Lachlan Blackhall

On the structural controllability of networks of linear systems

Abstract Results on the joint (or global) controllability of networks of interconnected linear systems using the linear structured systems viewpoint are presented. Criteria to determine the joint structural controllability of a dynamical network using only the local structural controllability properties and the interconnection topology are detailed. These results provide a computationally tractable method of determining the controllability properties of large scale and complex dynamical networks and represent necessary conditions for the controllability, in the usual sense, of dynamical networks. The results hold for networks of structurally reachable linear systems with arbitrary connection topologies.

Recursive Sparse Estimation using a Gaussian Sum Filter

Abstract We develop a recursive estimator that systematically arrives at sparse parameter estimates. The algorithm is computationally feasible for moderate parameter estimation problems and leverages the Gaussian sum filter to provide both sparse parameter estimates and credible Bayesian intervals for non-zero parameters in a recursive fashion. Simulations show extremely promising accuracy, as well as a robustness not enjoyed by other sparse estimators.

Using an information filter to speed computation of sparse parameter estimates

This paper discusses the development of a recursive estimator which systematically arrives at sparse parameter estimates. Prior work achieved this by utilizing a Gaussian sum filter. This paper shows the relationship between the implementation using a Gaussian sum filter, where the mean and covariance of each component is propagated, and the equivalent representation using an information filter. We see that the information filter representation requires only a single information filter to be updated for each new measurement instead of the exponential number of measurement updates that were required when using the Gaussian sum filter. We thus see that using the information filter provides computational benefits when recursively estimating sparse parameters, reducing running time as well as data storage.

Diagnosability of Networks of Hybrid Systems

Abstract Results for the diagnosability of hybrid dynamical networks are presented. These results give the conditions for which arbitrary events (including faults) in hybrid networks can be detected and isolated using a general class of indicator functions. These results emerge from the overlap of the control theoretic fault detection and isolation and diagnosis communities. The interaction of the many systems in the network is exploited to achieve diagnosability conditions dependent only on the number of events in the network rather than the number of interconnected systems. The algorithmic complexity of the diagnosability conditions and methods of choosing a minimal indicator set that guarantee diagnosability are also addressed.

Diagnosing Hybrid Dynamical Systems

Abstract A method of diagnosing the occurrence of arbitrary events in hybrid dynamical systems is presented. The methodology unifies results from the Fault Detection and Isolation (FDI) and Diagnosis (DX) communities. In this approach the diagnosis is not performed on the output trajectory of the system but rather on the fundamental governing dynamics, thus not requiring the computation of residuals. These results are an important step in being able to diagnose, repair and control hybrid dynamical systems which are rapidly becoming ubiquitous in the engineering domain. Computational results are presented for a hybrid dynamical system experiencing events that cause cause both structural and parametric mode changes.