Distribution-free consistency of empirical risk minimization and support vector regression

In this paper, we focus on the generalization ability of the empirical risk minimization technique in the framework of agnostic learning, and consider the support vector regression method as a special case. We give a set of analytic conditions that characterize the empirical risk minimization methods and their approximations that are distribution-free consistent. Then utilizing the weak topology of the feature space, we show that the support vector regression, possibly with a discontinuous kernel, is distribution-free consistent. Moreover, a tighter generalization error bound is shown to be achieved in certain cases if the value of the regularization parameter grows as the sample size increases. The results carry over to the ν-support vector regression.     

Constrained Infinite-Horizon Linear Quadratic Regulation of Discrete-Time Systems

We are concerned with the output norm-constrained infinite-horizon linear quadratic regulation problem, where the underlying state-control constraints are specified by curved, rather than polyhedral, surfaces. Each suboptimal problem admits an exact convex synthesis condition expressed by an increasing union of linear matrix inequalities and results in an eventually time-invariant controller satisfying the desired performance level subject to given constraints and closed-loop stability. The output norm-constrained minimum-time control problem is also dealt with as a corollary.     

Robust stability of feedback control systems with uncertain parameters and unmodeled dynamics

Recent results on a generalization of Kharitonov’s interval polynomial problem allow linearly dependent perturbations in the coefficients of a polynomial, and the main objective is to provide computationally tractable criteria for robust stability. In this paper robust-stability criteria are provided in an even more general setting—one which also accommodates unmodeled dynamics. In addition, the test given for robust stability totally avoids so-called “edge combinatorics,” greatly facilitating numerical computation. This research was supported by the National Science Foundation under Grants ECS-8612948 and ECS-8451519 and in part by AFOSR Grant 880020, Honeywell and GE.     

On the robust stability of linear time-invariant plants with unstructured uncertainty

We consider general families of linear time-invariant plants described by a nominal plant model with unstructured uncertainty. We show, under a rather weak assumption, that when a family of systems is not robustly stabilizable by any linear time-invariant feedback controller, then no nonlinear time-varying controller can robustly stabilize the given family.     

Robust parameter adjustment with nonparametricweighted-ball-in-H∞ uncertainty

Using a parameter adjustment law, robust monotonic parameter error reduction is proved for a linear parameter estimation problem in which the signal is corrupted by the presence of nonparametric dynamical uncertainty. The nonparameterized dynamics are characterized by a known frequency-domain magnitude bound. A nonconservative bound on the finite-time energy of the nonparametric-dynamics output is constructed in real time. When the error single energy is small enough to be due to nonparametric dynamics alone, the parameter adjustment is shut off to avoid misadjustment. The approach is an extension of existing adaptive control error-dead-zone ideas to the case of frequency-domain bounded uncertainty     

Methodology for feedback variable selection for control of semiconductor manufacturing processes - Part 2: Application to reactive ion etching

The PVVM methodology for feedback variable selection introduced in a companion paper (Patterson et al., 2003) is applied to a gate etch process. The primary purpose of this paper is to illustrate the practical aspects of utilizing this methodology. Particular attention is given to the challenging task of process modeling. The model-building procedure and constraint-limited exhaustive search is demonstrated to perform superior to other model-building procedures including principal component regression and partial least squares regression for use in this methodology. A second purpose is to present the results for the etch process. Advanced sensors considered for real-time process control of this process include an RF probe, mass spectroscopy and optical emission spectroscopy. Feedback variables are selected to reduce variation in etch rate, nonuniformity and lateral etch rate. The advantages of treating location on the wafer as a disturbance to the etch rate model so that both etch rate and nonuniformity may be captured in one model are presented and experimentally verified.     

Filtering and smoothing in an H∞ setting

The problems of filtering and smoothing are considered for linear systems in an H^∞ setting, i.e. the plant and measurement noises have bounded energies (are in L₂), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered; the initial condition is assumed known in one case, while in the other the initial condition is not known but the initial condition, the plant, and measurement noise are in some weighted ball of RⁿXL₂. Finite-horizon and infinite-horizon cases are considered. Necessary and sufficient conditions are presented for the existence of estimators (both filters and smoothers) that achieve a prescribed performance bound, and algorithms that result in performance within the bounds are developed. In case of smoothers, the optimal smoother is also presented. The approach uses basic quadratic optimization theory in a time-domain setting, as a consequence of which both linear time-varying and time-invariant systems can be considered with equal ease. (In the smoothing problem, for linear time-varying systems, one considers only the finite-horizon case)     

Control of semiconductor manufacturing equipment: real-timefeedback control of a reactive ion etcher

This paper describes the development of real-time control technology for the improvement of manufacturing characteristics of reactive ion etchers. A general control strategy is presented. The principal ideas are to sense key plasma parameters, develop a dynamic input-output model for the subsystem connecting the equipment inputs to the key plasma variables, and design and implement a multivariable control system to control these variables. Experimental results show that this approach to closed-loop control leads to a much more stable etch rate in the presence of a variety of disturbances as compared to current industrial practice     

Pointwise stabilizability of families of linear time-invariantplants

The topic of (robust) pointwise stabilizability of families of linear time-invariant (LTI) plants arising from unstructured modeling uncertainty is addressed. The results presented extend some earlier work and show that there is no advantage in using general nonlinear time-varying (NLTV) controllers over LTI ones for certain problems of (robust) pointwise stabilization     

Robust control of linear time-invariant plants using periodic compensation

This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.