Fast moving horizon estimation for a two-dimensional distributed parameter system

Jang, Hong; Lee, Jay H.; Braatz, Richard D.; Kim, Kwang Ki Kevin

doi:10.1016/j.compchemeng.2013.12.005

Cited by 12 publications

(4 citation statements)

References 15 publications

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“…Theorem 2. Consider the slow system (5) and the DPS (1) - (3). Given τ M , if there exist positive definite matrices P 0 , P 1 , and P 2 such that the matrix inequality…”

Section: Resultsmentioning

confidence: 99%

“…D ISTRIBUTED parameter systems (DPSs) have been listed as one of the most popular subjects due to their effective and successful modeling of chemical reactor processes, transport-reaction processes and curing oven [1]. Recent years, significant efforts have been devoted into different control problems for DPSs, such as approximation [2], estimation [3], consensus [4], optimization [5].…”

Section: Introductionmentioning

confidence: 99%

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Sampled-Data Control of Distributed Parameter Systems via an Event-Based Communication Scheme

Zhu

2021

IEEE Access

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This paper studies the problem of event-triggered control for a class of networked distributed parameter systems with Markov jump parameters. To reduce the number of packages transmitted over the communication network, an adaptive event-triggered mechanism is introduced. The Galerkin method is employed to obtain the nonlinear ordinary differential equation systems, which can accurately describe the dynamics of the dominant modes of the considered distributed parameter systems. The systems are subsequently parameterized by a multilayer neural network with one-hidden layer and zero bias terms, and the linear ordinary differential equation systems are derived. Then, Lyapunov approach is used to analyze stability of the considered systems, and by employing the strong law of large numbers and Gronwall inequality technique, almost surely exponential stability condition is derived. Moreover, a linear sampleddata-based controller is designed to stabilize the closed-loop systems. Finally, a practical example is shown to demonstrate the effectiveness of the achieved theoretical results.INDEX TERMS Distributed parameter systems, Markov jump parameters, Galerkin method, neural model, adaptive event-triggered networked control, almost surely exponential stability.

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“…Theorem 2. Consider the slow system (5) and the DPS (1) - (3). Given τ M , if there exist positive definite matrices P 0 , P 1 , and P 2 such that the matrix inequality…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sampled-Data Control of Distributed Parameter Systems via an Event-Based Communication Scheme

Zhu

2021

IEEE Access

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“…When it comes to the filter design issue, the concept of MHE is of particular engineering significance especially when encountering the parametric uncertainties and networked constraints. [20][21][22][23][24][25][26] MHE has become popular owing to its ability to handle explicitly linear and nonlinear systems and constraints on decision variables. 20,21 Under the decentralized/distributed frameworks, several results have been developed in the framework of MHE.…”

Section: Introductionmentioning

confidence: 99%

“…20,21 Under the decentralized/distributed frameworks, several results have been developed in the framework of MHE. [22][23][24][25][26] Recently, distributed MHE schemes were also developed for constrained linear systems, 25 which were developed with local MHE designed based on a centralized model. Moreover, DMHE was also developed with local MHE designed based on the subsystem model.…”

Section: Introductionmentioning

confidence: 99%

Decentralized state estimation for networked spatial-navigation systems with mixed time-delays and quantized complementary measurements: The moving horizon case

Gao

Zhao

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part G:

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In this paper, the navigational state estimation problem is investigated for a class of networked spatial-navigation systems with quantization effects, mixed time-delays, and network-based observations (i.e. complementary measurements and regional estimations). A decentralized moving horizon estimation approach, featuring complementary reorganization and recursive procedure, is proposed to tackle this problem. First, through the proposed reorganized scheme, a random delayed system with complementary observations is reconstructed into an equivalent delay-free one without dimensional augment. Second, with this equivalent system, a robust moving horizon estimation scheme is presented as a uniform estimator for the navigational states. Third, for the demand of real-time estimate, the recursive form of decentralized moving horizon estimation approach is developed. Furthermore, a collective estimation is obtained through the weighted fusion of two parts, i.e. complementary measurements based estimation, and regional estimations directly from the neighbors. The convergence properties of the proposed estimator are also studied. The obtained stability condition implicitly establishes a relation between the upper bound of the estimation error and two parameters, i.e. quantization density and delay occur probability. Finally, an application example to networked unmanned aerial vehicles is presented and comparative simulations demonstrate the main features of the proposed method.

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Estimation of local concentration from measurements of stochastic adsorption dynamics using carbon nanotube-based sensors

Jang

Lee

Braatz

2015

Korean J. Chem. Eng.

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Abstract−This paper proposes a maximum likelihood estimation (MLE) method for estimating time varying local concentration of the target molecule proximate to the sensor from the time profile of monomolecular adsorption and desorption on the surface of the sensor at nanoscale. Recently, several carbon nanotube sensors have been developed that can selectively detect target molecules at a trace concentration level. These sensors use light intensity changes mediated by adsorption or desorption phenomena on their surfaces. The molecular events occurring at trace concentration levels are inherently stochastic, posing a challenge for optimal estimation. The stochastic behavior is modeled by the chemical master equation (CME), composed of a set of ordinary differential equations describing the time evolution of probabilities for the possible adsorption states. Given the significant stochastic nature of the underlying phenomena, rigorous stochastic estimation based on the CME should lead to an improved accuracy over than deterministic estimation formulated based on the continuum model. Motivated by this expectation, we formulate the MLE based on an analytical solution of the relevant CME, both for the constant and the time-varying local concentrations, with the objective of estimating the analyte concentration field in real time from the adsorption readings of the sensor array. The performances of the MLE and the deterministic least squares are compared using data generated by kinetic Monte Carlo (KMC) simulations of the stochastic process. Some future challenges are described for estimating and controlling the concentration field in a distributed domain using the sensor technology.

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Fast moving horizon estimation for a two-dimensional distributed parameter system

Cited by 12 publications

References 15 publications

Sampled-Data Control of Distributed Parameter Systems via an Event-Based Communication Scheme

Sampled-Data Control of Distributed Parameter Systems via an Event-Based Communication Scheme

Decentralized state estimation for networked spatial-navigation systems with mixed time-delays and quantized complementary measurements: The moving horizon case

Estimation of local concentration from measurements of stochastic adsorption dynamics using carbon nanotube-based sensors

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