Associate Professor Adrian Wills

In 1959, the integrated circuit (IC) was invented simultaneously by Jack Kilby of Texas Instruments and Robert Noyce of Shockley Semiconductor [Ki lby, 2000]. This development has been considered one of mankind's most significant innovations.

Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the loglikelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher's identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results.

This paper develops and illustrates a new maximum-likelihood based method for the identification of Hammerstein-Wiener model structures. A central aspect is that a very general situation is considered wherein multivariable data, non-invertible Hammerstein and Wiener nonlinearities, and colored stochastic disturbances both before and after the Wiener nonlinearity are all catered for. The method developed here addresses the blind Wiener estimation problem as a special case. © 2012 Elsevier Ltd. All rights reserved.

This paper addresses the design of gradient based search algorithms for multivariable system estimation. in particular, the work here considers so-called 'full parametrization' approaches, and establishes that the recently developed 'Data Driven Local Coordinate' (DDLC) methods can be seen as a special case within a broader class of techniques that are designed to deal with rank-deficient Jacobians. This informs the design of a new algorithm that, via a strategy of dynamic Jacobian rank determination, is illustrated to offer enhanced performance. Copyright © 2005 IFAC.

This paper describes a MATLAB-based software package for estimation of dynamic systems. A wide range of standard estimation approaches are sup- ported. These include the use of non-parametric, subspace-based and prediction- error algorithms coupled (in the latter case) with either MIMO state space or MISO polynomial model structures. A key feature of the software is the implementation of several new techniques that have been investigated by the authors. These include the estimation of non-linear models, the use of non-standard model parametrizations, and the employment of Expectation Maximisation (EM) methods. Copyright © 2005 IFAC.

This paper considers the system architecture and design issues for implementation of on-line Model Predictive Control (MPC) in Field Programmable Gate Arrays (FPGAs) and Application Specific Integrated Circuits (ASICs). In particular, the computationally itensive tasks of fast matrix QR factorisation, and subsequent sequential quadratic programming, are addressed for control law computation. An important aspect of this work is the study of appropriate data word-lengths for various essential stages of the overall solution strategy.

This article reviews authors' recently developed algorithm for identification of nonlinear state-space models under missing observations and extends it to the case of unknown model structure. In order to estimate the parameters in a state-space model, one needs to know the model structure and have an estimate of states. If the model structure is unknown, an approximation of it is obtained using radial basis functions centered around a maximum a posteriori estimate of the state trajectory. A particle filter approximation of smoothed states is then used in conjunction with expectation maximization algorithm for estimating the parameters. The proposed approach is illustrated through a real application. © 2009 IFAC.

The standard continuous time state space model with stochastic disturbances contains the mathematical abstraction of continuous time white noise. To work with well defined, discrete time observations, it is necessary to sample the model with care. The basic issues are well known, and have been discussed in the literature. However, the consequences have not quite penetrated the practise of estimation and identification. One example is that the standard model of an observation being a snapshot of the current state plus noise independent of the state cannot be reconciled with this picture. Another is that estimation and identification of time continuous models require a more careful treatment of the sampling formulas. We discuss and illustrate these issues in the current contribution. An application of particular practical importance is the estimation of models based on irregularly sampled observations. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

The Wiener model is a block oriented model having a linear dynamic system followed by a static nonlinearity. The dominating approach to estimate the components of this model has been to minimize the error between the simulated and the measured outputs. We show that this will in general lead to biased estimates if there is other disturbances present than measurement noise. The implications of Bussgang's theorem in this context are also discussed. For the case with general disturbances we derive the Maximum Likelihood method and show how it can be efficiently implemented. Comparisons between this new algorithm and the traditional approach confirm that the new method is unbiased and also has superior accuracy. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.

The nonlinearity that arises in constrained MPC (model predictive control) satisfies an IQC (integral quadratic constraint), provided zero is feasible. It is thus possible to construct a robust stability test against any model uncertainty that also satisfies an IQC. In particular the test may be applied to structured and unstructured infinity-norm bound uncertainty. The test may be applied with predictive controllers of arbitrary horizon. The test is illustrated for several simple MPC schemes and simulation results are shown for a two-input two-output plant with left matrix fraction uncertainty. Copyright © 2006 IFAC.

We show that a sufficient condition for the robust stability of constrained linear model predictive control is for the plant to be open-loop stable, for zero to be a feasible solution of the associated quadratic programme and for the input weighting be sufficiently high. The result can be applied equally to state feedback and output feedback controllers with arbitrary prediction horizon. If integral action is included a further condition on the steady state modelling error is required for stability. Copyright © 2005 IFAC.

In constrained linear model predictive control a quadratic program must be solved on-line at each control step. If zero is feasible the resultant static nonlinearity is sector bound. We show that the nonlinearity is also monotone nondecreasing and slope restricted; furthermore it may be expressed as the gradient of a convex potential function. Hence we show the existence of Zames-Falb multipliers for such a nonlinearity. For completeness, we construct such multipliers both for the general case of multi-input multi-output static nonlinearities and for the particular case where the nonlinearity arises from a quadratic program. We also express the results in terms of integral quadratic constraints. These multipliers may be used in a general and versatile analysis of the robust stability of constrained model predictive control. © 2005 IEEE.

The theory of self-concordant barriers was introduced by Nesterov and Nemirovskii (1994) in the context of interior-point methods for convex optimisation. Their development is general, elegant and enjoys widespread implementation in state-of-the-art. algorithms. In this paper we exploit the theory of self-concordant functions with application to nonlinear MPC. In particular we construct an invariant terminal constraint set via properties of self-concordant functions. We also extend earlier results on recentred barrier function MPC to nonlinear MPC (model predictive control) with state constraints. We show nominal closed-loop stability for a wide class of nonlinear systems under full state feedback. Copyright

We discuss the design of cross-directional controllers which are guaranteed to be robustly stabilizing while incorporating a quadratic program for steady state performance. In particular we propose implementing cross-directional controllers in modal form with a constrained internal model control structure. Nominal optimal steady state performance is guaranteed via a non-linear element that incorporates a quadratic program. The quadratic program can be expressed as a continuous sector bounded nonlinearity together with two linear transformations. Thus the multivariable circle criterion can be used to guarantee closed-loop stability in the presence of disturbances and modeling uncertainties.

© 2003 EUCA. Actuator constraint handling is necessary for many cross-directional controllers. We discuss how optimal steady state performance can be guaranteed by modifying an internal model control structure with a non-linear element. For the simple dynamics associated with most web processes this also gives good closed-loop dynamic behaviour. Thus unconstrained control design techniques may be applied directly to the constrained control problem.

Actuator constraint handling is necessary for many cross-directional controllers. We discuss how optimal steady state performance can be guaranteed by modifying an internal model control structure with a non-linear element. For the simple dynamics associated with most web processes this also gives good closed-loop dynamic behaviour. Thus unconstrained control design techniques may be applied directly to the constrained control problem.