Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

An efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10³⁰⁰, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.     

Improvement of the contraction‐type LP test algorithm for finding all solutions of piecewise‐linear resistive circuits

In this letter, an effective technique is proposed for improving the computational efficiency of the contraction‐type LP test algorithm, which is an algorithm for finding all solutions of piecewise‐linear resistive circuits. Using the proposed technique, all solutions of a large‐scale problem, where the number of variables is 100 and the number of linear regions is 10¹⁰⁰, could be found in less than 10 min using a 360 MHz computer. Copyright 2001 John Wiley & Sons, Ltd.     

An efficient algorithm for finding all DC solutions of piecewise‐linear circuits

An efficient algorithm is proposed for finding all DC solutions of transistor circuits where characteristics of transistors are represented by piecewise‐linear (PWL) convex monotone functions. This algorithm is based on a simple test (termed the linear programming, LP, test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem by surrounding component PWL functions by rectangles. Then the dual simplex method is applied, by which the number of pivotings per region becomes very small. In this letter, we propose a new LP test using the dual simplex method and triangles. The proposed test is not only efficient but also more powerful than the conventional test using the simplex method or rectangles. Copyright © 2008 John Wiley & Sons, Ltd.     

Bilinear models in adaptive control

A key issue, which is addressed in the paper, is the development of an efficient adaptive control algorithm for disturbed, non‐linear objects. A generalized non‐linear model of the controlled plant is proposed. Model of disturbances is assumed to be a bilinear time‐series model. Minimum‐variance control of non‐linear systems with bilinear model of disturbances is considered. For a generalized system model simple, weighed and generalized adaptive control algorithms are proposed. A comparison of different non‐linear adaptive control algorithms is performed. Copyright © 2000 John Wiley & Sons, Ltd.     

A combined approach for the identification of continuous non‐linear systems

The identification of a non‐linear continuous output‐only system from a time series is considered for the case that the functional form of the model is not known beforehand. To estimate both functions and parameters, a combination of non‐parametric modelling based on non‐linear regression and parametric modelling based on a multiple shooting algorithm is proposed. This strategy to determine non‐linear differential equations is exemplified on experimental data from a chaotic circuit where an accurate reconstruction of the observed attractor is obtained. Copyright © 2003 John Wiley & Sons, Ltd.     

On simplex‐based piecewise‐linear approximations of non‐linear mappings

Simplex‐based piecewise‐linear (PWL) approximations of non‐linear mappings are needed when the robust PWL analysis is used to directly solve non‐linear equations. This paper proposes a straightforward technique for transforming the well‐known approximations into another form. This new form is computationally more efficient, since it preserves the sparse structure of the original Jacobian matrix. Furthermore, this new form of PWL approximation explicitly relates the simplex‐based PWL analysis to the conventional formulation of the Katzenelson algorithm. The proposed transform technique is also extended to treat groupwise‐separable mappings and, finally, non‐separable but sparse mappings that arise in real‐life simulation of large electronic circuits. In this paper, all these (transformed) simplex‐based PWL approximations are compared in terms of their generality and efficiency. The computational efficiency of the PWL approximation that utilizes sparsity is validated with realistic simulations. Copyright © 2005 John Wiley & Sons, Ltd.     

A hybrid TLM‐FDTD method for the modelling of diffusion

A new hybrid TLM‐FDTD algorithm for solving diffusion problems is described. The method utilizes the transmission line model to define the time step and the FDTD's leap‐frog algorithm to determine the voltages and currents of the network analogue of the diffusion equation. Unlike the standard TLM method, the proposed one does not generate spurious oscillations. The method is explicit and can be used to solve highly non‐linear problems without the need to solve non‐linear equations. The implementation of a simple adaptive time‐stepping algorithm is also described. Copyright © 2000 John Wiley & Sons, Ltd.     

A new adaptive backstepping control algorithm for motion control systems — an implicit and symbolic computation approach

A new adaptive integral backstepping control algorithm for motion control systems is proposed. The design approach is non‐conventional in that it only implicitly incorporates error states into a design Lyapunov function and computes time derivative of the Lyapunov function symbolically to the point of getting parameter estimate update laws on which desirable structures are imposed. The closed‐loop error system turns out to be linear and time‐varying and can be reformulated as a linear–non‐linear cascade system. Uniform exponential stability or absolute stability can be achieved. The design is robust against system parameter variations. The effectiveness and robustness of the control algorithm are verified by numerical examples. Copyright © 2002 John Wiley & Sons, Ltd.     

