Simple linear profiles monitoring in the presence of within profile autocorrelation

Quality of some processes or products can be characterized effectively by a function referred to as profile. Many studies have been done by researchers on the monitoring of simple linear profiles when the observations within each profile are uncorrelated. However, due to spatial autocorrelation or time collapse, this assumption is violated and leads to poor performance of the proposed control charts. In this paper, we consider a simple linear profile and assume that there is a first order autoregressive model between observations in each profile. Here, we specifically focus on phase II monitoring of simple linear regression. The effect of autocorrelation within the profiles is investigated on the estimate of regression parameters as well as the performance of control charts when the autocorrelation is overlooked. In addition, as a remedial measure, transformation of Y-values is used to eliminate the effect of autocorrelation. Four methods are discussed to monitor simple linear profiles and their performances are evaluated using average run length criterion. Finally, a case study in agriculture field is investigated.     

Phase II monitoring of multivariate simple linear profiles

In some quality control applications, quality of a product or process can be characterized by a relationship between two or more variables that is typically referred to as profile. Moreover, in some situations, there are several correlated quality characteristics, which can be modeled as a set of linear functions of one explanatory variable. We refer to this as multivariate simple linear profiles structure. In this paper, we propose the use of three control chart schemes for Phase II monitoring of multivariate simple linear profiles. The statistical performance of the proposed methods is evaluated in term of average run length criterion and reveals that the control chart schemes are effective in detecting shifts in the process parameters. In addition, the applicability of the proposed methods is illustrated using a real case of calibration application.     

Completion-of-squares: Revisited and extended

Due to its simplicity, the completion-of-squares technique is quite popular in linear optimal control. However, this simple technique is limited to linear quadratic Gaussian systems. In this note, by interpreting the completion-of-squares from a new angle, we extend this technique to performance optimization of general Markov systems with the long run average criterion, leading to a new approach to performance optimization based on direct comparisons of the performance of two policies.     

The explicit linear quadratic regulator for constrained systems

For discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton-Jacobi-Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.     

A group theoretic approach to construct cryptographically strong substitution boxes

In this paper, we present a method to construct a substitution box used in encryption applications. The proposed algorithm for the construction of substitution box relies on the linear fractional transform method. The design methodology is simple, while the confusion-creating ability of the new substitution box is complex. The strength of the proposed substitution box is evaluated, and an insight is provided to quantify the confusion-creating ability. In addition, tests are performed to assess the vulnerability of the encrypted data to algebraic and statistical attacks. The substitution box is critically analyzed by strict avalanche criterion, bit independent criterion, differential approximation probability test, linear approximation probability test, non-linearity test, and majority logic criterion. The performance of the proposed substitution box is also compared with those of some of the well-known counterparts including AES, APA, Gray, S₈, Skipjack, Xyi, and prime of residue substitution boxes. It is apparent that the performance, in terms of confusion-creating ability, of the new substitution box is better than those of some of the existing non-linear components used in encryption systems. The majority logic criterion is applied to these substitution boxes to further evaluate the strength and usefulness.     

A performance criterion for the depth estimation with application to robot visual servo control

This article deals with the depth observability problem of a robot visual system with a moving camera. In the visual system, the unknown depth of a feature point is estimated from the input of the camera velocity and the output of the image of the feature point. Although it is well known that the linear velocity of the camera must satisfy some constraints for successful depth estimation, this proposes a criterion to measure the performance of the depth estimation, which is a heuristic extension from an estimation result of a linear system. This performance criterion depends on both the image position and the linear velocity of the camera. Some simulation and experiment examples demonstrate and verify the proposed performance criterion. Furthermore, this criterion is used to develop a new visual servo control scheme that has good performance in both the depth estimation and the visual control. This control scheme is also verified by a simulation example. © 2001 John Wiley & Sons, Inc.     

