773 research outputs found

    Fault detection and isolation using viability theory and interval observers

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    This paper proposes the use of interval observers and viability theory in fault detection and isolation (FDI). Viability theory develops mathematical and algorithmic methods for investigating the viability constraints characterisation of dynamic evolutions of complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behaviour by using simple sets that approximate the exact set of possible behaviour (in the parameter or state space). In this paper, FDI is based on checking for an inconsistency between the measured and predicted behaviours using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approachPeer ReviewedPostprint (author's final draft

    Backward Reachability Analysis of Perturbed Continuous-Time Linear Systems Using Set Propagation

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    Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that can be steered into the target set or all states that cannot avoid entering it -- the corresponding solutions can be used for controller synthesis and safety verification, respectively. A popular technique for backward reachable set computation solves Hamilton-Jacobi-Isaacs equations, which scales exponentially with the state dimension due to gridding the state space. In this work, we instead use set propagation techniques to design backward reachability algorithms for linear time-invariant systems. Crucially, the proposed algorithms scale only polynomially with the state dimension. Our numerical examples demonstrate the tightness of the obtained backward reachable sets and show an overwhelming improvement of our proposed algorithms over state-of-the-art methods regarding scalability, as systems with well over a hundred states can now be analyzed.Comment: 16 page

    Attenuation of Persistent L∞-Bounded Disturbances for Nonlinear Systems

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    A version of nonlinear generalization of the L1-control problem, which deals with the attenuation of persistent bounded disturbances in L∞-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the L1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the L1-control of a continuous-time system and the l1-control of its Euler approximated discrete-time systems is established
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