46]. Here, we omit its derivation and give the implementation procedure simply in Algorithm 1.…”

Section: A Computing Empirical Eigenfunctions With Data-driven Kldmentioning

confidence: 99%

Data-Driven <inline-formula> <tex-math notation="LaTeX">$H_\infty$ </tex-math></inline-formula> Control for Nonlinear Distributed Parameter Systems

Luo

Huang

et al. 2015

IEEE Trans. Neural Netw. Learning Syst.

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The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

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“…Many control methods based on model reduction techniques have been reported in the past few decades (e.g. [1][2][3][4][5][6][7][8][9][10][11]). However, it should be noted that the existing results mainly focus on designing continuous-time controllers for PPDE systems.…”

Section: Introductionmentioning

confidence: 99%

sampled‐data fuzzy control for non‐linear parabolic distributed parameter systems with control inputs missing

Wang

2017

IET Control Theory & Applications

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Output feedback control of dissipative PDE systems with partial sensor information based on adaptive model reduction

Cited by 22 publications

References 28 publications

Handling state constraints and economics in feedback control of transport-reaction processes

Handling state constraints and economics in feedback control of transport-reaction processes

Data-Driven <inline-formula> <tex-math notation="LaTeX">$H_\infty$ </tex-math></inline-formula> Control for Nonlinear Distributed Parameter Systems

sampled‐data fuzzy control for non‐linear parabolic distributed parameter systems with control inputs missing

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