A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems

in IEEE Transaction on Automatic Control (2016), 61(1), 182-187

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated ... [more ▼]

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear functional forms and their associated parameters from a limited number of time-series data points. For this, we cast this identification problem as a sparse linear regression problem and take a Bayesian viewpoint to solve it. As such, this approach typically leads to nonconvex optimisations. We propose a convexification procedure relying on an efficient iterative re-weighted ℓ1-minimisation algorithm that uses general sparsity inducing priors on the parameters of the system and marginal likelihood maximisation. Using this approach, we also show how convex constraints on the parameters can be easily added to our proposed iterative re-weighted ℓ1-minimisation algorithm. In the supplementary material \cite{appendix}, we illustrate the effectiveness of the proposed identification method on two classical systems in biology and physics, namely, a genetic repressilator network and a large scale network of interconnected Kuramoto oscillators. [less ▲]

Online Fault Diagnosis for Nonlinear Power Systems

in Automatica (2015), 55

In this paper, automatic fault diagnosis in large scale power networks described by second-order nonlinear swing equations is studied. This work focuses on a class of faults that occur in the transmission ... [more ▼]

In this paper, automatic fault diagnosis in large scale power networks described by second-order nonlinear swing equations is studied. This work focuses on a class of faults that occur in the transmission lines. Transmission line protection is an important issue in power system engineering because a large portion of power system faults is occurring in transmission lines. This paper presents a novel technique to detect, isolate and identify the faults on transmissions using only a small number of observations. We formulate the problem of fault diagnosis of nonlinear power network into a compressive sensing framework and derive an optimisationbased formulation of the fault identification problem. An iterative reweighted `1-minimisation algorithm is finally derived to solve the detection problem efficiently. Under the proposed framework, a real-time fault monitoring scheme can be built using only measurements of phase angles of nonlinear power networks. [less ▲]

Decentralised minimum-time consensus

in Automatica (2013), 49(5), 1227-1235

We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically ... [more ▼]

We consider the discrete-time dynamics of a network of agents that exchange information according to a nearest-neighbour protocol under which all agents are guaranteed to reach consensus asymptotically. We present a fully decentralised algorithm that allows any agent to compute the final consensus value of the whole network in finite time using the minimum number of successive values of its own state history. We show that the minimum number of steps is related to a Jordan block decomposition of the network dynamics, and present an algorithm to compute the final consensus value in the minimum number of steps by checking a rank condition of a Hankel matrix of local observations. Furthermore, we prove that the minimum number of steps is related to graph theoretical notions that can be directly computed from the Laplacian matrix of the graph and from the minimum external equitable partition. [less ▲]

Global State Synchronization in Networks of Cyclic Feedback Systems

in IEEE Transactions on Automatic Control (2012), 57(2), 478-483

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback ... [more ▼]

This technical note studies global asymptotic state synchronization in networks of identical systems. Conditions on the coupling strength required for the synchronization of nodes having a cyclic feedback structure are deduced using incremental dissipativity theory. The method takes advantage of the incremental passivity properties of the constituent subsystems of the network nodes to reformulate the synchronization problem as one of achieving incremental passivity by coupling. The method can be used in the framework of contraction theory to constructively build a contracting metric for the incremental system. The result is illustrated for a network of biochemical oscillators. [less ▲]

The circadian oscillator gene GIGANTEA mediates a long-term response of the Arabidopsis thaliana circadian clock to sucrose

in PNAS (2011), 108(12), 51045109

Circadian clocks are 24-h timing devices that phase cellular responses; coordinate growth, physiology, and metabolism; and anticipate the day–night cycle. Here we report sensitivity of the Arabidopsis ... [more ▼]

Circadian clocks are 24-h timing devices that phase cellular responses; coordinate growth, physiology, and metabolism; and anticipate the day–night cycle. Here we report sensitivity of the Arabidopsis thaliana circadian oscillator to sucrose, providing evidence that plant metabolism can regulate circadian function. We found that the Arabidopsis circadian system is particularly sensitive to sucrose in the dark. These data suggest that there is a feedback between the molecular components that comprise the circadian oscillator and plant metabolism, with the circadian clock both regulating and being regulated by metabolism. We used also simulations within a three-loop mathematical model of the Arabidopsis circadian oscillator to identify components of the circadian clock sensitive to sucrose. The mathematical studies identified GIGANTEA (GI) as being associatedwith sucrose sensing. Experimental validation of this prediction demonstrated that GI is required for the full response of the circadian clock to sucrose. We demonstrate that GI acts as part of the sucrose-signaling network and propose this role permits metabolic input into circadian timing in Arabidopsis. [less ▲]