Breast cancer diagnosis using genetic programming generated feature

This paper proposes a novel method for breast cancer diagnosis using the feature generated by genetic programming (GP). We developed a new feature extraction measure (modified Fisher linear discriminant analysis (MFLDA)) to overcome the limitation of Fisher criterion. GP as an evolutionary mechanism provides a training structure to generate features. A modified Fisher criterion is developed to help GP optimize features that allow pattern vectors belonging to different categories to distribute compactly and disjoint regions. First, the MFLDA is experimentally compared with some classical feature extraction methods (principal component analysis, Fisher linear discriminant analysis, alternative Fisher linear discriminant analysis). Second, the feature generated by GP based on the modified Fisher criterion is compared with the features generated by GP using Fisher criterion and an alternative Fisher criterion in terms of the classification performance. The classification is carried out by a simple classifier (minimum distance classifier). Finally, the same feature generated by GP is compared with a original feature set as the inputs to multi-layer perceptrons and support vector machine. Results demonstrate the capability of this method to transform information from high-dimensional feature space into one-dimensional space and automatically discover the relationship among data, to improve classification accuracy.     

A stability criterion for asynchronous multirate linear systems

A stability criterion is developed for linear, asynchronous multirate sampled-data systems. Such systems typically include a linear, time variant, continuous-time plant and several unsynchronized digital controllers. The analysis method uses a time-domain approach based on the closed-loop state transition matrix. The result is sufficient stability criterion which gives an objective measure of long-term and short-term stability. A simple example illustrates the method     

Superposition in efficient robust constrained predictive control

A stabilizing control method, which does not require on-line optimizations, is developed for linear systems with polytopic model uncertainties and hard input constraints. This work is motivated by the constrained robust MPC (CRMPC) approach (IEEE Trans. Automat. Control 45 (2000a) 1765) which adopts the dual mode prediction strategy (i.e. free control moves and invariant set) and minimizes a worst case performance criterion. Based on the observation that, a feasible control sequence for a particular state can be found as a linear combination of feasible sequences for other states, we suggest a stabilizing control algorithm providing sub-optimal and feasible control sequences using pre-computed optimal sequences for some canonical states. The on-line computation of the proposed method reduces to simple matrix multiplication.     

A nonlinear control law for a stochastic infinite time problem

The expectation of a particular class of nonquadratic performance criterion involving even powers of the state variables up to sixth order is minimized, over an infinite horizon, subject to a linear stochastic system. The process noise is composed of both additive white noise and state dependent white noise processes. The resulting controller is composed of a linear and cubic function of the state. Furthermore, this controller depends upon the noise variances of both the additive and state dependent noise processes. For partially observable systems with no state dependent noise, similar results as the completely observable system are implied by the separation theorem. For state dependent noise alone, a stochastic Lyapunov function is obtained from which simple probability bounds for the trajectory to exit from a given region of the state space are determined.     

基于准则的KMSE分类模型的改造

在再生核理论基础之上,可认为KMSE模型对应的特征空间的鉴别向量可以表示为部分训练样本的线性组合。可据此对一般的KMSE方法(GKMSE)通过某些手段加以改进。文章的准则被首次提出并应用于KMSE的改造,据此提出的改进的KMSE方法在很大程度上提高了KMSE模型的分类效率,同时实验结果也证明了该算法具有比较好的分类效果。     

Minimax control of a process in a linear uncertain-stochastic system with incomplete data

Consideration is given to the control problem in a linear stochastic differential system where constant noise intensities in equations of state and observation are prescribed only accurate within the membership of some known sets. For control optimization, an integral root-mean-square performance criterion is used. The problem is solved by the transition to a dual one, which makes it possible to prove the existence of a saddle point of the criterion and obtain an explicit expression for the minimax control operator as functions of the solution to the dual problem. To solve the latter, an iteration algorithm is proposed; the convergence of the algorithm is proved and investigated by a model example.     

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified L ²-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to linear matrix inequality conditions.     

