Hong Yue

Minimum entropy control of closed-loop tracking errors for dynamic stochastic systems

The entropy has been used to characterize the uncertainty of the tracking error for general nonlinear and non-Gaussian stochastic systems. A recursive optimization solution has been developed and the local stability condition of the closed-loop system has been established. The generality of this algorithm has been proved by the special case study of the minimum variance control for linear Gaussian systems.

Recent developments in stochastic distribution control: a review

Figure 1: MWD in chemical control reaction system Mokcumrwe~htd~tributionconuolm polymerisation processes It is important to control a polymers molecular weight distribution (MWD) in industrial polymerisation processes because a polymers end-use properties are strongly dependent on its MWD. Though it is still not an easy control task, extensive studies have been made on how to get a polymers MWD when the polymerisation kinetic model is available5.6.25. Mostly the MWD is calculated by numerical integration of the polymer material balances or by using the moment generating function. In certain cases, some stochastic models have been proposed for MWD description. For example, for linear chains, Florys distribution can be used to describe the instantaneous MWD of polyolefin made with single-site-type catalystslI. Industry-scale closed-loop control of MWD is still a challenging subject because the feasibility of on-line measurement of MWD for polymerisation processes remains to be demonstrated. Most research is based on simulated reactors. In order to get a target MWD, especially for batch processes, normally optimal or sub-optimal control trajectories are determined by optimisation design either off-line6,27 or on-linelB.26. and then efforts are made to implement these trajectories using control strategies. State observers are often needed to get on-line trajectories lB , while for off-line control trajectories, batch-to-batch modifications to the optimal trajectories may be added so that the target MWD can be achieved after several batches4• Figure 1 shows a general MWD system.

A rational spline model approximation and control of output probability density functions for dynamic stochastic systems

This paper presents a new method to model and control the shape of the output probability density functions for dynamic stochastic systems subjected to arbitrary bounded random input. A new rational model is proposed to approximate the output probability density function of the system. This is then followed by the design of a novel nonlinear controller, which guarantees the monotonic decreasing of the functional norm of the difference between the measured probability density function and its target distribution. This leads to a desired tracking performance for the output probability density function. A simple example is utilized to demonstrate the use of the proposed modelling and control algorithm and encouraging results have been obtained.

Minimum entropy of B-spline PDF systems with mean constraint

For the B-spline approximation of the continuous probability density function (PDF), the relationships between the B-spline weights and entropy both in general and under the mean constraint have been analyzed. It provides the conditions under which the minimum entropy can be achieved subject to the mean constraint. The difference between the entropy of continuous and discrete distributions has also been clarified. A minimum entropy controller with the mean constraint is then developed and several simulations are performed to verify the main results. (c) 2006 Elsevier Ltd. All rights reserved.

A systematic survey of the response of a model NF-κB signalling pathway to TNFα stimulation.

Whites lab established that strong, continuous stimulation with tumour necrosis factor-α (TNFα) can induce sustained oscillations in the subcellular localisation of the transcription factor nuclear factor κB (NF-κB). But the intensity of the TNFα signal varies substantially, from picomolar in the blood plasma of healthy organisms to nanomolar in diseased states. We report on a systematic survey using computational bifurcation theory to explore the relationship between the intensity of TNFα stimulation and the existence of sustained NF-κB oscillations. Using a deterministic model developed by Ashall et al. in 2009, we find that the systems responses to TNFα are characterised by a supercritical Hopf bifurcation point: above a critical intensity of TNFα the system exhibits sustained oscillations in NF-kB localisation. For TNFα below this critical value, damped oscillations are observed. This picture depends, however, on the values of the models other parameters. When the values of certain reaction rates are altered the response of the signalling pathway to TNFα stimulation changes: in addition to the sustained oscillations induced by high-dose stimulation, a second oscillatory regime appears at much lower doses. Finally, we define scores to quantify the sensitivity of the dynamics of the system to variation in its parameters and use these scores to establish that the qualitative dynamics are most sensitive to the details of NF-κB mediated gene transcription.

