J. Goncalves

E. Yeung, J. Goncalves, H. Sandberg et al.

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces the complete computational structure of a system as a common baseline for comparing different simplified representations. Linear systems are then used as a vehicle for comparing and contrasting distinct partial structure representations. Such representations simplify the description of a system's complete computational structure at various levels of fidelity while retaining a full description of the system's input-output dynamic behavior. Relationships between these various partial structure representations are detailed, and the landscape of new realization, minimality, and model reduction problems introduced by these representations is briefly surveyed.

J. Jin, Y. Yuan, A. Webb et al.

Increasing attention has recently been given to the inference of sparse networks. In biology, for example, most molecules only bind to a small number of other molecules, leading to sparse molecular interaction networks. To achieve sparseness, a common approach consists of applying weighted penalties to the number of links between nodes in the network and the complexity of the dynamics of existing links. The selection of proper weights, however, is non-trivial. Alternatively, this paper proposes a novel data-driven method, called GESBL, that is able to penalise both network sparsity and model complexity without any tuning. GESBL combines Sparse Bayesian Learning (SBL) and Group Sparse Bayesian Learning (GSBL) to introduce penalties for complexity, both in terms of element (system order of nonzero connections) and group sparsity (network topology). The paper considers a class of sparse linear time-invariant networks where the dynamics are represented by multivariable ARX models. Data generated from sparse random ARX networks and synthetic gene regulatory networks indicate that our method, on average, considerably outperforms existing state-of-the-art methods. The proposed method can be applied to a wide range of fields, from systems biology applications in signalling and genetic regulatory networks to power systems.

J. Jin, Y. Yuan, W. Pan et al.

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With identifiability of the network guaranteed, this paper presents an identification method that infers both the Boolean structure of the network and the internal dynamics between nodes. Identification is performed directly from data without any prior knowledge of the system, including its order. The proposed method solves the identification problem using Maximum a posteriori estimation (MAP) but with inseparable penalties for complexity, both in terms of element (order of nonzero connections) and group sparsity (network topology). Such an approach is widely applied in Compressive Sensing (CS) and known as Sparse Bayesian Learning (SBL). We then propose a novel scheme that combines sparse Bayesian and group sparse Bayesian to efficiently solve the problem. The resulted algorithm has a similar form of the standard Sparse Group Lasso (SGL) while with known noise variance, it simplifies to exact re-weighted SGL. The method and the developed toolbox can be applied to infer networks from a wide range of fields, including systems biology applications such as signaling and genetic regulatory networks.