Professor Brett Ninness

This letter considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modeled by a nonlinear state-space model, but where the model parameters, state and future disturbances are not known and are treated as random variables. Central to our formulation is that the joint distribution of these unknown objects is conditioned on the observed data. Crucially, as new measurements become available, this joint distribution continues to evolve so that control decisions are made accounting for uncertainty as evidenced in the data. The resulting problem is intractable which we obviate by providing approximations that result in finite dimensional deterministic optimization problems. The proposed approach is demonstrated in simulation on a nonlinear system.

This paper presents a method for calculating the smoothed state distribution for Jump Markov Linear Systems. More specifically, the paper details a novel two-filter smoother that provides closed-form expressions for the smoothed hybrid state distribution. This distribution can be expressed as a Gaussian mixture with a known, but exponentially increasing, number of Gaussian components as the time index increases. This is accompanied by exponential growth in memory and computational requirements, which rapidly becomes intractable. To ameliorate this, we limit the number of allowed mixture terms by employing a Gaussian likelihood mixture reduction strategy, which results in a computationally tractable, but approximate smoothed distribution. The approximation error can be balanced against computational complexity in order to provide an accurate and practical smoothing algorithm that compares favourably to existing state-of-the-art approaches.

Jump Markov linear systems (JMLS) are a useful model class for capturing abrupt changes in system behaviour that are temporally random, such as when a fault occurs. In many situations, accurate knowledge of the model is not readily available and can be difficult to obtain based on first principles. This paper presents a method for learning parameter values of this model class based on available input¿output data using the maximum-likelihood framework. In particular, the expectation¿maximisation method is detailed for this model class with attention given to a deterministic and numerically stable implementation. The presented algorithm is compared to state-of-the-art methods on several simulation examples with favourable results.

Bayesian tracking is a general technique for state estimation of nonlinear dynamic systems, but it suffers from the drawback of computational complexity. This paper is concerned with a class of Wiener systems with multiple nonlinear sensors. Such a system consists of a linear dynamic system followed by a set of static nonlinear measurements. We study a maximum-likelihood Kalman filtering (MLKF) technique which involves maximum-likelihood estimation of the nonlinear measurements followed by classical Kalman filtering. This technique permits a distributed implementation of the Bayesian tracker and guarantees the boundedness of the estimation error. The focus of this paper is to study the extent to which the MLKF technique approximates the theoretically optimal Bayesian tracker. We provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large. Two case studies are analyzed in detail.

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.

A recent but rapidly maturing field in the area of system identification has been that of ¿estimation in H infinty¿. Greatly influencing this work has been the phenomenon that no linear (in-the-data) algorithm exists which is ¿robustly convergent¿. This paper conducts a study of this issue by combining specific new analysis together with existing results from the mathematics literature on the topic of polynomial approximation theory. Particular attention is paid to the role of model order, and this leads to the consideration of model order selection from a deterministic worst-case perspective. © 1999 Taylor and Francis Group, LLC.

On the basis of a previous expectation maximization (EM) algorithm, this paper applies the particle Markov chain Monte Carlo (MCMC) technique to estimate nonlinear state-space models (SSMs). The smoothed simultaneous particles for joint states are generated by importance resampling (IR) and are directly used to compute a log-likelihood function and its Jacobian vector and Hessian matrix. As a result, a relatively less computational load can thus be obtained, which is crucial to practical applications of the particle MCMC. In addition, the SSM parameters can be recursively iterated by the more efficient Newton method, in which an optimal step length for parameter update in each iteration is optimized by a 1-D search method. This presented identification method has a good global parameter convergence in case iteration parameters are initialized from quite large intervals of their respective true values. Finally, a numerical simulation for identification of a classical SSM is used to show the effectiveness of the studied identification method.

This paper improves on a noted square-root RTS Kalman smoothing algorithm proposed by Park and Kailath for the application purpose. This improved square-root RTS algorithm is able to additionally accommodate arbitrary exogenous known input, as such case is quite common in the real-world applications. In addition, hyperbolic Householder transformations are employed to avoid the computation of the difference of two positive semi-definite matrices. The Givens rotations based unitary transformations are further used to make the resulting algorithm have higher computational efficiency. The relevant implementation steps of this algorithm is also addressed. Finally, a numerical simulation is given to verify this improved algorithm.

A robust slice sampler, which guarantees no repeated samples, is found as a special case of Metropolis sampling that can interact with parallel chains to efficiently sample from multi-modal densities even with possibly isolated support sets. The algorithm is completely automated with no tuning required. Implications to particle filtering design for on-line state and parameter joint estimation is also discussed.

A generalised framework for Metropolis-Hastings admits many algorithms as specialisations and allows for synthesis of multiple methods to create a parallel algorithm, with no tuning required, to efficiently draw uncorrelated samples, from the posterior density in Bayesian systems identification, at lower computational cost in comparison with conventional samplers. Two automatic annealing schemes demonstrate complementary robustness in detecting multi-modal distribution.

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 paper takes a Bayesian approach to the problem of dynamic system estimation, and illustrates how posterior densities for system parameters, or more abstract and rather arbitrary system properties (such a frequency response, phase margin etc.) may be numerically computed. In achieving this, the key idea of constructing an ergodic Markov chain with invariant distribution equal to the desired posterior is fundamental, and it is inspired by recent developments in the mathematical statistics literature. An essential point of the work here is that via the associated posterior computation from the Markov chain, error bounds on estimates are provided that do not rely on asymptotic in data length arguments, and hence they apply with arbitrary accuracy for arbitrarily short data records.