Minimum entropy control of non-Gaussian dynamic stochastic systems

This paper presents a new method to minimize the closed loop randomness for general dynamic stochastic systems using the entropy concept. The system is assumed to be subjected to any bounded random inputs. Using the linear B-spline model for the shape control of the system output probability density function, a control input is formulated which minimizes the output entropy of the closed loop system. Since the entropy is the measure of randomness for a given random variable, this controller can thus reduces the uncertainty of the closed loop system. A set of sufficient conditions have been established to guarantee the local minimum property of the obtained control input and the stability of the closed loop system. Discussions on the design of minimum entropy tracking error have also been made. An illustrative example is utilized to demonstrate the use of the control algorithm, and satisfactory results have been obtained.

ILC-based Generalised PI Control for Output PDF of Stochastic Systems Using LMI and RBF Neural Networks

In this paper, a fixed-structure iterative learning control (ILC) control design is presented for the tracking control of the output probability density functions (PDF) in general stochastic systems with non-Gaussian variables. The approximation of the output PDF is firstly realized using a radial basis function neural network (RBFNN). Then the control horizon is divided to certain intervals called batches. ILC laws are employed to tune the PDF model parameters between two adjacent batches. A three-stage method is proposed which incorporates: a) identifying nonlinear parameters of the PDF model using subspace system identification methods; b) calculating the generalised PI controller coefficients using LMI-based convex optimisation approach; and c) updating the RFBNN parameters between batches based on ILC framework. Closed-loop stability and convergence analysis together with simulation results are also included in the paper

Modelling and control of the flame temperature distribution using probability density function shaping

This paper presents three control algorithms for the output probability density function (PDF) control of the 2D and 3D flame distribution systems. For the 2D flame distribution systems, control methods for both static and dynamic flame systems are presented, where at first the temperature distribution of the gas jet flames along the cross-section is approximated. Then the flame energy distribution (FED) is obtained as the output to be controlled by using a B-spline expansion technique. The general static output PDF control algorithm is used in the 2D static flame system, where the dynamic system consists of a static temperature model of gas jet flames and a second-order actuator. This leads to a second-order closed-loop system, where a singular state space model is used to describe the dynamics with the weights of the B-spline functions as the state variables. Finally, a predictive control algorithm is designed for such an output PDF system. For the 3D flame distribution systems, all the temperature values of the flames are firstly mapped into one temperature plane, and the shape of the temperature distribution on this plane can then be controlled by the 3D flame control method proposed in this paper. Three cases are studied for the proposed control methods and desired simulation results have been obtained.

Improving Data Fitting of a Signal Transduction Model by Global Sensitivity Analysis

Based on a simplified model of the (TNF-alpha mediated) IkappaBalpha-NF-kappaB signal transduction pathway, global sensitivity analysis has been performed to identify those parameters that exert significant control on the system outputs. The permutation operation in Morris method is modified to work for log-uniform sampling parameters. The identified sensitive parameters are then estimated using multivariable search such that the output of the model matches experimental data representing the nuclear concentration of NF-kappaB. Such parameter tuning leads to much better agreement between the model and the experimental time series relative to those previously published. This shows the importance of global sensitivity analysis in Systems Biology models.

Robust Iterative Learning Control of Output PDF in Non-Gaussian Stochastic Systems Using Youla Parametrization

In this paper a robust iterative learning control (ILC) based control strategy is proposed for the shape control of the output probability density functions (PDF) for dynamic stochastic systems subjected to non-Gaussian variables. Using the radial basis function neural network (RBFNN) approximations to instant output PDFs, the output PDF tracking problem has been reduced to the weight control of the neural network. Furthermore, by separating the whole control horizon into certain number of the time domain sub- intervals called Batches, a control algorithm is established where the Youla parametrization technique has been used together with a proportional plus differential (PD) version of the ILC. The proportional part of the ILC law looks after the tuning of the RBFNN basis function parameters (i.e., the RBF centers and widths) whilst the differential part of the ILC law is used to tune the parameters of Youla-parameterized controller so that the closed-loop output PDF tracking performance is improved versus the advances of batches along the time horizon. The analysis on the proposed ILC convergence is made and demonstrable simulation results are also provided to show the effectiveness of the obtained control algorithm.