Mathematical models are essential for describing complex systems across all fields of engineering and natural sciences. In general terms, a model is used to capture important system behaviour such as the response to changed environment and causal relationships between system components. The remarkable utility of mathematical system modelling stems from the fact that models:

  • Enable prediction of system behaviour under new environmental scenarios;
  • Remove the need for dangerous and/or prohibitively expensive experiments;
  • Accelerate the analysis and design processes;
  • Enable simulation of systems at greatly accelerated time-scales;
  • Are fundamental to detecting faults or changes in the system;
  • Are essential to the design and analysis of advanced feedback control and automation systems.

By way of example, mathematical system models are essential for estimation and control of autonomous vehicles, fault detection and diagnosis within advanced manufacturing processes, and management of networked systems.

While the impact and importance of modelling is well recognised across many fields, it is equally well recognised that constructing these models based purely on fundamental physical principles is often difficult or even impossible since it requires the careful combination of known physical principles such as Newtonian mechanics, electromagnetics, thermodynamics and material conservation principles and in addition, it requires accurate knowledge of many physical parameters such as moments of inertia, thermal conductivity coefficients, chemical concentrations and frictional coefficients. In practice, the cost of constructing models in this manner is often prohibitive and in some cases not even possible due to inability to ascertain parameters coupled with their potential variation in space and time. 

In this research area, members of the Autonomous Systems Research Centre are developing new theory and supporting algorithms to identify system models based on observed data.


This research area concerns the development of numerically robust and efficient algorithms for estimating probabilistic state distributions based on observed system behaviour. Such problems frequently arise in all areas of Engineering and Science from estimating vehicle pose to disease infection rates.

Bayes’ rule is employed as the principle theoretical framework, where its application to more flexible model structures is of primary interest. This work spans development of algorithms for linear systems with additive Gaussian noise through to much more general non-linear systems.

Specific areas of research include filtering for Gaussian mixture models and Jump Markov Linear Systems. These model classes span a large subset of practical models for real-world phenomena. 



Bayesian non-parametric modelling provides a flexible approach to estimating mathematical models from data. These non-parametric models are capable of increasing their complexity as the amount of data increases, providing ultimate flexibility. Primary tools in this area include Gaussian processes and neural networks, and both are enjoying a wide range of applications.

As an example, novel manufacturing methods such as as 3D metallic printing require techniques to determine the residual stress that is generated within the produced components. Diffraction of neutrons and X-rays allows for measurement of strain and hence stress within polycrystalline samples. The development of models that satisfy the physical properties of equilibrium and boundary conditions has is critical to the estimation of the full strain fields from these measurements.

These non-parametric methods are also finding application within dynamic system modelling areas, where phenomenological modelling is inhibitory. 


Automation of complex physical systems requires a good understanding of the underlying physics which governs the systems dynamic behavior and the ways in which the behavior can be influenced. However, our engineering models are always flawed, limiting our ability to accurately understand and automate complex systems. This problem is well summarised by the aphorism ‘all models are wrong, but some are useful’.

In this line of research, several members of the Autonomous Systems Research Centre are investigating the development of nonlinear control and observer design methods that utilise the underlying physical structure present in physical systems. By considering the underlying structure, the effects of model error can be directly considered and robustness of the proposed control and observer methods can be assessed. This line of inquiry has resulted in several scholarly publications on the topics of disturbance rejection, control of constrained mechanical systems and observer design for mechanical systems, amongst others.


The past decade has seen considerable interest and progress in the development of autonomous systems, including vehicles, in part due to the economies of scale and improved performance of embedded computer hardware, sensors, and battery technology. The use of semi-autonomous or fully-autonomous systems in civilian applications that were previously not economically or technologically feasible now appears imminent. For such systems to become accepted within society at large, an unprecedented level of reliability and safety must first be demonstrated.

While guidance, navigation and control (GNC) technologies are relatively mature in their proven domains, the supervisory systems that monitor these components are far less proven and the behaviour of autonomous systems in unknown conditions is difficult to quantify, much less certify. In particular, such systems must be capable of detecting and isolating faults with low-cost sensors and actuators and then make appropriate decisions under uncertainty to reconfigure the system to continue operating in degraded state or abort to a safe state.

In this line of research, several members of the Autonomous Systems Research Centre are investigating the development of online algorithms to compute the joint distribution of the system states and the health status of the sensors and actuators. This enables appropriate reconfiguration actions for sensors and actuators to be taken while fully accounting for ambiguities arising when similar observations have different underlying causes. Such fault-tolerant systems are key to implementing robust autonomy.


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