Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor

Aksikas, Ilyasse; Winkin, Joseph J.; Dochain, Denis

doi:10.1016/j.sysconle.2006.08.012

Cited by 35 publications

(24 citation statements)

References 9 publications

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“…It follows that the operator (I − λA 0 ) −1 is also compact, as a diagonal matrix of compact operators. Then, by using the strict dissipativity of N 0 the conclusion follows directly from [2], Theorem 4.3.1, pp. 59-60.…”

Section: Definition 51 Let a Be An Operator On A Banach Space X Witmentioning

confidence: 89%

“…By using [6], Corollary 13, p. 126, the asymptotic stability follows from [6], Comment 14, p. 126, since…”

Section: Definition 51 Let a Be An Operator On A Banach Space X Witmentioning

confidence: 99%

“…Now we are interested in the asymptotic stability of the system (5.1) when the operator N 0 is defined on a convex closed subset F ⊂ H. First the following technical concept is recalled: On the other hand, the following result, whose proof can be found in [2,6], is needed. …”

Section: Definition 51 Let a Be An Operator On A Banach Space X Witmentioning

confidence: 99%

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Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

2008

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Abstract. The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential equation in the space variable. Then the latter is applied to the nonlinear model, and the resulting closed-loop system dynamical performances are analyzed. Mathematics Subject Classification.

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Section: Definition 51 Let a Be An Operator On A Banach Space X Witmentioning

confidence: 89%

“…By using [6], Corollary 13, p. 126, the asymptotic stability follows from [6], Comment 14, p. 126, since…”

Section: Definition 51 Let a Be An Operator On A Banach Space X Witmentioning

confidence: 99%

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Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

2008

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“…For example, Riemann invariants are applied in Dick, Gugat, and Leugering (2010) to provide feedback laws for local stability using a Lyapunov function. LaSalle's invariance principle (Aksikas, Winkin, & Dochain, 2007) has also been applied to yield asymptotic stability conditions for semi-linear systems. Note that water hammer mitigation can be viewed as a boundary stabilization problem for the pipeline transmission PDEs.…”

Section: Introductionmentioning

confidence: 99%

Water hammer mitigation via PDE-constrained optimization

Chen

Lin

et al. 2015

Control Engineering Practice

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a b s t r a c tThis paper considers an optimal boundary control problem for fluid pipelines with terminal valve control. The goal is to minimize pressure fluctuation during valve closure, thus mitigating water hammer effects. We model the fluid flow by two coupled hyperbolic PDEs with given initial conditions and a boundary control governing valve actuation. To solve the optimal boundary control problem, we apply the control parameterization method to approximate the time-varying boundary control by a linear combination of basis functions, each of which depends on a set of decision parameters. Then, by using variational principles, we derive formulas for the gradient of the objective function (which measures pressure fluctuation) with respect to the decision parameters. Based on the gradient formulas obtained, we propose a gradient-based optimization method for solving the optimal boundary control problem. Numerical results demonstrate the capability of optimal boundary control to significantly reduce pressure fluctuation.

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“…Among other control methodologies, model predictive control has also been proposed for hyperbolic distributed parameter systems in a number of publications [3,[19][20][21]. Recently, LQ optimal control has been proposed for different classes of hyperbolic PDE model using matrix Riccati differential equation [22,23] and using spectral factorisation and operator Diophantine equation [24,25]. These methods [22][23][24][25] are only suitable for a neighbourhood of operating condition [1].…”

Section: Introductionmentioning

confidence: 99%

Non‐quadratic exponential stabilisation of non‐linear hyperbolic partial differential equation systems

Sadeghi

Vafamand

Babaei

2014

IET Science, Measurement & Technology

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In this study, a new systematic approach is proposed to design the fuzzy controller for a class of Takagi-Sugeno fuzzypartial differential equation (TS fuzzy-PDE) systems which describe the non-linear distributed parameter system formulated by first-order semi-linear hyperbolic PDEs. In this study, non-quadratic Lyapunov function is utilised and some slack matrices are introduced to derive stability conditions in terms of linear matrix inequalities (LMIs). The proposed approach has three main features. First, stability conditions are not derived in the form of spatial differential LMI. Second, conservativeness of LMI conditions is reduced. Third, there is no restriction on the form of semi-linear hyperbolic PDE systems and therefore more semi-linear systems classes can be stabilised. Also, the proposed approach is more suitable for practical implementation compared with the recently published papers.

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Asymptotic stability of infinite-dimensional semilinear systems: Application to a nonisothermal reactor

Cited by 35 publications

References 9 publications

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

Water hammer mitigation via PDE-constrained optimization

Non‐quadratic exponential stabilisation of non‐linear hyperbolic partial differential equation systems

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