Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Identification of nonlinear interconnected systems

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724)

Uncertainty remodeling for robust control of linear time-invariant plants

The paper proposes a measure of robust performance based on frequency domain experimental data that allows non-conservative modeling of uncertainty. Given the nominal model of the plant and closed-loop performance specifications the iterative control design and remodeling of model uncertainty based on that measure leads to a controller with improved robust performance. The structured dynamic uncertainty is allowed to act on the nominal model in a linear fractional transformation (LFT) form. The proposed method is a modification of the structured singular value with implicit constraints on model consistency. The usefulness of the method is demonstrated on a vehicle control simulation example

Robustness and performance trade-offs in control design for flexible structures

Linear control design models for flexible structures are only an approximation to the “real” structural system. There are always modeling errors or uncertainty present. Descriptions of these uncertainties determine the trade-off between achievable performance and robustness of the control design. In this paper it is shown that a controller synthesized for a plant model which is not described accurately by the nominal and uncertainty models may be unstable or exhibit poor performance when implemented on the actual system. In contrast, accurate structured uncertainty descriptions lead to controllers which achieve high performance when implemented on the experimental facility. It is also shown that similar performance, theoretically and experimentally, is obtained for a surprisingly wide range of uncertain levels in the design model. This suggests that while it is important to have reasonable structured uncertainty models, it may not always be necessary to pin down precise levels (i.e., weights) of uncertainty. Experimental results are presented which substantiate these conclusions

How are junior doctors managing patients with self-limiting illnesses at their first presentation? A video vignette study

Purpose: To conduct a video vignette survey of medical students and doctors investigating test ordering for patients presenting with self-limiting or minor illness. Methods: Participants were shown six video vignettes of common self-limiting illnesses and invited to devise investigation and management plans for the patients’ current presentation. The number of tests ordered was compared with those recommended by an expert panel. A Theory of Planned Behaviour Questionnaire explored participants’ beliefs and attitudes about ordering tests in the context of self-limiting illness. Results: Participants (n=61) were recruited from across Australia. All participants ordered at least one test that was not recommended by the experts in most cases. Presentations that focused mainly on symptoms (eg, in cases with bowel habit disturbance and fatigue) resulted in more tests being ordered. A test not recommended by experts was ordered on 54.9% of occasions. With regard to attitudes to test ordering, junior doctors were strongly influenced by social norms. The number of questionable tests ordered in this survey of 366 consultations has a projected cost of $17 000. Conclusions: This study suggests that there is some evidence of questionable test ordering by these participants with significant implications for costs to the health system. Further research is needed to explore the extent and reasons for test ordering by junior doctors across a range of clinical settings

Sets and Constraints in the Analysis Of Uncertain Systems

This thesis is concerned with the analysis of dynamical systems in the presence of model uncertainty. The approach of robust control theory has been to describe uncertainty in terms of a structured set of models, and has proven successful for questions, like stability, which call for a worst-case evaluation over this set. In this respect, a first contribution of this thesis is to provide robust stability tests for the situation of combined time varying, time invariant and parametric uncertainties. The worst-case setting has not been so attractive for questions of disturbance rejection, since the resulting performance criteria (e.g., ℋ∞,) treat the disturbance as an adversary and ignore important spectral structure, usually better characterized by the theory of stochastic processes. The main contribution of this thesis is to show that the set-based methodology can indeed be extended to the modeling of white noise, by employing standard statistical tests in order to identify a typical set, and performing subsequent analysis in a worst-case setting. Particularly attractive sets are those described by quadratic signal constraints, which have proven to be very powerful for the characterization of unmodeled dynamics. The combination of white noise and unmodeled dynamics constitutes the Robust ℋ2 performance problem, which is rooted in the origins of robust control theory. By extending the scope of the quadratic constraint methodology we obtain a solution to this problem in terms of a convex condition for robustness analysis, which for the first time places it on an equal footing with the ℋ∞ performance measure. A separate contribution of this thesis is the development of a framework for analysis of uncertain systems in implicit form, in terms of equations rather than input-output maps. This formulation is motivated from first principles modeling, and provides an extension of the standard input-output robustness theory. In particular, we obtain in this way a standard form for robustness analysis problems with constraints, which also provides a common setting for robustness analysis and questions of model validation and system identification