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Deformation formulas and boundary control problems of first-order Volterra integro-differential equations with nonlocal boundary conditions (2013)

Nakagiri, S.-I.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: This paper deals with the boundary control problems for the system described by first-order hyperbolic partial integro-differential equations with nonlocal boundary conditions by means of the deformation formulas. It is shown that the associated operator with nonlocal terms generates a C 0 -semigroup and the system defines an abstract boundary control system in L 2 -space. On the basis of the construction of integral kernel function, the ordinal and evolutional deformation formulas are established for a general class of Volterra integro-differential equations with nonlocal terms. By applying a special form of the formulas, a design of feedback boundary control law is given, which makes the scalar boundary control system null controllable in finite time. Furthermore, the null controllability result is extended to coupled nonsymmetric first-order hyperbolic systems by using appropriate linear transformations. Applications to physically important coupled systems are also given.

Print ISSN: 0265-0754

Electronic ISSN: 1471-6887

Topics: Mathematics

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Adaptation of sliding modes (2013)

Bartolini, G., Levant, A., Plestan, F., Taleb, M., Punta, E.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: Adaptive sliding-mode strategies of first and second sliding orders are developed for single-input single-output systems of the first and second relative degrees, respectively. Since the only concrete known uncertainty bounds are assumed to be the upper bounds of logarithmic derivatives, no standard sliding-mode technique can solve the problem.

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Electronic ISSN: 1471-6887

Topics: Mathematics

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Guaranteed cost control for uncertain stochastic hybrid complex delayed networks (2013)

Li, S., Tang, W., Zhang, J., Zhang, W.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: This paper investigates the robust guaranteed cost control problem of uncertain stochastic hybrid complex delayed networks with Markovian jump parameters and external stochastic disturbances. The main goal of this paper is to design state-feedback controllers such that the complex networks achieve mean-square stability, and meanwhile the optimal upper bound of cost function is guaranteed. Based on Lyapunov–Krasovskii stability theory and Dynkin's formula, a sufficient condition for the existence of the optimal guaranteed cost control law is given in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method.

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Electronic ISSN: 1471-6887

Topics: Mathematics

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Forced second-order consensus in directed networks with time delays (2013)

Rong, L., Xu, S., Xie, D., Zou, Y.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: This paper investigates the forced second-order consensus problem in directed networks with time delays. First, a general forced consensus protocol is studied and some sufficient and necessary conditions on control parameters are obtained to guarantee the forced consensus; based on these conditions, several convenient methods for choosing parameters are provided. Then, by analysing the poles of the closed-loop system, the delay sensitivity of the protocol is investigated. The maximal upper bound of the allowable delays is provided. Simulation examples are presented to illustrate the effectiveness of the theoretical results.

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Electronic ISSN: 1471-6887

Topics: Mathematics

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On two natural extensions of Vinnicombe's metric: their non-coincidence yet equivalence on stabilizable plants over A+ (2013)

Rupp, R., Sasane, A.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: Let A + be the ring of Laplace transforms of complex Borel measures on R with support in [0,+) which do not have a singular nonatomic part. We compare the -metric d A + for stabilizable plants over A + given in Ball & Sasane (2012, Complex Analysis and Operator Theory , 6 , 65–89). with yet another metric d H | A + , namely the one induced by the metric d H for the set of stabilizable plants over H given in Sasane (2012, Mathematical Control and Related Fields , 2 , 29–44). Both d A + and d H coincide with the classical Vinnicombe metric defined for rational transfer functions, but we show here by means of an example that these two possible extensions of the classical -metric for plants over A + do not coincide on the set of stabilizable plants over A + . We also prove that they nevertheless give rise to the same topology on stabilizable plants over A + .

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Topics: Mathematics

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Robust stability and stabilization of uncertain discrete singular time-delay systems based on PNP Lyapunov functional (2013)

Weng, F., Mao, W.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: The problems of delay-dependent robust stability and stabilization for discrete singular time-delay systems with norm-bounded uncertainties are investigated in this paper. By introducing some non-positive items to compensate the redundant energy caused by the positive items, an improved Lyapunov functional, namely partial non-positive (PNP) Lyapunov functional, is presented for achieving less conservative results. On the basis of the forward difference of this PNP Lyapunov functional, modified strict linear matrix inequality (LMI)-based delay-dependent conditions are established for the singular time-delay system to be regular, causal and stable. By solving these LMIs, an explicit expression for the desired state-feedback control law is obtained. Finally, numerical examples are given to illustrate that the proposed results are effective and less conservative than the existing ones.

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Topics: Mathematics

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Estimator design for networked control systems with nonstationary packet dropouts (2013)

Mahmoud, M. S.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: In this paper, we investigate the problem of estimating the states of networked systems that involves random measurement and subject to nonstationary packet dropouts. The developed estimation algorithm is suitable for networked systems with any type of delays. Using the delay information in the measurement model, new and less conservative estimation conditions for networked systems are derived. The criterion is formulated in terms of linear matrix inequalities. An illustrative example is presented to show the applicability of the proposed design technique.

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Topics: Mathematics

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Passivity analysis for switched generalized neural networks with time-varying delay and uncertain output (2013)

Hu, M., Cao, J., Yang, Y., Hu, A.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2013-09-18

Description: This paper is concerned with the issue of passivity analysis for switched generalized neural networks (SGNNs). Parametric uncertainty is considered and assumed to be time-variant and norm bounded. We first give the passivity condition for SGNNs without uncertainties, and then extend the result to the cases with time-varying parametric uncertainties both in network parameters and output matrices. By using the Lyapunov–Krasovskii functional and some analysis techniques, the passivity criteria are presented in terms of linear matrix inequalities. Two numerical examples are given to show the effectiveness of the theoretical results.

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Topics: Mathematics

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Lyapunov-based settling time estimate and tuning for twisting controller (2012)

Oza, H. B., Orlov, Y. V., Spurgeon, S. K.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2012-12-11

Description: A novel switched control synthesis is developed and an upper bound on the settling time is obtained for a robust second-order sliding mode controller. The framework is based on step-by-step application of classical linear feedback design and the well-known ‘twisting’ controller. The underlying philosophy is to utilize globally exponentially stable linear feedback so that the trajectories enter an arbitrarily defined domain of attraction in finite time and then switch to the ‘twisting’ controller so that the trajectories settle at the origin in finite time. The proposed method is applied to the linear inverted pendulum to obtain an upper bound on the settling time of the closed-loop system in a full-state feedback setting in the presence of disturbances. Tuning rules to achieve the desired settling time are explicitly derived without recourse to the differential inequality of the Lyapunov function.

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Topics: Mathematics

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Consensus of multi-agent systems on time scales (2012)

Shen, J., Cao, J.

Oxford University Press

In: IMA Journal of Mathematical Control and Information

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Publication Date: 2012-12-11

Description: This paper studies consensus problems of multi-agent systems over a directed network topology on time scales. Based on the theory of time scales, we discuss continuous-time and discrete-time consensus protocols under a unified framework by employing a Lyapunov-like technique. We find that consensus can be realized exponentially if the graininess function of the time scale is bounded and the coupling strength of the network is sufficiently small. Many existing results of both continuous-time and discrete-time consensus conditions are shown to be special cases of this paper. Moreover, our derived results contain both continuous-time and discrete-time cases simultaneously. Finally, several illustrative examples are presented to show the effectiveness of the theoretical results.

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Topics: Mathematics

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