Identification of Wiener–Hammerstein benchmark model via rank minimization

In this paper, a Wiener–Hammerstein system identification problem is formulated as a semidefinite programming (SDP) problem which provides a sub-optimal solution for a rank minimization problem. In the proposed identification method, the first linear dynamic system, the static nonlinear function, and the second linear dynamic system are parameterized as an FIR model, a polynomial function, and a rational transfer function respectively. Subsequently the optimization problem is formulated by using the over-parameterization technique and an iterative approach is proposed to update two unmeasurable intermediate signals. For the modeling of static nonlinearity, the monotonically non-deceasing condition was applied to limit the number of possible selections for intermediate signals. At each step of iteration, the over-parametrized parameters are estimated and then system parameters are separated by using a singular value decomposition (SVD). The proposed method is applied to the benchmark problem and the estimation result shows the effectiveness of the proposed algorithm.     

Fast extremum-seeking for Wiener–Hammerstein plants

This paper considers an observer-based extremum-seeking (ES) scheme acting on a Wiener–Hammerstein (WH) plant. The ES scheme utilises a high-frequency sinusoidal dither in order to achieve fast minimisation of the plant’s static nonlinearity. Unlike the prevailing analyses of “fast” ES schemes acting on WH plants, the presented result is semi-global and applicable to plants with fairly general, unknown nonlinearities. Design of the ES scheme requires knowledge of the relative orders of both the input and output dynamics of the plant. Two different tunings of the ES parameters are considered: one which forces the ES dynamics to be fast, and one which is less restrictive. It is shown that approximate knowledge of the phase of the plant’s input dynamics is required if the ES scheme is to use the less restrictive tuning. For both tunings, it is shown how the ES scheme may be designed in order to simultaneously achieve arbitrarily fast and accurate minimisation of the static nonlinearity from an arbitrarily large set of initial conditions. Moreover, the result shows that a WH plant with unstable input dynamics can, in fact, be stabilised by the ES scheme.     

Discrete-time extremum-seeking for Wiener–Hammerstein plants

This paper presents a new formulation of extremum-seeking control for discrete-time Wiener–Hammerstein plants. A novel method of analysis using Linear Parameter-Varying (LPV) system theory demonstrates semi-global stability of the control scheme. Assuming only limited plant knowledge, the stability result ensures convergence of the plant output in steady state to a point in an arbitrarily small neighbourhood of the extremum, for appropriately chosen controller parameters. The behaviour of the control scheme is analysed on a simple simulated system, prior to being implemented on an internal combustion engine. Experiments demonstrate how the scheme is able to maximise engine output torque in the presence of an uncertain fuel composition by modifying the spark timing.     

Recursive identification for multi-input–multi-output Hammerstein–Wiener system

In this paper, an identification method based on the recursive auxiliary variable least squares algorithm is proposed for a multi-input–multi-output Hammerstein–Wiener system with process noise. In the proposed identification method, the system is converted into the multivariate regression form under the condition that the nonlinear block in the output part is invertible. Then, the auxiliary variable is constructed, the parameters of the regression equations are identified, and the system parameter matrices can be obtained by matrix composition of the parameter product matrix. A theoretical analysis showed that the proposed method has uniform convergence when the process noise is white and has a finite variance. The effectiveness of the proposed method is validated through the experiments.     

A quantum Jensen–Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen–Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen–Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) 27 and 28 to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen–Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen–Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.     

Adaptive control of Hammerstein–Wiener nonlinear systems

The Hammerstein–Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein–Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.     

On human–machine relations

Cognition, Technology & Work - This paper presents an approach to human–machine interactions based on the concept of teamwork and the psychological theory of object relations. We envision...     

Joint input–output identification of unstable systems with kernel regularization

This paper discusses closed-loop identification of unstable systems. In particular, we first apply the joint input–output identification method and then convert the identification problem of unstable systems into that of stable systems, which can be tackled by using kernel-based regularization methods.We propose to identify two transfer functions by kernel regularization, the one from the reference signal to the input, and the one from the reference signal to the output. Since these transfer functions are stable, kernel regularization methods can construct their accurate models. Then the model of unstable system is constructed by ratio of these functions. The effectiveness of the proposed method is demonstrated by a numerical example and a practical experiment with a DC motor.     

Nonlinear process monitoring based on kernel global–local preserving projections

A new nonlinear dimensionality reduction method called kernel global–local preserving projections (KGLPP) is developed and applied for fault detection. KGLPP has the advantage of preserving global and local data structures simultaneously. The kernel principal component analysis (KPCA), which only preserves the global Euclidean structure of data, and the kernel locality preserving projections (KLPP), which only preserves the local neighborhood structure of data, are unified in the KGLPP framework. KPCA and KLPP can be easily derived from KGLPP by choosing some particular values of parameters. As a result, KGLPP is more powerful than KPCA and KLPP in capturing useful data characteristics. A KGLPP-based monitoring method is proposed for nonlinear processes. T² and SPE statistics are constructed in the feature space for fault detection. Case studies in a nonlinear system and in the Tennessee Eastman process demonstrate that the KGLPP-based method significantly outperforms KPCA, KLPP and GLPP-based methods, in terms of higher fault detection rates and better fault sensitivity.     

Wiener–Hammerstein system identification – an evolutionary approach

The problem of identifying parametric Wiener–Hammerstein (WH) systems is addressed within the evolutionary optimisation context. Specifically, a hybrid culture identification method is developed that involves model structure adaptation using genetic recombination and model parameter learning using particle swarm optimisation. The method enjoys three interesting features: (1) the risk of premature convergence of model parameter estimates to local optima is significantly reduced, due to the constantly maintained diversity of model candidates; (2) no prior knowledge is needed except for upper bounds on the system structure indices; (3) the method is fully autonomous as no interaction is needed with the user during the optimum search process. The performances of the proposed method will be illustrated and compared to alternative methods using a well-established WH benchmark.     

