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piecewise-linear lyapunov functions for structural stability of biochemical networks

AUTOMATICA 2014年第10期50卷 2482-2493页

作者： Blanchini, Franco Giordano, Giulia Univ Udine Dipartimento Matemat & Informat I-33100 Udine Italy

We consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates, namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values. We investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral lyapunov function proper to the considered network structure. A numerical recursive procedure is devised to test stability. For a wide class of mono- and bimolecular reaction networks, which we name unitary, the procedure is shown to be very efficient since, due to the particular structure of the problem, it requires iterations in the space of integer-valued matrices. We also consider a similar, less conservative procedure that allows us to test, even when the lyapunov function cannot be found, whether the system evolution is structurally bounded. In this case, we absorb the equations in a positive linear differential inclusion. To show the effectiveness of the proposed procedure, we report the outcomes of both a stability and a boundedness test, for many non-trivial biochemical reaction networks, and we analyze well established models in the literature. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Biochemical networks Biochemical systems Structural stability Global stability piecewise-linear lyapunov functions Graph

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Robust constrained stabilization of a boost DC-DC converter with lyapunov-based control and piecewise-linear lyapunov functions 13

Robust constrained stabilization of a boost DC-DC converter ...

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13th European Control Conference (ECC)

作者： Yfoulis, C. Giaouris, D. Stergiopoulos, F. Ziogou, C. Voutetakis, S. Papadopoulou, S. Alexander Technol Educ Inst Thessaloniki Automat Engn Dept Thessaloniki Greece Ctr Res & Technol Hellas CERTH CPERI Thermi Greece

ISBN: (纸本)9783952426913

In this paper we describe a new methodology for designing robust and efficient state-feedback control laws for a switched-mode boost DC-DC power converter. The proposed design is adopting the so-called lyapunov-based control law and attempts to solve the robust constrained stabilization problem under large parameter variations. With the methodology proposed static or switching state-feedback control laws are generated so that a number of further key issues are addressed, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, robustness to supply voltage variations, set-point and load changes. The control design procedure is based on the generation of controlled invariant polytopes (safety domains) using piecewise-linear lyapunov functions. The proposed technique is numerically evaluated using the exact switched model of the converter.

关键词： DC-DC boost converter constrained stabilization piecewise-linear lyapunov functions lyapunov-based control

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Constrained switching stabilization of a dc-dc boost converter using piecewise-linear lyapunov functions

Constrained switching stabilization of a dc-dc boost convert...

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21st Mediterranean Conference on Control and Automation (MED)

作者： Yfoulis, Christos Giaouris, Damian Voutetakis, Spyridon Papadopoulou, Simira Alexander Technol Educ Inst Thessaloniki Dept Automat Thessaloniki Greece

ISBN: (纸本)9781479909957;9781479909971

This paper describes a new methodology for designing robust and efficient control laws for power converters. In addition to guaranteed closed-loop robust stability, the proposed design is capable of addressing a number of further key issues, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, and robustness to supply voltage variations and setpoint changes. The control design is of a set-theoretic nature. The iterative algorithms used for controller generation are based on the ray-gridding approach, that generates piecewise-linear lyapunov functions and corresponding controlled invariant polytopes, induced by systematic conic decompositions of the state-space and state-dependent switching control actions. The proposed technique is evaluated on a boost converter case study. Simulation results in the MATLAB/SIMULINK (TM) environment are reported. The bifurcation behaviour of the system is further studied by numerical and analytical nonlinear stability analysis.

关键词： DC-DC boost converter ray-gridding constrained stabilization piecewise-linear lyapunov functions

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Constrained switching stabilization of a dc-dc boost converter using piecewise-linear lyapunov functions

Constrained switching stabilization of a dc-dc boost convert...

