Minimum Entropy Control Research Articles

Performance assessment for non-Gaussian systems by minimum entropy control and dynamic data reconciliation

Control performance of the industrial process is inevitably influenced by the measurement noises and non-Gaussian external disturbances. This influence has not been fully considered in the traditional variance-based controller design. To reduce the influence, a novel scheme that can enhance the control performance is developed by integrating dynamic data reconciliation (DDR) into minimum rational entropy control (MREC) in this paper. Firstly, the influence of measurement noise is fully considered, and a novel DDR method is proposed to deal with the minimum entropy control (MEC) process such that the influence of measurement noise can be reduced, and the control performance will be improved. Then, based on the DDR-MREC performance index, a benchmark for evaluating the control performance of non-Gaussian systems is established. Finally, the proposed control performance assessment (CPA) method is applied to the wind energy conversion system and compared with the CPA method based on DDR-minimum variance control. The experimental results have demonstrated that the proposed new method is more effective than existing works.

DYNAMICAL INTERPRETATIONS OF A GENERALIZED CUBIC SYSTEM

Chaotic map is a typical route in mathematics to describe the dynamical interpretations in various applications of science and engineering. However, the dynamics in the traditional logistic chaotic map $r\vartheta(1-\vartheta)$ depends on the single control parameter $r$. In this article, a generalized cubic chaotic map with three changeable parameters $a$, $b$ and $r$ is introduced and its dynamical properties are studied. The added new control parameter increases the flexibility in the system due to which it can fit in various applications. A few cases are discussed showing the effectiveness of the changeable parameters in various properties such as stationary and periodic states, stability in stationary states, Lyapunov exponent property, bifurcation interpretation, and the minimum entropy control. Further, the developments are illustrated mathematically as well as experimentally followed by period-doubling bifurcation and Lyapunov exponent diagrams. Moreover, it is noticed that as compared to traditional chaotic systems, a bifurcation self-similarity is seen along the x-axis in all the cases of the cubic map. Moreover, a brief summary on Shannon minimum entropy is also given to control the unstable stationary and periodic states in chaotic regime.

Disturbance Observer-Based Minimum Entropy Control for a Class of Disturbed Non-Gaussian Stochastic Systems

In this article, a novel control algorithm is developed for a class of nonlinear stochastic systems subject to multiple disturbances, including exogenous dynamic disturbance and general non-Gaussian noise. An observer is designed to estimate the exogenous disturbance, and then the disturbance compensation is incorporated into a feedback control strategy for the non-Gaussian system. Considering the ability of entropy in randomness quantification, a performance index is established based on the generalized entropy optimization principle. Furthermore, it is adjusted to be available for the controller solution, which also solves the coupling between two kinds of disturbances. On this basis, the optimal controller is provided in a recursive way, with which the closed-loop stability and good antidisturbance ability can be guaranteed simultaneously. Compared with the existing studies on the non-Gaussian stochastic systems, the proposed control algorithm has merits in multiple disturbances decoupling and enhanced antidisturbance performance. Finally, a simulation example is given to demonstrate the effectiveness of theoretical results.

Performance Assessment of Cascade Control System with Non-Gaussian Disturbance Based on Minimum Entropy

Due to the fact that cascade control can improve the single-loop’s performance well and reduce the integral error from disturbance response, it has been one of the most important control strategies in industrial production, especially in thermal power plant and chemical engineering. However, most of the existing research is based on the Gaussian system and other few studies on the non-Gaussian cascade disturbance system also have obvious defects. In this paper, an effective control loop performance assessment (CPA) of cascade control system for many non-Gaussian distributions even the unknown mixture disturbance noise has been proposed. Compared to the minimum variance control (MVC) approach, the minimum entropy control (MEC) method can obtain a more accurate estimate. In this method, like MVC, the primary loop output and secondary loop output can be represented as invariant and dependent terms, then adopted estimated distribution algorithm (EDA) is used to achieve the system model and disturbances. In order to show the effectiveness of MEC, some simulation examples based on different perturbations are given.