A fractional approach to identify Wiener–Hammerstein systems

Block-oriented nonlinear models are appealing due to their simplicity and parsimony. Existing methods to identify the Wiener–Hammerstein model suffer from one or several drawbacks. This paper shows that it is possible to generate initial estimates in an alternative way. A fractional model parameterization is the key to the success of this approach. Advantages are that no more than two iterative optimizations are needed and that large model orders can be handled. As illustrated through a simulation example and experimental benchmark data, it gives superior initial estimates and comparable optimized results.     

A subspace-based identification of Wiener–Hammerstein benchmark model

This paper develops a subspace-based method of identifying the Wiener–Hammerstein system, where a nonlinearity is sandwiched by two linear subsystems. First, a state space model of the best linear approximation of it is identified by using a subspace identification method and the poles of the best linear model are allocated between two linear subsystems by a state transformation. Unknown system parameters and coefficients of a basis function expansion of the nonlinearity are estimated by using the separable least-squares for all possible allocations of poles, so that there is a possibility that many iterative minimization problems should be solved. Finally, the best Wiener–Hammerstein system that yields the minimum mean square error is selected. Numerical results for a benchmark model show the applicability of the proposed method.     

On random 2–3 trees

Summary It is shown that ¯n (N), the average number of nodes in an N-key random 2–3 tree, satisfies the inequality 0.70 N < ¯n(N) <0.79 N for large N. A similar analysis is done for general B-trees. It is shown that storage utilization is essentially ln 269% for B-tree of high orders.This work was done while the author was at University of Illinois, partially supported by NSF Grant GJ 41538. The preparation of this paper has also been partially supported by NSF Grants MCS 72-06336 A04 and MCS 72-03752 A03     

Generalised Hammerstein–Wiener system estimation and a benchmark application

This paper examines the use of a so-called “generalised Hammerstein–Wiener” model structure that is formed as the concatenation of an arbitrary number of Hammerstein systems. The latter are taken here to be memoryless non-linearities followed by linear time invariant dynamics. Hammerstein, Wiener, Hammerstein–Wiener and Wiener–Hammerstein models are all special cases of this structure. The parameter estimation of this model is investigated using a standard prediction error criterion coupled with a robust gradient based search algorithm. This approach is profiled using a Wiener–Hammerstein Benchmark example, which illustrates it to be effective and, via Monte-Carlo simulation, relatively robust against capture in local minima.     

Parlay-based service engineering in a converged Internet–PSTN environment

This paper examines current approaches to signalling and service interworking between Internet and public switched telephone network (PSTN). It notes that until now convergence between the two networks has for the most part taken place in the transport and signalling layers. Signalling interworking architectures cater for the specific class of telephony-like services and although they can accommodate the extension of the intelligent network's (IN) realm of control in the Internet, they do not provide a generic platform for service interworking. Through the adoption of the Parlay APIs, a way is foreseen for (a) consolidation of telephone service over both Internet and PSTN through the imposition of a uniform call control API while allowing the installed IN infrastructure to be used also for Internet telephony services and (b) for service interworking between telephony-like services and open distributed services in the Internet. The paper proposes a service architecture that can be used as a platform for Parlay-based service interworking while offsetting some drawbacks that the Parlay approach incurs.     

A comprehensive Lagrangian flame–kernel model to predict ignition in SI engines

A Lagrangian model to predict the first stages of the combustion process in SI engines, when the size of flame kernel is small compared with the mesh size, and flame development is influenced by heat transfer from the spark, local flow, turbulence and air/fuel mixture distribution is presented. The spark channel is initially represented by a set of Lagrangian particles that are convected by the mean flow. Flame kernels are launched locally for all the particles satisfying an ignition criterion based on the local Karlovitz number. For each of them, equations of energy and mass are solved accounting for electrical power transferred from the electrical circuit, local turbulence and flame speed. The proposed model has been validated with experimental data provided by Herweg et al.; a computational mesh reproducing the geometrical details of the optical, pre-chamber SI engine was built, including the electrodes. Initially, cold-flow simulations were carried out to verify the validity of the computed flow-field and turbulent distribution at ignition time. Then, the combustion process was simulated accounting for the effects of different engine speeds, air/fuel ratio and spark-plug position. Encouraging results were achieved for a wide range of operating conditions.     

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions in which the constraint initial condition is satisfied, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation form in the Hilbert space \( W_{2}^{2} \left( \varOmega \right) \oplus W_{2}^{2} \left( \varOmega \right) \). Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations.

     

On Nesterov's smooth Chebyshev–Rosenbrock function

We discuss a modification of the chained Rosenbrock function introduced by Nesterov. This function r _N is a polynomial of degree 4 defined for x∈? ⁿ . Its only stationary point is the global minimizer x*=(1, 1, …, 1)^T with optimal value zero. A point x ⁽⁰⁾ in the box B:=<texlscub>x |?1≤x _i ≤1 for 1≤i≤n</texlscub>with r _N (x ⁽⁰⁾)=1 is given such that there is a continuous piecewise linear descent path within B that starts at x ⁽⁰⁾ and leads to x*. It is shown that any continuous piecewise linear descent path starting at x ⁽⁰⁾ consists of at least an exponential number of 0.72·1.618 ⁿ linear segments before reducing the value of r _N to 0.25. Moreover, there exists a uniform bound, independent of n, on the Lipschitz constant for the second derivative of r _N within B.