Design of piecewise-linear switching functions for relay control systems

The design of piecewise-linear switching functions is investigated for linear, constant, lumped systems with a single ideal relay controller with respect to a transient response (minimum-time) performance criterion. A design method is presented which consists of a series of steps leading finally to the optimization of parameters by a gradient or other search technique suitable for computer implementation. The preliminary steps are devoted to reducing the dimensionality of the parameter space which must be searched, defining the criterion function so as to yield a surface which is reasonably smooth and free of relative minima, and insuring that the search is started with a feasible parameter set. It is concluded that easily implemented piecewise-linear switching functions can be designed so as to yield improved performance, both in terms of settling times and region of stability in the state space, over that attainable with linear switching functions. The complexities of the performance surface are such, however, that it is felt that frequently the determination of a switching function by the heuristic guides described, constitutes an adequate design without the refinement of parameter optimization.     

Effectiveness and limitation of circle criterion for LTI robust control systems with control input nonlinearities of sector type

This paper considers linear time invariant systems with sector type nonlinearities and proposes regional ??₂ performance analysis and synthesis methods based on the circle criterion. In particular, we consider the effect of non‐zero initial states and/or an ??₂ disturbance inputs on the ??₂ norm of a selected performance output. We show that both analysis and synthesis problems can be recast as linear matrix inequality (LMI) optimization problems, where, for synthesis, the outputs of the nonlinear elements are assumed available for control. Moreover, it is shown when the circle criterion does or does not help to improve the performance bound in robust control synthesis when compared with the existing linear analysis method. Copyright © 2005 John Wiley & Sons, Ltd.     

A dual optimization procedure for linear quadratic robust control problems

This paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system. The model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional. This problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found. Although the direct solution of this problem will be discussed briefly, the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available.     

Robust adaptive motion/force tracking control design for uncertain constrained robot manipulators

In the presence of uncertain constraint and robot model, an adaptive controller with robust motion/force tracking performance for constrained robot manipulators is proposed. First, robust motion and force tracking is considered, where a performance criterion containing disturbance and estimated parameter attenuations is presented. Then the proposed controller utilizes an adaptive scheme and an auxiliary control law to deal with the uncertain environmental constraint, disturbances, and robotic modeling uncertainties. After solving a simple linear matrix inequality for gain conditions, the effect from disturbance and estimated parameter errors to motion/force errors is attenuated to an arbitrary prescribed level. Moreover, if the disturbance and estimated parameter errors are square-integrable, then an asymptotic motion tracking is achieved while the force error is as small as the inversion of control gain. Finally, numerical simulation results for a constrained planar robot illustrate the expected performance.     

Linear programming and model predictive control

The practicality of model predictive control (MPC) is partially limited by the ability to solve optimization problems in real time. This requirement limits the viability of MPC as a control strategy for large scale processes. One strategy for improving the computational performance is to formulate MPC using a linear program. While the linear programming formulation seems appealing from a numerical standpoint, the controller does not necessarily yield good closed-loop performance. In this work, we explore MPC with an l₁ performance criterion. We demonstrate how the non-smoothness of the objective function may yield either dead-beat or idle control performance.     

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

The H∞ filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H∞ attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality (LMI) representation of H∞ performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a suficient condition for the exi...     

MLP Based Linear Fea ure Ex rac ion for Nonlinearly Separable Data

A novel approach to linear feature extraction is presented. Most supervised feature extraction algorithms use mean square error or other measures based on the difference between expected and actual output values as a performance criterion. The novel approach presented here uses data visualisation together with an empirical classification error (percentage of cases classified incorrectly) as performance criterion. To find the optimal data transformation weights, the Multilayer Perceptron cost function with a special regularisation term is applied. The technique proposed is verified and compared with five competing mapping techniques with respect to visualisation and different classification error criteria. For comparison, two artificial and 12 real world data sets are used.