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Conformal mapping and inverse conductivity problem with one measurement

Marc Dambrine, Djalil Kateb (2007)

ESAIM: Control, Optimisation and Calculus of Variations

This work deals with a two-dimensional inverse problem in the field of tomography. The geometry of an unknown inclusion has to be reconstructed from boundary measurements. In this paper, we extend previous results of R. Kress and his coauthors: the leading idea is to use the conformal mapping function as unknown. We establish an integrodifferential equation that the trace of the Riemann map solves. We write it as a fixed point equation and give conditions for contraction. We conclude with a series...

Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane

Yuri L. Sachkov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.

Consensus and trajectory tracking of SISO linear multi-agent systems under switching communication topologies and formation changes

Carlos López-Limón, Javier Ruiz, Alejandro Cervantes-Herrera, Antonio Ramírez-Treviño (2013)

Kybernetika

The simultaneous problem of consensus and trajectory tracking of linear multi-agent systems is considered in this paper, where the dynamics of each agent is represented by a single-input single-output linear system. In order to solve this problem, a distributed control strategy is proposed in this work, where the trajectory and the formation of the agents are achieved asymptotically even in the presence of switching communication topologies and smooth formation changes, and ensuring the closed-loop...

Consensus of heterogeneous multi-agent systems with uncertain DoS attack: Application to mobile stage vehicles

Wen-Hai Yu, Hong-Jie Ni, Hui Dong, Dan Zhang (2020)

Kybernetika

In this paper, the consensus of heterogeneous multi-agent systems (MASs) with uncertain Deny-of-Service (DoS) attack strategies is studied. In our system, all agents are time synchronized and they communicate with each other with a constant sampling period normally. When the system is under attack, all agents use the hold-input mechanism to update the control protocol. By assuming that the attack duration is upper bounded and the occurrence of the attack follows a Markovian jumping process, the...

Consensus seeking in multi-agent systems with an active leader and communication delays

Lixin Gao, Yutao Tang, Wenhai Chen, Hui Zhang (2011)

Kybernetika

In this paper, we consider a multi-agent consensus problem with an active leader and variable interconnection topology. The dynamics of the active leader is given in a general form of linear system. The switching interconnection topology with communication delay among the agents is taken into consideration. A neighbor-based estimator is designed for each agent to obtain the unmeasurable state variables of the dynamic leader, and then a distributed feedback control law is developed to achieve consensus....

Consensus seeking of delayed high-order multi-agent systems with predictor-based algorithm

Cheng-Lin Liu, Fei Liu (2018)

Kybernetika

This paper investigates the high-order consensus problem for the multi-agent systems with agent's dynamics described by high-order integrator, and adopts a general consensus algorithm composed of the states' coordination control. Under communication delay, consensus algorithm in usual asynchronously-coupled form just can make the agents achieve a stationary consensus, and sufficient consensus condition is obtained based on frequency-domain analysis. Besides, a predictor-based consensus algorithm...

Consensus-based impact-time-control guidance law for cooperative attack of multiple missiles

Qing Zhu, Xiaoli Wang, Qianyu Lin (2017)

Kybernetika

In this paper, a new guidance problem with the impact time constraint for cooperative attack of multiple missiles is investigated, which can be applied to salvo attack of anti-ship missiles. It can be used to guide multiple missiles to hit a stationary target simultaneously at a desirable impact time. The considered impact time control problem can be transformed into a range tracking problem. Then the range tracking problem can be viewed a consensus problem of multi-missile systems. As the application...

Constrained controllability of nonlinear stochastic impulsive systems

Shanmugasundaram Karthikeyan, Krishnan Balachandran (2011)

International Journal of Applied Mathematics and Computer Science

This paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.

Constrained robust adaptive stabilization for a class of lower triangular systems with unknown control direction

Jianglin Lan, Weijie Sun, Yunjian Peng (2014)

Kybernetika

This paper studies the constrained robust adaptive stabilization problem for a class of lower triangular systems with unknown control direction. A robust adaptive feedback control law for the systems is proposed by incorporating the technique of Barrier Lyapunov Function with Nussbaum gain. Such a controlled system arises from the study of the constrained robust output regulation problem for a class of output feedback systems with the unknown control direction and a nonlinear exosystem. An application...

Constrained stabilization of a dynamic systems: a case study

Franco Blanchini, S. Cotterli, G. Koruza, S. Miani, R. Siagri, Luciano Tubaro (1999)

Kybernetika

In this work we consider the problem of determining and implementing a state feedback stabilizing control law for a laboratory two-tank dynamic system in the presence of state and control constraints. We do this by exploiting the properties of the polyhedral Lyapunov functions, i. e. Lyapunov functions whose level surfaces are polyhedra, in view of their capability of providing an arbitrarily good approximation of the maximal set of attraction, which is the largest set of initial states which can...

Construction of a controller with a generalized linear immersion

Javier Diaz-Vargas, Dennis Tuyub-Puc, Celia Villanueva-Novelo (2011)

Kybernetika

Gröbner bases for modules are used to calculate a generalized linear immersion for a plant whose solutions to its regulation equations are polynomials or pseudo-polynomials. After calculating the generalized linear immersion, we build the controller which gives the robust regulation.

Construction of algebraic and difference equations with a prescribed solution space

Lazaros Moysis, Nicholas P. Karampetakis (2017)

International Journal of Applied Mathematics and Computer Science

This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse...

Construction of sampling and interpolating sequences for multi-band signals. the two-band case

Sergei Avdonin, Anna Bulanova, William Moran (2007)

International Journal of Applied Mathematics and Computer Science

Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.

Continuous dependence on parameters and boundedness of solutions to a hysteresis system

Alexander M. Kamachkin, Dmitriy K. Potapov, Victoria V. Yevstafyeva (2022)

Applications of Mathematics

We analyze an ordinary differential system with a hysteresis-relay nonlinearity in two cases when the system is autonomous or nonautonomous. Sufficient conditions for both the continuous dependence on the system parameters and the boundedness of the solutions to the system are obtained. We give a supporting example for the autonomous system.

Continuous extension of order-preserving homogeneous maps

Andrew D. Burbanks, Colin T. Sparrow, Roger D. Nussbaum (2003)

Kybernetika

Maps f defined on the interior of the standard non-negative cone K in ℝ N which are both homogeneous of degree 1 and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least...

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