Synchronous interval observer design for switched LPV systems using multiple quadratic ISS-Lyapunov functions
03 Jul 2017-pp 388-393
TL;DR: The proposed approach is based on switched interval observers which provide guaranteed lower and upper bounds allowing to evaluate the set of admissible values of the real state vector and is applied to robust estimation of vehicle lateral dynamics.
Abstract: This paper deals with the problem of robust state estimation for switched LPV continuous-time systems with measurable and unmeasurable scheduling parameters. The switching law is assumed to be uncontrollable but online available, while the unmeasurable varying parameters are assumed to be bounded with a priori known bounds. The proposed approach is based on switched interval observers which provide guaranteed lower and upper bounds allowing to evaluate the set of admissible values of the real state vector. The stability and positivity conditions of the switched interval error are expressed in terms of linear matrix inequalities (LMIs), which have been established using multiple quadratic ISS-Lyapunov functions (MQLF) and average dwell-time concept. In order to enhance estimation accuracy and robustness an explicit bound of the interval error is guaranteed. The proposed approach is applied to robust estimation of vehicle lateral dynamics. Tests are conducted on experimental data in order to prove the effectiveness of the proposed switched interval observer.
Citations
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01 Jan 2014
TL;DR: Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.
Abstract: Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.
65 citations
TL;DR: By adopting multiple quadratic ISS-Lyapunov function and average dwell time concept, new and less conservative stability conditions are derived, and a set of numerical feasible linear matrix inequalities (LMIs) are given.
27 citations
TL;DR: This paper is concerned with the robust passive fault detection problem for switched continuous-time linear parameter-varying systems with mensurable and unmeasurable scheduling parameters, and the designed interval observer is designed to estimate the set of admissible state values.
Abstract: This paper is concerned with the robust passive fault detection problem for switched continuous-time linear parameter-varying systems with mensurable and unmeasurable scheduling parameters. A switched Takagi–Sugeno (TS) interval observer is designed to estimate the set of admissible state values. Using multiple fuzzy input to state stability-Lyapunov function and average dwell time (ADT) concept, sufficient conditions to guarantee the convergence and the robustness of the proposed observer are obtained. These conditions are formulated as a linear matrix inequality (LMI) problem. In contrast to the existing results based on multiple Lyapunov function and ADT switching, the derived conditions lead to less conservative LMIs characterization. Subsequently, the residual intervals are generated using the designed interval observer and used directly for fault detection (FD) decision making. Finally, the proposed methodology is tested using two examples. First, an academic example is used to illustrate the obtained relaxation. Second, a nonlinear vehicle model corrupted by faults is considered. Longitudinal velocity and cornering stiffness coefficients are treated, respectively, as the measurable and unmeasurable scheduling parameters. Simulation results based on experimental data show the effectiveness of the proposed FD schema.
20 citations
Cites background from "Synchronous interval observer desig..."
...Definition 3: [27] For a switching signal σ(t) and any t2 > t1 > t0 , let Nσ (t1 , t2) be the number of switching over the interval [t1 , t2)....
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...Generally and as stated in [15], stability under restricted switching with ADT method (See for instance [28], [27], and references therein) needs the conditions (17), (18), and an additional condition as Vi(x(t)) ≤ μVl(x(t)), μ > 1, i = l, i, l ∈ I....
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TL;DR: In this article, the authors propose an interval-based state estimation method for nonlinear systems, based on a parameter bounding approach that is implemented by means of a correlation analysis as well as a suitable principle axes transformation of the parameter space.
6 citations
Cites background from "Synchronous interval observer desig..."
...(10) In previous work, Ifqir et al. (2017); Rauh et al. (2018); Ifqir et al. (2019), it was considered that the individual uncertain entries in the system matrix A (x,p) as well as in the input vector b (x,p) are independent of each other....
