Control design for first-order processes: shaping the probability density of the process state

Forbes, Michael G.; Guay, Martin; Forbes, J. Fraser

doi:10.1016/j.jprocont.2003.07.002

Cited by 78 publications

(42 citation statements)

References 5 publications

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“…Therefore, a control methodology defined on the PDF would provide an accurate and flexible control strategy that could accommodate a wide class of objectives. For this reason, in [5,12,13,31] probability density function control schemes were proposed, where the cost functional depends on the PDF of the stochastic state variable. In this way, a deterministic objective results and no average is needed.…”

Section: Introductionmentioning

confidence: 99%

“…In [12,13], the objective is defined by the Kullback-Leibler [18] distance between the state PDF and a desired one. On the other hand, in [5,31] a square distance between the state PDF and a desired PDF is considered.…”

Section: Introductionmentioning

confidence: 99%

“…Notice that in contrast to LQR-type feedback schemes, employed in, e.g., [5,31], the closed-loop schemes based on the RH-MPC approach do not optimize a true performance index; see [8] for a method to quantify the performance degradation. Nevertheless, these schemes provide robust controllers that apply equally well to linear and nonlinear models and allow to accommodate different control-and state constraints [8,10].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control of Probability Density Functions of Stochastic Processes

Annunziato

Borzì

2010

Mathematical Modelling and Analysis

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Abstract. A Fokker-Planck framework for the formulation of an optimal control strategy of stochastic processes is presented. Within this strategy, the control objectives are defined based on the probability density functions of the stochastic processes. The optimal control is obtained as the minimizer of the objective under the constraint given by the Fokker-Planck model. Representative stochastic processes are considered with different control laws and with the purpose of attaining a final target configuration or tracking a desired trajectory. In this latter case, a receding-horizon algorithm over a sequence of time windows is implemented.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal Control of Probability Density Functions of Stochastic Processes

Annunziato

Borzì

2010

Mathematical Modelling and Analysis

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“…This is pointed out by Forbes et al [16], who used a Gram-Charlier PDF to obtain a standard state-space model of the process. In the framework of dynamic processes, Wang [17] proposed a general time-evolving model of the process PDF based on B-splines.…”

Section: The Generalized Lambda Distributionsmentioning

confidence: 99%

Application of Lambda Distributions and Bootstrap analysis to the prediction of fatigue lifetime and confidence intervals

Bigerelle

Najjar

Fournier

et al. 2006

International Journal of Fatigue

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractIn statistical process control (SPC) methodology, quantitative standard control charts are often based on the assumption that the observations are normally distributed. In practice, normality can fail and consequently the determination of assignable causes may result in error. After pointing out the limitations of hypothesis testing methodology commonly used for discriminating between Gaussian and non-Gaussian populations, a very flexible family of statistical distributions is presented in this paper and proposed to be introduced in SPC methodology: the generalized lambda distributions (GLD). It is shown that the control limits usually considered in SPC are accurately predicted when modelling usual statistical laws by means of these distributions. Besides, simulation results reveal that an acceptable accuracy is obtained even for a rather reduced number of initial observations (approximately a hundred). Finally, a specific user-friendly software have been used to process, using the SPC Western Electric rules, experimental data originating from an industrial production line. This example and the fact that it enables us to avoid choosing an a priori statistical law emphasize the relevance of using the GLD in SPC.

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“…Motivated by several typical examples in practical systems such as paper and board making, a new group of control strategies for the output probability density function (PDF), namely PDF control, have been a subject of research in recent years (Shalom and Li 2000;Srikanth, Kesavan, and Peter 2000;Yue and Wang 2003;Forbes, Guay, and Forbes 2004;Wang 2004, 2005a, b;Elbeyli, Hong, and Sun 2005). The objective of the controller design is to find a crisp control input, so that the shape of output PDF can follow a given distribution.…”

Section: Introductionmentioning

confidence: 99%

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

Cao

2009

International Journal of Systems Science

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This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

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Control design for first-order processes: shaping the probability density of the process state

Cited by 78 publications

References 5 publications

Optimal Control of Probability Density Functions of Stochastic Processes

Optimal Control of Probability Density Functions of Stochastic Processes

Application of Lambda Distributions and Bootstrap analysis to the prediction of fatigue lifetime and confidence intervals

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

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