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Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976) established necessary and sufficient conditions for the controllability of homogeneous networked systems where the individual nodes are linear time-invariant (LTI) systems and the network topology matrix is diagonalizable. In this paper, we consider a class of heterogeneous networked systems having triangularizable network topology. Here, we establish a result which gives necessary and sufficient conditions for controllability of a class of heterogeneous systems, which generalizes the result of Hao et al. (Int J Robust Nonlinear Control 28(5):1778–1788, 1976). Also, we provide some necessary conditions for the controllability of general heterogeneous networked systems having some restrictions on the network topology matrix. Theoretical results are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

This paper examines the controllability of a class of heterogeneous networked systems where the nodes are linear time-invariant systems (LTI), and the network topology is triangularizable. The literature contains necessary and sufficient conditions for the controllability of such systems where the control input matrices are identical in each node. Here, we extend this result to a class of heterogeneous systems where the control input matrices are distinct in each node. Additionally, we discuss the controllability of a more general system with triangular network topology and obtain necessary and sufficient conditions for controllability. Theoretical results are supplemented with numerical examples. [ABSTRACT FROM AUTHOR]

This work studies the controllability property of consensus problem of multi-agent networks in leader–follower framework over the random-walk normalised Laplacian dynamics on a continuous time-scale. The interconnection topology is time-invariant. Graphical interpretations are provided to gain more insight on the interactions between the agents of the network, which also helps in designing the communication protocols. Using the tools of algebraic graph theory and spectral analysis, we propose several necessary and sufficient controllability conditions for the dynamics of followers' states through the selected leaders. The formula to determine the minimum number of leaders which ensures the controllability of the network (in leader–follower framework) is presented, and is used to find such controlling leaders in some standard networks. It is confirmed that the choice of selecting the minimum number of controlling leaders in the network depends not only on the interconnection topology graph, but also on the underlying dynamics of the network. Furthermore, it is confirmed that the least possible number of controlling leaders which control the dynamics of rest of the agents (the followers) in the network is greater or equals to the least possible number of external agents which control the dynamics of all agents in the network. [ABSTRACT FROM AUTHOR]

This article proposes various sufficient controllability criteria for a class of networked higher dimensional systems under the influence of impulses exhibited by their state functions. The conditions obtained are characterised in terms of impulse matrices, inner coupling matrix, network topology and the system matrices. It is demonstrated that Kalman's rank condition and Popov–Belevitch–Hautus (PBH)-rank condition are just sufficient conditions for the controllability of these systems, but not necessary unlike as that of the networked systems without impulses. Various numerical examples are provided to validate the theoretical results. Further, the control function and controlled trajectory are plotted for the systems considered, that helps to estimate the cost of controller. [ABSTRACT FROM AUTHOR]

This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthe- sised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are pro- vided that demonstrate|for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider a nonlinear system governed by fractional differential equations in a Banach space. Used the semigroup theory of linear operators and Gronwal's inequality to show the trajectory controllability of the system. Also, we extend our results to nonlocal and integro-differential equations. Finally, we give an example to illustrate the applications of these results. [ABSTRACT FROM AUTHOR]

In this article, the existence and uniqueness of generalized nonlinear impulsive evolution equation is derived. The proposed system is modeled with nonlinear perturbed force which changes after every impulse. The Banach contraction principle is applied to prove the existence and uniqueness of mild solution. The existence and uniqueness of classical solution is obtained by fixing the impulse and the conditions in which mild solution becomes classical solution also obtained. Finally an example is illustrated to the effectiveness of main results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some sufficient conditions for the complete controllability of linear and semilinear impulsive systems. For the semilinear systems, we assume that nonlinearities are Lipschitzian type. We invoke the tools of nonlinear functional analysis and fixed point theorems to establish the results. The results are also compared with the existing results in the literature in order to show the effectiveness of the results obtained. Few illustrative examples are provided to substantiate the results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, sufficient conditions for trajectory controllability of nonlinear fractional integro‐differential systems involving Caputo fractional derivative of order α∈(1,2] in finite and as well as in infinite dimensional Hilbert spaces are obtained. Our tools of study include set‐valued functions, theory of monotone operators and α‐order cosine family of operators. The main results are well illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish the controllability conditions for a finite-dimensional dynamical control system modelled by a linear impulsive matrix Lyapunov ordinary differential equations having multiple constant time-delays in control for certain classes of admissible control functions. We characterize the controllability property of the system in terms of matrix rank conditions and are easy to verify. The obtained results are applicable for both autonomous (time-invariant) and non-autonomous (time-variant) systems. Two numerical examples are given to illustrate the theoretical results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate controllability of fractional dynamical systems involving monotone nonlinearities of both Lipchitzian and non-Lipchitzian types. We invoke tools of nonlinear analysis like fixed point theorem and monotone operator theory to obtain controllability results for the nonlinear system. Examples are provided to illustrate the results. Control-lability results of fractional dynamical systems with monotone nonlinearity is new. [ABSTRACT FROM AUTHOR]

In this article, we study an inverse problem of reconstructing a space dependent coefficient in a generalized Korteweg-de Vries (KdV) equation arising in physical systems with variable topography from final time overdetermination data. First the identification problem is transformed into an optimization problem by using optimal control framework and existence of a minimizer for the cost functional is established. Then we prove a stability estimate for retrieving the unknown coefficient in KdV equation with the upper bound of given measurements. The local uniqueness of the coefficient is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, optimal control problem described by discrete-time linear Volterra system is studied by the conventional minimization method of Lagrange multipliers. [ABSTRACT FROM AUTHOR]