Response to comment on ‘Persistent inputs and the standard H2 multivariable control problem’ by K. Park and J.J. Bongiorno Jr

Layered networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. A state space model of the plant is obtained to define the zero dynamics, which are assumed to be stable. A linearizing feedback control is derived in terms of some unknown nonlinear functions. To identify these functions, it is assumed that they can be modelled by layered neural networks. The weights of the networks are updated and used to generate the control. A local convergence result is given. Computer simulations verify the theoretical result.     

Comment on ‘H∞robust controller for self-tuning control applications’

Grimble and Fairbairn's recently published results on H^∞ robust self-tuning control are discussed. It is pointed out that further explanation about the system model is needed, and the identified system model should be revised. Grimble (1987 a, b) and Fairbairn and Grimble (1990) give a new approach to designing self-tuning controllers for SISO discrete-time stochastic systems. There are some points that call for further discussion.     

Comment on ‘ Model reduction by minimizing the weighted equation error ’

A method for the control of time delay systems is presented. The systems are represented by moving models established by the use of block pulse functions. This approach permits the linear feedback control law to be applied to non-linear systems. The moving model representation and the optimal feedback control of time delay systems are presented to demonstrate that the method exhibits satisfactory results.     

Comment on ‘ Some Recent Experiments on Learning and their Training Implications’

This study describes the relation between types and frequency of exercises and cardiopulmonary fitness. Of the 255 subjects studied, 69 (27·1%) were non-exercisers, 66 (25·9%) exercised 1 to 2 times/week, 82 (32·1%) exercised 3 to 4 times/week and 38 (14·9%) exercised 5 to 7 times/week. Of the exercisers, 131 (51·3%) subjects were engaged in aerobic exercises and 55 (21·7%) in non-aerobic activities for at least 6 months prior to this study. The 2·4–km run test and the maximum oxygen consumption (V˙O₂ max) determination were used as indicators of aerobic performance or cardiopulmonary fitness. The V˙O₂ max was measured by direct analyses of the expired gases of subjects using a Beckman Metabolic Cart during an all-out run on a treadmill. Regular exercisers who exercised three or more times/week were aerobically fitter than non-exercisers (p< 0·001) and those who exercised less frequently than three times/week (p<0·001). Subjects involved in aerobic exercises had significantly shorter mean 2·4-km run times (p< 0·001) and higher mean V˙O₂ max values (p< 0·001) when compared with non-exercisers or those engaged in non-aerobic activities.     

Comment on ‘Projection-based identification algorithm for grey-box continuous-time models’ by Ichiro Maruta and Toshiharu Sugie

Although the paper by Maruta and Sugie (2013) makes an interesting contribution to the literature on the estimation of parameters in grey-box, continuous-time transfer function models, some of the simulation results are flawed and give a misleading impression of how the algorithm suggested by the authors compares with the well known and closely related SRIVC algorithm.     

Comment on ‘Precision tracking control of non-minimum phase systems with zero phase error’

This paper comments on a technical problem arising in the article ‘ Precision tracking control of non-minimum phase systems with zero phase error’ by Xia and Menq.     

Comment on ‘Sufficient condition for the asymptotic stability of interval matrices’

A simplified proof is given for the main conclusion of the previous paper.     

Comment on ‘On sufficient conditions for the stability of interval matrices’

Some new sufficient conditions for the stability of interval matrices were given by Argoun (1986). These conditions, however, are incorrect.     

Numerical algorithm for the standard pairing problem based on the Heine–Stieltjes correspondence and the polynomial approach

We present a detailed study of the computational complexity of a numerical algorithm based on the Heine–Stieltjes correspondence following the new approach we proposed recently for solving the Bethe ansatz (Gaudin–Richardson) equations of the standard pairing problem. For k$k$ pairs of valence nucleons in n$n$ non-degenerate single-particle energy levels, the approach utilizes that solutions of the Bethe ansatz equations can be obtained from two matrices of dimensions (k+1)×(k+1)$(k+1)\times (k+1)$ and (n−1)×(k+1)$(n-1)\times (k+1)$, which are associated with the extended Heine–Stieltjes and Van Vleck polynomials, respectively. Since the coefficients in these polynomials are free from divergence with variations in contrast to the original Bethe ansatz equations, the approach provides an efficient and systematic way to solve the problem. The method reduces to solving a system of k$k$ polynomial equations, which can be efficiently implemented by the fast Newton–Raphson algorithm with a Monte Carlo sampling procedure for the initial guesses. By extension, the present algorithm can also be used to solve a large class of Gaudin-type quantum many-body problems, including an efficient angular momentum projection method for multi-particle systems.     