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Mediterranean Conference on Control & Automation

作者： Christos Yfoulis Damian Giaouris Spyridon Voutetakis Simira Papadopoulou Department of Automation Alexander Technological Educational Institute of Thessaloniki Chemical Process Engineering Research Institute (C.P.E.R.I.) Centre for Research and Technology Hellas (CE.R.T.H.) Thermi-Thessaloniki

ISBN: (纸本)9781479909964

This paper describes a new methodology for designing robust and efficient control laws for power converters. In addition to guaranteed closed-loop robust stability, the proposed design is capable of addressing a number of further key issues, i.e. low complexity of the implementation, accurate nonlinear dynamics incorporation, nonconservative handling of hard state and control constraints, and robustness to supply voltage variations and setpoint changes. The control design is of a set-theoretic nature. The iterative algorithms used for controller generation are based on the ray-gridding approach, that generates piecewise-linear lyapunov functions and corresponding controlled invariant polytopes, induced by systematic conic decompositions of the state-space and state-dependent switching control actions. The proposed technique is evaluated on a boost converter case study. Simulation results in the MATLAB/SIMULINK environment are reported. The bifurcation behaviour of the system is further studied by numerical and analytical nonlinear stability analysis.

关键词： DC-DC boost converter Ray-gridding Constrained stabilization piecewise-linear lyapunov functions

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Polyhedral lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular

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AUTOMATICA 2017年 86卷 183-191页

作者： Blanchini, Franco Giordano, Giulia Univ Udine Dipartimento Sci Matemat Informat & Fis Via Sci 206 I-33100 Udine Italy Delft Univ Technol Delft Ctr Syst & Control Mekelweg 2 NL-2628 CD Delft Netherlands

For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral lyapunov function (PLF) implies structural (i.e., parameter free) local stability. Global structural stability is ensured under the additional assumption that each of the variables (chemical species concentrations in CRNs) is subject to a spontaneous infinitesimal dissipation. This paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation, showing that the existence of a PLF structurally ensures global convergence if and only if the system Jacobian passes a structural non-singularity test. It is also shown that, if the Jacobian is structurally non-singular, under positivity assumptions for the system partial derivatives, the existence of an equilibrium is guaranteed. For systems subject to positivity constraints, it is shown that, if the system admits a PLF, under structural non-singularity assumptions, global convergence within the positive orthant is structurally ensured, while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise-linear-in-rate lyapunov function. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Dynamical networks piecewise-linear lyapunov functions Structural stability Global stability Chemical reaction networks

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Robust constrained stabilization of boost DC-DC converters through bifurcation analysis

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CONTROL ENGINEERING PRACTICE 2015年 35卷 67-82页

作者： Yfoulis, C. Giaouris, D. Stergiopoulos, F. Ziogou, C. Voutetakis, S. Papadopoulou, S. Alexander Technol Educ Inst Thessaloniki Automat Engn Dept Thessaloniki 57400 Greece Ctr Res & Technol Hellas CE RTH Chem Proc Engn Res Inst GR-57001 Thessaloniki Greece

This paper proposes a new methodology for designing robust affine state-feedback control laws, so that wide-range safe and efficient operation of switched-mode DC-DC boost converters is guaranteed. Several undesirable nonlinear phenomena such as unstable attractors and subharmonic oscillations are avoided through bifurcation analysis based on the bilinear averaged model of the converter. The control design procedure also relies on constrained stabilization principles and the generation of safety domains using piecewise linear lyapunov functions, so that robustness to supply voltage and output load variations is ensured, while input saturation is avoided and additional state constraints are also respected. The technique has been numerically and experimentally validated. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： DC-DC boost converter Bifurcation analysis Constrained stabilization piecewise-linear lyapunov functions

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Structural Stability of Biochemical Networks: Quadratic vs. Polyhedral lyapunov functions

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IFAC-PapersOnLine 2015年第14期48卷 278-283页

作者： Franco Blanchini Giulia Giordano Dipartimento di Matematica e Informatica Universita degli Studi di Udine Via delle Scienze 206 33100 Udine Italy

Due to the intrinsic uncertainty and variability affecting biochemical reaction networks, it is fundamental to assess their structural stability, i.e., to establish if all the networks having a given structure are stable independent of specific parameter values. For basic motifs in biochemical networks, we show that stability cannot be structurally proved by quadratic lyapunov functions. However, structural stability of these motifs can be shown resorting to piecewise-linear lyapunov functions, based on the results by Blanchini and Giordano (2014), who provide a theoretical framework and efficient numerical methods to evaluate structural stability of biochemical reaction networks with monotone reaction rates.

关键词： biochemical networks biochemical systems structural stability quadratic lyapunov functions piecewise-linear lyapunov functions graph

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