James M. Krause

A time-domain approach to model validation

In this paper we offer a novel approach to control-oriented model validation problems. The problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input-output data. Our approach directly uses time-domain input-output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally nondifferentiable) convex feasibility problems or to linear programming problems. In special cases, we give analytical solutions to these problems. >

Parameter identification in the presence of non-parametric dynamic uncertainty

Abstract This paper provides identification laws which yield monotonic parameter error reduction in the absence of external noise inputs, but in the presence of non-parametric dynamic uncertainty (unmodelled dynamics). This paper considers two non-parametric uncertainty sets motivated by robust control: the weighted ball in H∞, and the weighted ball in the induced-L2 norm. The non-parametric uncertainty produces signals which corrupt the signals used in identification. This paper shows that the corruption is non-conservatively bounded in an L2 sense. This L2 bound is then compared with the signal energy, with the result used to enable/disable the parameter adjustment of a gradient least-squares adjustment mechanism. It is proved that the resulting parameter adjustment yields non-increasing parameter errors, with strictly decreasing parameter errors whenever the parameter errors are distinguishable from zero given the system input and output histories.

Robust adaptive control: stability and asymptotic performance

Robust stability and asymptotic performance results are provided for adaptive control in the presence of both compact real parametric uncertainty and frequency-weighted bounded unstructured uncertainty. It is shown that a class of parameter adaptive control systems is robustly stable. The asymptotic robust performance bound can be made arbitrarily close to that of the nonadaptive design which would result from perfect parameter estimation. The key assumptions are: (1) the unknown parameters lie in a known compact convex set, (2) a certain bound on the initial state of the system is known, (3) the control design rule is Lipschitzian, and (4) the control design rule would produce a robust controller if given perfect parameter information. In addition, the location of the parametric and nonparametric uncertainty within the known system dynamic must satisfy certain structural assumptions. >

A Time-Domain Approach to Model Validation

In this paper we offer a novel approach to control-oriented model validation problems. This approach differs from other available techniques in that it directly uses time-domain input output data to validate uncertainty models. The algorithms we develop are computationally tractable and reduce to (generally non-differentiable) convex feasibility programming problems.

Sufficient conditions for robust performance of adaptive controllers with general uncertainty structure

Sufficient conditions are given under which an adaptive control system is robustly stable and achieves a guaranteed robust asymptotic performance level equal to that of the robust controller given perfect parameter information. The conditions are general in several respects. For example, structured non-parametric uncertainty (e.g. block diagonal) is allowed, as well as exogenous noise inputs. In addition, the structure of the parametric uncertainty is very general, and even allows for parameters which scale the uncertainty magnitudes. This allows one to identify the size of the non-parametric uncertainty and to schedule the controller based on this size. Finally, the robust gain scheduled controller is largely unrestricted. Identification mechanisms which are proven to satisfy the sufficient conditions are not given here and, for the general problem, have not yet been developed. However, an example of such a mechanism for a subclass of systems does exist and is referenced. For the general problem, this paper provides properties to be sought in the development of robust identification laws for robust adaptive control.

On an identification problem arising in robust adaptive control

A plant is assumed to have both parametric uncertainty and nonparameterized dynamics. The nonparameterized dynamics are characterized as a stable factor perturbation with a known frequency-domain magnitude bound. A nonconservative bound on the finite-time energy of the perturbation output is constructed in real-time. The bound is used to achieve robust monotonic parameter convergence of a model reference adaptive controller.

Robust parameter adjustment with nonparametric weighted-ball-in-H/sup infinity / 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. >

A comparison of classical stochastic estimation and deterministic robust estimation

The formulation and solution of two linear parameter estimation problems are compared. The basic distinction in the problem formulation is the nature of the uncertainty. In one case, the uncertainty is generated by white Gaussian noise, and the solution is the Kalman filter. In the other case, the uncertainty is unmodeled dynamics in the unit ball in H/sup infinity / or its nonlinear cover, and the particular solution studied is a deterministic robust estimator. Certain parallels between classical stochastic estimation (Kalman filtering) and the deterministic robust estimation are examined. The similarities and differences are discussed in geometric terms, in philosophical terms, and in terms of the estimators recursive implementation. >

Comments on Grimble's comments on Stein's comments on rolloff of H/sup infinity / optimal controllers

In M.J. Grimbles comments (see ibid., vol.35, p.762-5, 1990), the polynomial systems approach to H/sup infinity / is shown to have an advantage over the state-space approach in that improper weighting functions can be used, allowing one to obtain controllers that roll off at high frequencies. It is shown that the same controller can be found with the state-space approach using a simple problem reformulation. >

An adaptive control concept for flexible launch vehicles

We propose an adaptive control method for robust stabilization of a class of modern launch vehicles. Our a p proach applies to vehicles with lightly damped flexure modes, whose resonant frequencies are both relatively low (with respect to rigid body modes) and uncertain. The concept implements robust identification of the dominant flexure frequencies coupled with closed loop notch filtering at those frequencies. The concept has been used to robustly stabilize a 23-state time-varying, linear model of an unmanned rocket booster.