Comment on ‘ Tolerance analysis using fuzzy sets ’ and ‘ A procedure for multiple aspect decision making ’

The problem of tracking a reference vector variable from a given class is considered for discrete time linear multiple input-output plants. The plant and the reference are both described by an input-output relation and the objective is to track so that a quadratic criterion is minimized. This tracking problem is solved by reformulating it as a regulator problem for an augmented system. The optimal control law is shown to contain both feedback and feedforward terms and it is obtained by applying polynomial matrix techniques. The design procedure consists in spectral factorization and the solution of linear equations in polynomial matrices. The case of unstable references is included and a natural solvability condition is derived in the form of divisibility of polynomial matrices.     

Comment on ‘Fault tolerance analysis for stochastic systems using switching diffusion processes’ by Yang,Jiang and Cocquempot

Results are given in Yang, Jiang and Cocquempot (Yang, H., Jiang, B., and Cocquempot, V. (2009), ‘Fault Tolerance Analysis for Stochastic Systems using Switching Diffusion Processes’, International Journal of Control, 82, 1516–1525) regarding the overall stability of switched diffusion processes based on stability properties of separate processes combined through stochastic switching. This article argues two main results to be empty, in that the presented hypotheses are logically inconsistent.     

Comment on ‘Parameters identification of chaotic systems by quantum-behaved particle swarm optimization’ [Int. J. Comput. Math. 86(12) (2009), pp. 2225–2235]

This note comments on a published article ‘Parameters identification of chaotic systems by quantum-behaved particle swarm optimization’. In this article, similarity between time series obtained from chaotic systems is considered as a measure of similarity between them; however, it is well known that this method is not suitable for chaotic systems.     

Comments on the ‘ fuzzy max ’ operator of Dubois and Prade

The aim of this paper is to study controllability for systems described by first-order evolution equations and for systems described by second-order evolution equations in the case of discrete-time controls. For systems with finite-dimensional controls we present necessary and sufficient conditions for controllability. We show that distributed parameter systems are never finite-step controllable. We also investigate the relations between systems with discrete-time controls and systems with continuous -time controls from the view-point of controllability. Moreover we see the essential difference between the parabolic case and the hyperbolic case.     

Reply to Gordon and Evans ‘Comment on “Aerosol and Rayleigh radiance contributions to Coastal Zone Colour Scanner images” by Eckstein and Simpson’

A recent comment from Gordon and Evans took issue with two aspects of the analysis of Coastal Zone Color Scanner (CZCS) pigment extraction algorithms. This reply refuted the arguments of Gordon and Evans. The multiple Rayleigh scattering algorithm does not always make physical sense, nor has the physical validity of Ångström's coefficient been established as a means of parameterizing the aerosol scale factor. We also disagreed with the position put forward by Gordon and Evans that the artifacts in the CZCS data will disappear in the next generation sensor (SeaWiFS) because the problem of quantifying the aerosol contribution from these satellite measurements has not yet been solved to sufficient accuracy. Finally, these factors, coupled with electronic overshoot and the decay of the CZCS sensor's sensitivity over time, make it unlikely that the quality of derived pigment values will be significantly improved by reprocessing the CZCS archive yet one more time as suggested by Gordon and Evans.     

Additional considerations concerning the effects of ‘warm’ and ‘cool’ wall colours on energy conservation

The possibility of wall colours mediating thermal comfort was examined. Potential colour constancy problems in previous research were eliminated by painting laboratory walls either red, blue, or white. A total of 72 male and 72 female undergraduate college students were used in the study; each subject was exposed in a carrel to one of the possible combinations of the three colours and four room temperatures, 18, 22, 29 and 35°C. Data from forms completed by subjects under these conditions indicated that temperature influenced personal comfort, arousal, and perceived ambient temperature, and that colour influenced personal comfort and perceived environmental quality. However, colour did not influence perceived temperature, suggesting that energy conservation may not be facilitated by selected wall colours.