Fault Tolerant Control for Nonlinear Singular Stochastic Distribution Systems Based on Fuzzy Modeling

When the desired output probability density function (PDF) is unknown, the active fault-tolerant control (FTC) method for the non-Gaussian nonlinear singular stochastic distribution control (SDC) system is investigated in this paper. Algebraic constraints and the nonlinearity in singular systems make the design of fault diagnosis and fault-tolerant control more complex. Different from traditional static modeling methods, the linear fuzzy logic system is served for approximating the output PDF. Takagi-Sugeno (T-S) fuzzy model is used to describe the nonlinear system. Subsequently, a fuzzy descriptor fault diagnosis (FD) observer is used to provide the unknown fault information for the fault-tolerant controller design. Combining minimum entropy control and fault compensation algorithm, the minimum Shannon entropy fault tolerant control strategy is developed to compensate the performance losses caused by the fault. At last, simulation results are applied to demonstrate the effectiveness of the proposed algorithms.

Mixed [formula omitted] control for automated highway driving

Automated highway driving combining longitudinal vehicle control and lane decision represents an important part on the way to autonomous driving. The general goal in this work is to investigate an ego-vehicle control approach for automated highway driving. For this, a multi-lane and multi-vehicle environment is considered where the vehicles around the controlled ego-vehicle represent disturbance inputs. The control law should be designed to increase local traffic flow stability around the ego-vehicle. The novelty in this work is represented by considering string stability in a multi-lane and multi-vehicle context, i.e. effects of ego-vehicle lane changes on surrounding traffic. The lane decision process results in a switching law based on the concept of minimum entropy control which represents a mixed H2−H∞ control design method. Since it is well known that string stability is implied by bounding the H∞ norm of a vehicle to vehicle transfer function it seems reasonable to apply this control strategy for automated highway driving. Thereby, each lane is assigned with an entropy value based on the actual traffic situation and the target lane is decided to balance local unequal distributions of traffic density. Lane changes are allowed only if local string stability can be assured. Longitudinal ego-vehicle control is realized with a compensator blending strategy where a dynamic compensator is derived targeting H2 and H∞ performance measure. The overall automated highway driving approach is evaluated by means of two test cases, namely a merging scenario and a highway driving scenario in a multi-lane and multi-vehicle traffic environment implemented in the high fidelity vehicle simulation tool IPG CarMaker.

Non-Gaussian Systems Control Performance Assessment Based on Rational Entropy.

Control loop Performance Assessment (CPA) plays an important role in system operations. Stochastic statistical CPA index, such as a minimum variance controller (MVC)-based CPA index, is one of the most widely used CPA indices. In this paper, a new minimum entropy controller (MEC)-based CPA method of linear non-Gaussian systems is proposed. In this method, probability density function (PDF) and rational entropy (RE) are respectively used to describe the characteristics and the uncertainty of random variables. To better estimate the performance benchmark, an improved EDA algorithm, which is used to estimate the system parameters and noise PDF, is given. The effectiveness of the proposed method is illustrated through case studies on an ARMAX system.

Minimum Entropy Active Fault Tolerant Control of the Non-Gaussian Stochastic Distribution System Subjected to Mean Constraint

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms.

Double-Objective Optimal Control for Non-Gaussian Systems: An Example Study on Analytical vs Numerical Solutions

Minimum entropy control has been proven to be an effective method in control of non-Gaussian stochastic systems. In this case, the entropy is proposed as a generalization of the variance measure to characterize the randomness of the process. Minimum entropy corresponds to small uncertainty (or derivation), but it cannot guarantee the tracking error approaching to zero. Therefore, mean square error also should be added in the criterion. In this paper, by using a simple example, the method of generating a representative approximation of the Pareto optimal control set is investigated in both analytical and numerical ways. And simulation results show the feasibility of the proposed double-objective optimal control method.