A new decoupling design of self‐tuning multivariable generalized predictive control

A novel robust decoupling method with multivariable generalized predictive control (MGPC) for a class of nonlinear systems is presented in an adaptive version. The cross‐coupling action and the non‐linear actors of the system are identified on‐line by a neural network. A feedforward compensation based on generalized predictive control, is proposed for decoupling control. A modified recursive least‐squares (RLS) algorithm can be used to estimate the linear parameters for time‐varying systems. Simulations are carried out and the results show the effectiveness of the proposed algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Performance evaluation of the LP test algorithm for finding all solutions of piecewise‐linear resistive circuits

In this letter, the performance of the LP test algorithm, which is an algorithm for finding all solutions of piecewise‐linear resistive circuits, is evaluated by numerical experiments. It is shown that the algorithm could find all solutions of large‐scale problems (including those where the number of variables is 200–300 and the number of linear regions is 10²⁰⁰–10³⁰⁰) in practical computation time. Copyright © 2000 John Wiley & Sons, Ltd.     

Non‐linear analog circuit fault diagnosis with large change sensitivity

Large change sensitivity has been proved efficient at, but restricted to, generating a linear circuit fault dictionary. This paper discusses the extension of large change sensitivity to non‐linear analog circuit fault diagnosis. The fault dictionary is divided into d.c. and a.c. sections. In the d.c. domain, non‐linear components are approximated with piecewise linear models. By relating the operating region of each piecewise linear model to the magnitude of a single fault in a procedure termed preconditioning, it is shown that large change sensitivity can efficiently compute the response of a faulty non‐linear circuit. Results presented of an analysis of computational complexity show a significant reduction in the cost of simulating single linear resistor faults in a non‐linear circuit using this method. In addition, after establishing that the resistive portion of the circuit is fault free, a fault dictionary is constructed for dynamic components using large change sensitivity in the small signal a.c. domain. Included with a discussion on the issues of large change sensitivity based simulation‐before‐test, a small non‐linear circuit is used to demonstrate the effectiveness of the proposed fault diagnosis algorithm. Copyright © 2000 John Wiley & Sons, Ltd.     

Hammerstein system identification by the Haar multiresolution approximation

The paper deals with recovering non‐linearities in the Hammerstein systems using the multiresolution approximation—a basic concept of wavelet theory. The systems are driven by random signals and are disturbed by additive, white or coloured, random noise. The a priori information about system components is non‐parametric and a delay in the dynamical part of systems is admitted. A non‐parametric identification algorithm for estimating non‐linear characteristics of static parts is proposed and investigated. The algorithm is based on the Haar multiresolution approximation. The pointwise convergence and the pointwise asymptotic rate of convergence of the algorithm are established. It is shown that neither the form nor the convergence conditions of the algorithm need any modification if the noise is not white but correlated. Also the asymptotic rate of convergence is the same for white and coloured noise. The theoretical results are confirmed by computer simulations. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptive estimation and rejection of unknown sinusoidal disturbances through measurement feedback for a class of non‐minimum phase non‐linear MIMO systems

This paper develops an adaptive estimation method to estimate unknown disturbances in a class of non‐minimum phase non‐linear MIMO systems. The unknown disturbances are generated by an unknown linear exosystem. The frequencies, phases and amplitudes of the disturbances are unknown, the only available information of the disturbances is the number of distinctive frequencies. The system considered in this paper is a class of MIMO non‐linear systems in the output feedback form which can be non‐minimum phase. The proposed estimation algorithm provides exponentially convergent estimates of system states, unknown disturbances in the system and frequencies of the disturbances characterized by the eigenvalues of the exosystem. Moreover, based on the stabilization controller for the disturbance free system, the estimates of the disturbances are used to solve the disturbance rejection problem. The unknown disturbances are compensated completely with the stability of the whole closed‐loop system. Copyright © 2006 John Wiley & Sons, Ltd.     

