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A Sparse Bayesian Approach to the Identification of Nonlinear State-Space Systems Pan, Wei ; ; Goncalves, Jorge et al 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 ▲] Detailed reference viewed: 226 (18 UL)Online Fault Diagnosis for Nonlinear Power Systems Pan, Wei ; ; et al 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 ▲] Detailed reference viewed: 106 (13 UL)Distributed reconstruction of nonlinear networks: An ADMM approach Pan, Wei ; ; 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 ▲] Detailed reference viewed: 63 (1 UL)Inference of switched biochemical reaction networks using sparse bayesian learning Pan, Wei ; ; et al in The proceedings of the 7th European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML/PKDD) (2014) This paper proposes an algorithm to identify biochemical reaction networks with time-varying kinetics. We formulate the problem as a nonconvex optimisation problem casted in a sparse Bayesian learning ... [more ▼] This paper proposes an algorithm to identify biochemical reaction networks with time-varying kinetics. We formulate the problem as a nonconvex optimisation problem casted in a sparse Bayesian learning framework. The nonconvex problem can be efficiently solved using Convex-Concave programming. We test the effectiveness of the method on a simulated example of DNA circuit realising a switched chaotic Lorenz oscillator. [less ▲] Detailed reference viewed: 41 (4 UL)Real-time Fault Diagnosis for Large-Scale Nonlinear Power Networks Pan, Wei ; ; et al 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 ▲] Detailed reference viewed: 52 (0 UL)Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach Pan, Wei ; ; Goncalves, Jorge et al in The proceedings of the 51st IEEE Conference on Decision and Control (2012) Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system ... [more ▼] Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution. [less ▲] Detailed reference viewed: 251 (0 UL)Robust stability of delayed genetic regulatory networks with different sources of uncertainties Pan, Wei ; ; in Asian Journal of Control (2011), 13(5), 645-654 Gene regulation is inherently a stochastic process due to intrinsic and extrinsic noises which cause the fluctuations and uncertainties of kinetic parameters. On the other hand, time delays are usually ... [more ▼] Gene regulation is inherently a stochastic process due to intrinsic and extrinsic noises which cause the fluctuations and uncertainties of kinetic parameters. On the other hand, time delays are usually inevitable due to different biochemical reactions in the genetic regulatory networks (GRNs) which are also affected by noises. Therefore, in this paper, we propose a GRN model that is subject to additive and multiplicative noises as well as time-varying delays. The time-varying delay is assumed to belong to an interval and no restriction on the derivative of the time-varying delay is needed, which allows the delay to be a fast time-varying function. Robust stochastic stability of such GRNs with disturbance attenuation is analyzed by applying the control theory and mathematical tools. Based on the Lyapunov method, new stability conditions are derived in the form of linear matrix inequalities that are dependent on the upper and lower bounds of time delays. An example is employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲] Detailed reference viewed: 57 (0 UL)Monostability and multistability of genetic regulatory networks with different types of regulation functions Pan, Wei ; ; et al in Nonlinear Analysis : Real World Applications (2010), 11(4), 31703185 Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by ... [more ▼] Monostability and multistability are proven to be two important topics in synthesis biology and system biology. In this paper, both monostability and multistability are analyzed in a unified framework by applying control theory and mathematical tools. The genetic regulatory networks (GRNs) with multiple time-varying delays and different types of regulation functions are considered. By putting forward a general sector-like regulation function and utilizing up-to-date techniques, a novel Lyapunov–Krasovskii functional is introduced for achieving delay dependence to ensure less conservatism. A new condition is then proposed for the general stability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the upper and lower bounds of the delays. Our general stability conditions are applicable to several frequently used regulation functions. It is shown that the existing results for monostability of GRNs are special cases of our main results. Five examples are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲] Detailed reference viewed: 32 (0 UL)Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise Pan, Wei ; ; et al 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 ▲] Detailed reference viewed: 48 (0 UL)Multistability of genetic regulatory networks Pan, Wei ; ; in International Journal of Systems Science (2010), 41(1), 107-118 Multistability is found to be an important recurring theme in synthesis biology. In this article, the multistability analysis problem is investigated by applying control theory and mathematical tools ... [more ▼] Multistability is found to be an important recurring theme in synthesis biology. In this article, the multistability analysis problem is investigated by applying control theory and mathematical tools. Both the modelling and analysis issues are discussed. Specifically, the genetic regulatory networks (GRNs) with multistability are modelled as switched systems with interval time-varying delays and parameter uncertainties, where the piecewise-affine models are used to approximate the inherent non-linearities existing in the GRNs. Then, by using a novel Lyapunov functional approach and linear matrix inequality (LMI) techniques, a few delay-dependent criteria for the multistability of such genetic regulatory networks are established in the form of LMIs, which can be readily verified by using standard numerical software. A three-component network and a genetic toggle switch with bistability are employed to illustrate the applicability and usefulness of the developed theoretical results. [less ▲] Detailed reference viewed: 65 (0 UL)On multistability of delayed genetic regulatory networks with multivariable regulation functions Pan, Wei ; ; et al 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 ▲] Detailed reference viewed: 49 (0 UL) |
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