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Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems Aalto, Atte in IMA Journal of Mathematical Control and Information (2018), 35(suppl_1), 51-72 We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step ... [more ▼] We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step estimate that takes values in a fixed finite dimensional subspace of the system’s state space — consider, for example, a Finite Element space. The structure of the obtained state estimator is like the Kalman filter, but with an additional optimal embedding operator mapping from the reduced space to the original state space. We derive a Riccati difference equation for the error covariance and use sensitivity analysis to obtain a bound for the error of the state estimate due to the state space discretization. [less ▲] Detailed reference viewed: 166 (17 UL)An application of linear algebra theory in networked control systems: stochastic cyber-attacks detection approach Li, Yumei ; Voos, Holger ; et al in IMA Journal of Mathematical Control and Information (2015) Based on the traditional linear algebra theory, this paper propose the attack detection schemes for networked control systems (NCSs) under single stochastic cyber-attack and multiple stochastic cyber ... [more ▼] Based on the traditional linear algebra theory, this paper propose the attack detection schemes for networked control systems (NCSs) under single stochastic cyber-attack and multiple stochastic cyber-attacks aiming at multiple communication channels of NCSs, respectively. The focus is on designing an anomaly detector for NCSs under cyber-attacks. First, we construct a model of stochastic NCSs with stochastic cyber-attacks which satisfy the Markovian stochastic process. And we also introduced the stochastic attack models that NCSs are possibly exposed to. Next, based on the frequency-domain transformation technique and linear algebra theory, we propose the algebraic detection schemes for possible stochastic cyber-attacks. We transform the detector error dynamics into algebraic equations. By applying the presented approaches, residual information that is caused by different attacks is, respectively, obtained and anomalies on the control system are detected. In addition, sufﬁcient and necessary conditions guaranteeing the detectability of the stochastic cyber-attacks are obtained. The presented detection approaches in this paper are simple, straightforward and easy to implement. The aim of this work is to use traditional mathematics tools to solve new problems that arise from the complex NCSs. Finally, two simulation examples are provided. The simulation results underline that the detection approaches are effective and feasible in practical application. [less ▲] Detailed reference viewed: 198 (10 UL)On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters ; ; Voos, Holger et al in IMA Journal of Mathematical Control and Information (2015) This paper presents the robust stabilization problem of linear and non-linear fractional-order systems with non-linear uncertain parameters. The uncertainty in the model appears in the form of the ... [more ▼] This paper presents the robust stabilization problem of linear and non-linear fractional-order systems with non-linear uncertain parameters. The uncertainty in the model appears in the form of the combination of ‘additive perturbation’ and ‘multiplicative perturbation’. Sufficient conditions for the robust asymptotical stabilization of linear fractional-order systems are presented in terms of linear matrix inequalities (LMIs) with the fractional-order 0<α<1. Sufficient conditions for the robust asymptotical stabilization of non-linear fractional-order systems are then derived using a generalization of the Gronwall–Bellman approach. Finally, a numerical example is given to illustrate the effectiveness of the proposed results. [less ▲] Detailed reference viewed: 140 (3 UL) |
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