Minimum entropy-based performance assessment of feedback control loops subjected to non-Gaussian disturbances

Control performance assessment (CPA) is a useful tool to establish the quality of industrial feedback control loops. While many current CPA techniques are developed solely for the controlled systems under the assumption of the Gaussian disturbance, the conventional minimum variance control (MVC) approach would not be applied when the disturbance distribution is non-Gaussian. In this paper, based on the information theory and the minimum entropy criterion, a more general CPA index for the feedback control loop subjected to unknown disturbance distribution is investigated. The fundamentals of MVC are first reexamined, and then an innovative performance index is given by incorporating the entropy. The feedback control algorithm based on minimum entropy, called MEC (minimum entropy control), is derived. MEC based CPA for the controlled system requires effective and systematic identification of the associated system models based on the closed-loop data. In this work, a new methodology based on the entropy criterion instead of the mean square error criterion is presented to estimate disturbances for the purpose of evaluating the performance of the control systems. To demonstrate the effective MEC based CPA method, both numerical and industrial examples are applied and compared with the MVC based CPA method.

Minimum entropy control for non-linear and non-Gaussian two-input and two-output dynamic stochastic systems

In this study, the problem of control algorithm design for a class of nonlinear two-input and two-output systems with non-Gaussian disturbances is investigated, where a general non-linear auto-regressive moving average with exogenous model is used to describe the system. Based on the deduced probability density functions of tracking errors, a new performance index is established using the entropy and joint entropy so as to characterise the uncertainty of the tracking errors of the closed-loop system. This performance also includes the expectations of tracking errors and the constrains of control energy. A recursive optimisation control algorithm is obtained by minimising the performance index. Moreover, the local stability condition of the closed-loop systems is established after some formulations. Finally, the comparative simulation results are presented to show that the performance of the proposed algorithm is superior to that of proportional–integral–derivative controller.

Controlling chaos in tapping mode atomic force microscopes using improved minimum entropy control

Minimum entropy control technique, an approach for controlling chaos without using the dynamical model of the system, can be improved by being combined with a nature-based optimization technique. In this paper, an ACO-based optimization algorithm is employed to minimize the entropy function of the chaotic system. The feedback gain of a delayed feedback controller is adjusted in the ACO algorithm. The effectiveness of the idea is investigated on suppressing chaos in the tapping-mode atomic force microscope equations. Results show a good performance. The PSO-based version of the minimum entropy control technique is also used to control the chaotic behavior of the AFM, and corresponding results are compared showing almost a same functionality for the two optimization algorithms of PSO and ACO as the minimizing engines of the minimum entropy strategy.

Minimum entropy control of chaos via online particle swarm optimization method

One of the recently developed approaches for control of chaos is the minimum entropy (ME) control technique. In this method an entropy function based on the Shannon definition, is defined for a chaotic system. The control action is designed such that the entropy as a cost function is minimized which results in more regular pattern of motion for the system trajectories. In this paper an online optimization technique using particle swarm optimization (PSO) method is developed to calculate the control action based on ME strategy. The method is examined on some standard chaotic maps with error feedback and delayed feedback forms. Considering the fact that the optimization is online, simulation results show very good effectiveness of the presented technique in controlling chaos.

An ILC-Based Adaptive PI Controller for Two-Link Robot Manipulator: Minimum Entropy Approach

In this paper, a new algorithm for an adaptive proportional-Integrator (PI) controller for nonlinear systems subject to stochastic non-Gaussian disturbance is studied. The minimum entropy control is applied to decrease the closed-loop tracking error under an iterative learning control (ILC) basis. The key issue here is to divide the control horizon into a number of equal time intervals called batches. Within each intervals there are a fixed number of sample points. The design procedure is divided into two main algorithms, within each batch and between any two adjacent batches. However, within each batch the (PI) coefficients are fixed. A sufficient condition has been established to guarantee the stability of the closed-loop system. An illustrated example of two-link is included to demonstrate the use of control algorithm, and satisfactory resultshave been obtained.

Stochastic feedback and its relation to the entropy criterion

In this paper, we generalize the interpretation of the entropy criterion by using stochastic feedback. When a common white Gaussian noise of zero mean and unit variance is applied, the entropy of a transfer function is shown to be equivalent to the maximum variance of the outputs fed back and added to the input through multiplication of a stochastic gain. It turns out that the existing minimum entropy control is useful for minimizing the worst effect of external noises on the outputs when stochastic feedback is applied.