Direct adaptive control for non‐linear uncertain systems with exogenous disturbances

A direct adaptive non‐linear control framework for multivariable non‐linear uncertain systems with exogenous bounded disturbances is developed. The adaptive non‐linear controller addresses adaptive stabilization, disturbance rejection and adaptive tracking. The proposed framework is Lyapunov‐based and guarantees partial asymptotic stability of the closed‐loop system; that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant. In the case of bounded energy L₂ disturbances the proposed approach guarantees a non‐expansivity constraint on the closed‐loop input–output map. Finally, several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

Self‐tuning control for polynomial systems using a receding horizon observer and control strategy

A receding horizon observer and control scheme is introduced for non‐linear systems described by polynomial maps. This control scheme has a natural interpretation as a two‐stage adaptive or self‐tuning control algorithm. The non‐linear feedback that results is defined only on the basis of past input and output measurements. The computational complexity aspects of this approach to adaptive or self‐tuning control are briefly discussed. A linear system and a Hénon map example are used to illustrate the ideas. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive control of non‐linear systems with unknown virtual control coefficients

This paper deals with state feedback adaptive control of parametric‐strict‐feedback (triangular) non‐linear systems with unknown virtual control coefficients. A priori knowledge of the signs of the virtual coefficients is not required, and control signals and adaptive laws are smooth. Asymptotic tracking of smooth reference signals is achieved while all the variables remain bounded. The proposed algorithms make use of backstepping and tuning functions, and enlarge the class of non‐linear systems with unknown parameters for which asymptotic output tracking can be achieved. Copyright © 2000 John Wiley & Sons, Ltd.     

A new adaptive multi‐bias S‐parameter measurement algorithm for transistor characterization

A new adaptive measurement algorithm is described for the control of an automated S‐parameter measurement set‐up used to characterize transistors for non‐linear modelling. The procedure differs from previous algorithms in that is uses both the device DC‐ and S‐parameter data to identify DC bias regions where the device characteristics are changing rapidly. By placing more bias points in these areas and less data points in regions where the device response stays constant, the non‐linear behaviour of the device can be characterized more accurately while keeping the total volume of the experimental data and hence the measurement time to an acceptable level. Experimental results are presented that illustrates the operation of the adaptive algorithm as well as the influence that the selection procedure has on non‐linear modelling results. Copyright © 2005 John Wiley & Sons, Ltd.     

On the terminal region of model predictive control for non‐linear systems with input/state constraints

This paper addresses the terminal region of model‐based predictive control (MPC) for non‐linear systems with control input and state constraints. Based on a stability condition of non‐linear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilizing control law to enlarge the terminal region and thus the domain of attraction of the non‐linear MPC is proposed. An LMI based optimization approach is developed to choose the terminal weighting item and fictitious terminal stabilizing control law so as to enlarge the terminal region of the non‐linear MPC method. The proposed method is illustrated by a numerical example and compares favourably with existing results. Copyright © 2003 John Wiley & Sons, Ltd.     

Finite‐model adaptive control using an LS‐like algorithm

Adaptive control problem of a class of discrete‐time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)‐like algorithm to design the feedback control law. For the finite‐model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed‐loop system is proved under a so‐called linear growth assumption, which is shown to be necessary in general by a counter‐example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non‐parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd.     

New self‐normalized blind source separation networks for instantaneous and convolutive mixtures

The main blind source separation networks proposed in this paper apply to convolutive mixtures (including instantaneous ones). They have a recurrent or direct structure and they may use channel‐specific separating functions. They are based on a self‐normalized weight adaptation rule, which adaptively estimates the average powers of non‐linear functions of the network outputs. This allows us to control several aspects of the operation of these networks, especially their convergence speed/accuracy trade‐off. It also makes them more robust with respect to non‐stationary situations. We analyse their convergence properties. We validate all these results by means of experimental tests performed with these networks, classical ones, and additionally proposed linear instantaneous direct networks based on a normalization of their outputs. These tests especially show that the proposed networks improve the convergence trade‐off and that only these networks apply to highly mixed non‐stationary sources. Copyright © 2002 John Wiley & Sons, Ltd.