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This paper presents a novel method for constructing controllers for a class of single-input multiple-output (SIMO) linear parameter varying (LPV) systems. This class of systems encompasses many physical systems, in particular systems where individual components vary with time, and is therefore of significant practical relevance to control designers. The control design presented in this paper has the properties that the system matrix of the closed loop is multi-affine in the various scalar parameters, and that the resulting controller ensures a certain degree of stability for the closed loop even when the parameters are varying, with the degree of stability related directly to a bound on the average rate of allowable parameter variations. Thus, if knowledge of the parameter variations is available, the conservativeness of the design can be kept at a minimum. The construction of the controller is formulated as a standard linear time-invariant (LTI) design combined with a set of linear matrix inequalities, which can be solved efficiently with software tools. The design procedure is illustrated by a numerical example.

I (GB) was fortunate that early in my career I had the opportunity to work with Keith Glover. Keith had just begun his obsession with golf. A simple game where a ball stands still and the player advances it from different parts of the landscape into a hole. During a golf outing, Keith vigorously struck a ball off the fairway. It drove through a water hazard and miraculously ended up a few feet off the green. I was amazed by the image I saw as the ball moved through the water. Due to its velocity, a cavitation bubble was generated behind it. I had no inkling that my golf outing with Keith would lead many years later to an interest in the control of supercavitating vehicles.

In his Doctoral thesis and subsequent publications (e.g., [1]) Keith Glover explored the parameterization of multivariable time invariant linear systems investigating identifiability and suitable standard forms for use in system identification. Over the years the idea of identifiability has come to play an important role in the literature. In this paper we describe some new results centering around a quantitative measure of identifiability defined in terms of a suitable Gramian. The motivation comes from a desire to provide a quantitative evaluation of the so-called “two dimensional method” widely used in nuclear magnetic resonance (NMR) spectroscopy and we provide this in terms of a Cramer-Rao bound. In the final section we expand the scope of these ideas, providing a more general system theoretic development which discusses a new role for feedback in system identification.

It is well-known that the gap metric, and its variants, provide a natural framework for studying the robustness of feedback interconnections [1–4]. In fact, for linear systems, it is known that the gap metric induces the weakest topology in which both feedback stability and closed-loop performance are both robust properties [5]. In this article, we study the gap metric for the class of finite-dimensional, linear systems, in . In particular, it is shown that the gap between two systems is equal to the norm of an operator composed of left and right representations of the system graphs. The development relies on tools familiar from the time-invariant setting. This is in contrast to the abstract results which underpin the discretetime generalisations of the gap framework to the time-varying setting [6,7]. Using ideas from [8,9], an alternative characterisation of the gap is also established in terms of a standard linear fractional synthesis problem from robust control theory. This characterisation appears to be useful for approximation in the gap, and might be extendable to other classes of system.

The problem of robust stabilization with respect to left coprime factor perturbations was first solved explicity for the rational case in Glover and McFarlane [14]. The irrational case was treated in Georgiou and Smith [12], where it was shown that a solution exists provided that the transfer function has a normalized doubly coprime factorization. Our new contribution is to solve this classic problem for the following very general class of transfer functions , where , and are separable Hilbert spaces and has the following realization.

This paper deals with the model reduction of nonstationary linear parametervarying (NLPV) systems. Our interest in LPV models is motivated by the desire to control nonlinear systems along prespecified trajectories. LPV models arise naturally in such scenarios as a method to capture the possible nonlinear dynamics, while maintaining a model that is amenable to control synthesis. Frequently, when pursuing such an LPV formulation, one ends up with models of relatively large dimension. Accordingly, finding control syntheses for such models, which usually involves solving a number of linear operator inequalities as discussed in [5], requires substantial computation. For this reason, developing a theory that provides systematic methods of approximating such models is beneficial.

Imagine mobile robots, i.e., rovers, moving in the plane without human supervision. In addition to a motor drive, each robot has onboard a computer and a camera with which it can see the positions of some others relative to itself. The robots are assumed not to possess a common coordinate system—they don’t have GPS receivers, and there are no landmarks in view of all. Also, they are unable to communicate with each other. So it’s problematic if they can meet at a common location by distributed control strategies alone. This is called the . Why take rendezvous to be the task? There are undoubtedly real situations where rendezvous is a goal: The robots should gather for servicing or recharging. In any event, rendezvous is the most basic formation task. It also arises in the notion of [6]: A group of autonomous and distributed automata should come to agree on a piece of information.

Optimal input design for system identi.cation was an active area of research in the 1970’s, with different quality measures of the identified model being used for this optimal design [1-3]. The questions at that time addressed open-loop identification and the objective functions that were minimized were various measures of the parameter covariance matrix , where is the parameter vector of the model structure.

This paper contains a survey of the application of control systems theory to automotive systems. For this application field, the most useful modeling approaches and control design methods are described. Some open problems are mentioned and possible trends for future developments are listed. A case study shows what role control systems may play for maximizing the efficiency of future vehicle propulsion systems.

In the early nineties, a multivariable flight control law, designated FCL005, was developed for the Defence Evaluation and Research Agency (DERA), now QinetiQ, Vectored thrust Aircraft Advanced flight Control (VAAC) research Harrier XW175, and has been previously reported [1–3]. It was developed within the Cambridge University Engineering Department (CUED) Control Group, and much of its success depended on parallel theoretical developments within the group. The design itself used loop-shaping [4], with increased understanding of how to select weights being deduced from the application. Gain scheduling was initially done using switching between controllers, but in piloted simulation the switching points were evident, even when using bumpless transfer techniques. At around this time it was shown that the loop-shaping controller could be written in observer form (see for example [5]), providing an improved scheduling method. When it came to implementation of the control law on the aircraft, the lack of processing power necessitated discrete time implementation at a relatively slow rate compared to the bandwidth. To support this, the discrete time solution for the optimal controller in observer form developed in [6] was used. Later research within the CUED Control Group looked at model (in)validation [7] using the Harrier as a vehicle for testing its practicality(.)