On the fuzzy minimum entropy control to stabilize the unstable fixed points of chaotic maps

This paper presents a fuzzy algorithm for controlling chaos in nonlinear systems via minimum entropy approach. The proposed fuzzy logic algorithm is used to minimize the Shannon entropy of a chaotic dynamics. The fuzzy laws are determined in such a way that the entropy function descends until the chaotic trajectory of the system is replaced by a regular one. The Logistic and the Henon maps as two discrete chaotic systems, and the Duffing equation as a continuous one are used to validate the proposed scheme and show the effectiveness of the control method in chaotic dynamical systems.

Multi-variable control of chaos using PSO-based minimum entropy control

The minimum entropy (ME) control is a chaos control technique which causes chaotic behavior to vanish by stabilizing unstable periodic orbits of the system without using mathematical model of the system. In this technique some controller type, normally delayed feedback controller, with an adjustable parameter such as feedback gain is used. The adjustable parameter is determined such that the entropy of the system is minimized. Proposed in this paper is the PSO-based multi-variable ME control. In this technique two or more control parameters are adjusted concurrently either in a single or in multiple control inputs. Thus it is possible to use two or more feedback terms in the delayed feedback controller and adjust their gains. Also the multi-variable ME control can be used in multi-input systems. The minimizing engine in this technique is the particle swarm optimizer. Using online PSO, the PSO-based multi-variable ME control technique is applied to stabilize the 1-cycle fixed points of the Logistic map, the Hénon map, and the chaotic Duffing system. The results exhibit good effectiveness and performance of this controller.

NONLINEAR/CHAOTIC MODELING AND CONTROL OF COMBUSTION INSTABILITIES

A discrete dynamic model accounting for both combustion and vaporization processes is proposed. In terms of different bifurcation parameters relevant to either combustion or evaporation, various bifurcation diagrams are presented. Furthermore, the corresponding Lyapunov exponent is calculated and employed to analyze the stability of the particular dynamic system. The study indicates conclusively that the evaporation process has a significant impact on the intensity and nonlinear behavior of the system of interest, vis-à-vis a model accounting for only the gaseous combustion process. Moreover, a minimum entropy control method is employed to control the chaotic behavior inherent to the system of interest. This algorithm is intended to be implemented for control of combustion instability numerically and experimentally to provide a basis for some of the control methodologies employed in the literature.

Minimum entropy control for a class of macro-micro robot based on ILC frame

A new scheme to minimise the closed loop randomness for a kind of intelligent welding robot system is presented. It is assumed that the system is subjected from bounded random disturbances. The parameters of controller have been optimised according to a minimum entropy index function by using minimum entropy control method based on an iterative learning frame. As the entropy is the measure of randomness for random variable, the control method advantages to reduce the uncertainty of the closed loop system, which help to obtain a better performance. The iterative learning frame about minimum entropy control has been proposed and is used to optimal the controller parameters. In addition, the convergence of the control algorithm has been analysed. Finally, the effectiveness and feasibility of the proposed control schemes are verified by using an experimental robot.

Minimum entropy based run-to-run control for semiconductor processes with uncertain metrology delay

A novel run-to-run control methodology for semiconductor processes with uncertain metrology delay which is developed by combining the minimum error entropy and the optimal control strategy is presented. In most semiconductor processes, the product quality data from the previous run are not often available before the start of the next run. Thus, the corrective step is often delayed by one batch or more, and the duration of the delay is uncertain with stochastic characteristics. Coupled with inaccurate process models, the delay may lead to significant variations of the process outputs even with the use of exponentially weighted moving average (EWMA) controllers. This paper proposes a new method of handling the uncertain metrology delay from a probability viewpoint. The fundamentals of the run-to-run control systems are first reexamined, and then an innovative performance index is given by incorporating the entropy (or information potential) and the mean value of tracking error with constraints on control input energy. The probability density function (PDF) based optimal control algorithm is proposed for processes where the disturbance and delay are non-Gaussian and the stability of the algorithm is analyzed. In addition, the methodology of the proposed control strategy is extended to include recursive PDF estimation and on-line real time implementation. The paper also includes a simulation example of minimum entropy control of a tungsten chemical-vapor deposition process to illustrate the methodology. Furthermore, comparisons between the conventional EWMA method and the proposed method are done to show the advantages of our newly proposed method.