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27 Jun 2018
TL;DR: Results show that the proposed estimation scheme succeeds to appropriately estimate the upper and lower bounds of vehicle lateral dynamics despite of the presence of unknown inputs.
Abstract: A systematic design methodology for interval estimation of switched uncertain linear systems subject to uncertainties and unknown inputs is presented. The uncertainties under consideration are assumed to be unknown but bounded with a priori known bounds. The proposed observer is used to robustly estimate the vehicle yaw rate and lateral velocity using a vision system measurement. The road curvature is treated as an unknown input and a linear adaptive tire model is considered to take into account the changes of the road adhesion. Sufficient conditions allowing the design of such observer are derived using Multiple Quadratic ISS-Lyapunov function and an LMIs (Linear Matrix Inequalities) formulation is obtained. Performance of the algorithm is evaluated using vehicle real data, results show that the proposed estimation scheme succeeds to appropriately estimate the upper and lower bounds of vehicle lateral dynamics despite of the presence of unknown inputs.
4 citations
Cites background or methods from "Synchronous interval observer desig..."
...[5] For a switching signal σ(t) and any t2 > t1 > t0, let Nσ(t1, t2) be the number of switching over the interval [t1, t2)....
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...Note that, an interval observer for switched LPV (Linear Parameter Varying) systems was proposed in [5] with application to vehicle lateral dynamics estimation....
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...It should be noticed that the ADT method proposed in [10], [5] needs the conditions (4)-(5) and an additional condition as...
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References
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TL;DR: In this paper, the authors survey three basic problems regarding stability and design of switched systems, including stability for arbitrary switching sequences, stability for certain useful classes of switching sequences and construction of stabilizing switching sequences.
Abstract: By a switched system, we mean a hybrid dynamical system consisting of a family of continuous-time subsystems and a rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.
3,566 citations
"Synchronous interval observer desig..." refers background in this paper
...The stability problem has been widely studied in the literature (see for example [17], [19] and references therein) and two main stability issues have been addressed....
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Book•
01 Mar 1995
TL;DR: Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equation Quasimonoteone systems of parabolic equations A competition model Appendix Bibliography as discussed by the authors
Abstract: Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.
2,282 citations
07 Dec 1999
TL;DR: In this article, it was shown that scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of adaptive control systems.
Abstract: It is shown that switching among stable linear systems results in a stable system provided that switching is "slow-on-the-average". In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.
2,197 citations
"Synchronous interval observer desig..." refers background in this paper
...[2] For a switching signal σ(t) and any t2 > t1 > t0, let Nσ(t1, t2) be the number of switching over the interval [t1, t2)....
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...Time (ADT)) and Multiple Lyapunov Functions ([2], [9])....
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01 Jan 1999
TL;DR: In this article, it was shown that switching among stable linear systems results in a stable system provided that switching is slow-on-the-average, i.e., the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small.
Abstract: It is shown that switching among stable linear systems results in a stable system provided that switching is \slow-on-the-average." In particular, it is proved that exponential stability is achieved when the number of switches in any nite interval grows linearly with the length of the interval, and the growth rate is suciently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.
2,028 citations
01 Jan 2005
TL;DR: Schur complements in statistics and probability have been used in Numerical Analysis as mentioned in this paper, where the Schur Complement has been applied in statistical and probability analysis. But their application is limited to statistical analysis.
Abstract: Historical Introduction: Issai Schur and the Early Development of the Schur Complement.- Basic Properties of the Schur Complement.- Eigenvalue and Singular Value Inequalities of Schur Complements.- Block Matrix Techniques.- Closure Properties.- Schur Complements and Matrix Inequalities: Operator-Theoretic Approach.- Schur complements in statistics and probability.- Schur Complements and Applications in Numerical Analysis.
1,465 citations
"Synchronous interval observer desig..." refers methods in this paper
...Applying the Schur complement argument [26] to (25), we obtain the following expression, [ μPj In In P −1 i ]...
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