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 ▲]

Distributed reconstruction of nonlinear networks: An ADMM approach

in Proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC 2014) (2014)

In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional ... [more ▼]

In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of large-scale nonlinear networks. In (Pan et al. (2013)), a nonlinear network reconstruction problem was formulated as a nonconvex optimisation problem based on the combination of a marginal likelihood maximisation procedure with sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative reweighted lasso algorithm was derived to solve the initial nonconvex optimisation problem. By exploiting the structure of the objective function of this reweighted lasso algorithm, a distributed algorithm can be designed. To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems. To illustrate the effectiveness of the proposed methods, we use our approach to identify a network of interconnected Kuramoto oscillators with different network sizes (500∼100,000 nodes). [less ▲]

Real-time Fault Diagnosis for Large-Scale Nonlinear Power Networks

in The proceedings of the IEEE 52nd Annual Conference on Decision and Control (2013)

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 optimisation-based formulation of the fault identification problem. An iterative reweighted ℓ1-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 ▲]

Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

in International Journal of Robust and Nonlinear Control (2010), 20(18), 2093-2107

Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal ... [more ▼]

Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design. [less ▲]

On multistability of delayed genetic regulatory networks with multivariable regulation functions

in Mathematical Biosciences (2010), 228(1), 100-109

Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and ... [more ▼]

Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov–Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲]