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Symbolic languages are increasingly being used in the analysis and implementation of control algorithms. Many of these control procedures involve some type of differentiation or Jacobian formulation. Automatic differentiation provides an alternative means of computing this information which is rarely considered in the control literature. This correspondence will discuss the use of automatic differentiation. Numerical results comparing the use of automatic differentiation and symbolic approaches in the context of a particular nonlinear control system will be given.

Recently the issue of fragile controllers (high sensitivity of closed-loop stability and/or performance to small changes in controller coefficients) produced by using popular robust and optimal control synthesis methods was raised by the above-mentioned paper. This paper had at least three serious flaws. First, the authors did not provide any references to the wide earlier work in which methods are given to analyze and solve fragility and related robustness issues. Second, Keel and Bhattacharyya used mostly simple textbook examples in which the optimization criteria for controller synthesis were so simple that they do not incorporate realistic design considerations. This also resulted in the third big flaw of the paper by Keel and Bhattacharyya; namely, the possible explanation given to the cause of these problems via holes in parametric stability space for high-order controllers is misplaced. A more direct explanation is in the badly chosen optimization criteria and controller parameterizations which make the controller synthesis and realization problems considered rather unrealistic and (mathematically) ill-posed. In the present paper we comment on the paper by Keel and Bhattacharyya and discuss fragility and other robustness issues through the well-established tools of coprime factorizations and robustness optimization. The main conclusion is that by adopting sensible optimization criteria, which take into account enough of the important design considerations directly, and numerically robust controller parameterizations, controller fragility should not be a big problem in applications of modern robust and optimal control theory. Index Terms - Coprime factorizations, fragility, optimality, robustness.

In the above-mentioned paper a variable structure sliding mode controller (VSSMC) design for the tip position control of a flexible one-link manipulator has been presented, where a switching line constructed from the tip position and its derivative was employed for the design. The claim was that if the slope of this line is chosen positive and the system variables are made to stay on this line, they will converge to zero exponentially, thus yielding a stable system in sliding mode (SM). The purpose of this comment is to show that the choice of a positive constant as the slope for this switching line will not guarantee the stability of the system in SM because, in view of the functional relationship of the tip position with the generalized coordinates of the system through the mode shape functions, what is presented as a switching line is in fact a switching hypersurface. Hence, the stability of the system in SM is guaranteed only if the motion on this hypersurface is asymptotically stable. A positive value for the slope of the switching line employed by Qian and Ma will not guarantee this stability because variations in the mode shape functions due to varying payload conditions or other disturbances at the tip will lead to a varying switching surface. These variations can be such that the resulting sliding motion becomes unstable. Also, the varying switching surface implies that the controller will fail to maintain sliding mode motion. Index Terms - Flexible manipulator, sliding mode, variable structure control.

A vigorous branch of automatic learning is directed at the task of locating a global minimum of an unknown multi-modal function f(theta) on the basis of noisy observations L(theta(i)) = f (theta(i)) + W(theta(i)) taken at sequentially-chosen control points {theta(i)}. In all preceding convergence deviations known to us, the noise is postulated to depend on the past only through control selection. The present paper contributes to the literature by allowing that the observation noise sequence may be stochastically dependent, being a function of an unknown underlying Markov decision process, the observations being the stage-wise losses. In a sense, in order to be made precise, the algorithm offered here is shown to attain asymptotically optimal performance, and rates are assured. A motivating example from the queueing theory is offered, and connections with classical problems of Markov control theory and other disciplines are mentioned.

In a recent paper, it was proved that the frequency response arc and the inner frequency response set associated with D-stable polynomial is convex. This note points out that clockwise property and positive curvature is sufficient for convexity based on a result in classical differential geometry and provides an alternative proof of the convexity based on curvature. It is felt that this line of proof may be more easily generalized to study the rational function cases.

This paper points out some misleading statements of the above-mentioned paper and shows that the proposed controller can be easily derived, under less restrictive conditions, from a previously proposed output feedback variable structure control scheme. Index Terms - Model reference adaptive control, output feedback, robustness, stability, variable structure systems.

In a recent paper, an asymptotic analysis was used to address the zero structure of discretized continuous-time systems expressed in the Euler (or forward difference) operator. Unfortunately, the analysis is flawed, so that Theorem 1 is true as stated only when the continuous-time relative degree is equal to two. In this paper, we indicate how the analysis may be rectified. Index Terms - Discrete-time systems, poles and zeros.

In a recent [paper.sup.1] a sufficient condition for memoryless stabilization of a class of uncertain linear systems with a variable-state delay and norm-bounded time-varying uncertainties is derived in terms of an algebraic Riccati equation. This Riccati equation depends on several free matrix variables, and a subsequent result in the above-mentioned [paper.sup.1], Theorem 2, states that failure or success of the stabilization algorithm is independent of the selection of these matrix variables. In this paper, we give a counter-example to this Theorem 2 as well as providing a fix. Index Terms - Algebraic Riccati equation, quadratic stabilization, robust control, uncertain time-delay system.

This paper notes that the proof of Appendix 7 in the above paper is wrong. A conterexample is given.

This paper presents a correction to [1, Theorem 4] which provides a necessary and sufficient condition for dispatchability.

In the above paper, Albertos presents a modeling technique to model linear, time-invariant systems with synchronous sampling. The model is derived from both the discrete transfer function and state-space representation of a given system and yields two similar expressions. Albertos equates the two in Lemma 2.1; there is, however, an inconsistency in Lemma 2.1, and this is discussed further.

In a recent note, the robust stability problem of a convex hull of a finite number of matrices was handled, and a sufficient condition was presented. In this note, we give another sufficient condition, and show, using an example, that our condition can be less conservative than the result. We also give a necessary and sufficient condition for the robust stability problem treated in the paper.