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The aging brain undergoes major changes in its topology. The mechanisms by which the brain mitigates age-associated changes in topology to maintain robust control of brain networks are unknown. Here we use diffusion MRI data from cognitively intact participants (n = 480, ages 40–90) to study age-associated differences in the average controllability of structural brain networks, topological features that could mitigate these differences, and the overall effect on cognitive function. We find age-associated declines in average controllability in control hubs and large-scale networks, particularly within the frontoparietal control and default mode networks. Further, we find that redundancy, a hypothesized mechanism of reserve, quantified via the assessment of multi-step paths within networks, mitigates the effects of topological differences on average network controllability. Lastly, we discover that average network controllability, redundancy, and grey matter volume, each uniquely contribute to predictive models of cognitive function. In sum, our results highlight the importance of redundancy for robust control of brain networks and in cognitive function in healthy-aging. A diffusion MRI study suggests that redundancy could mitigate the effects of age-associated changes in brain topology to support the average controllability of brain networks middle and old age. [ABSTRACT FROM AUTHOR]

This study is centered on the optimal controllability of differential equations involving fractional derivatives of Katugampola. We derive both necessary and sufficient conditions for optimal controllability by extending Gronwall's inequality with singular kernels. Furthermore, we establish conditions ensuring the existence and uniqueness of mild solutions using the Banach fixed-point theorem and the generalized Laplace transform. To underscore the practical relevance of our findings, we provide an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, our focus is on exploring the relative controllability of systems governed by linear fractional differential equations incorporating state delay. We introduce a novel counterpart to the Cayley-Hamilton theorem. Leveraging a delayed perturbation of the Mittag-Leffler function, along with a determining function and an analog of the Cayley-Hamilton theorem, we establish an algebraic Kalman-type rank criterion for assessing the relative controllability of fractional differential equations with state delay. Moreover, we articulate necessary and sufficient conditions for relative controllability criteria concerning linear fractional time-delay systems, expressed in terms of a new α -Gramian matrix and define a control which transfer the system from any initial state to any final state within a given time. The theoretical findings are exemplified through the presentation of illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, by extending the controllability and Brunovsky indices for a matrix pair to a matrix quadruple, three kinds of indices, say, the invertibility indices, the left invertibility indices, and the right invertibility indices, for linear time-invariant systems are introduced and studied. Based on properties of these indices, a neat expression for the Morse lists of a linear system is given without transforming it into its Morse normal form, which is a deep and fundamental result in linear systems theory, and takes an important role in many analysis and design problems for linear systems. Furthermore, the Morse normal form with only algebraic equivalence transformation is also investigated and is simplified. [ABSTRACT FROM AUTHOR]

The development of the smart grid (SG) offers a way to improve the generation of electrical energy as well as the corresponding transmission and distribution. Due to the versatile nature, the installing of SG consumes less area and time when compared to traditional grids. The major aim of SG is to provide controllability of assets and grid observability and enhance the security and performance of power system. An integration of internet of things (IoT) in smart grid ensures intelligent features with reduced human intervention, cost-effectiveness, and reliability. In order to communicate the useful information with the internet and other web applications, IoT-enabled sensors are widely utilized in the power grid system, which enables better grid management. A photovoltaic (PV) system and a high-gain integrated Luo converter are included in the IoT-based power monitoring system for the smart grid that is recommended as a result of these variables. The maximum solar power is tracked with a help of grey wolf optimized artificial neural network (GWO-ANN) which aids in enhanced operation of converter. The obtained converter output is applied to 3 ϕ grid through a 3 ϕ voltage source inverter (VSI). The parameters like temperature, intensity, converter voltage and current, and grid voltage and current are monitored by sensors and further stored in IoT webpage. The random forest (RF) classifier is used for the prediction of shortest path through which the monitored data are transmitted. The whole set-up contributes an improved monitoring of smart grid parameters which is proved by the generated results. [ABSTRACT FROM AUTHOR]

This article presents some controllability and stabilization results for a system of two coupled linear Schrödinger equations in the one-dimensional case where the state components are interacting through the Kirchhoff boundary conditions. Considering the system in a bounded domain, the null boundary controllability result is shown. The result is achieved thanks to a new Carleman estimate, which ensures a boundary observation. Additionally, this boundary observation together with some trace estimates, helps us to use the Gramian approach, with a suitable choice of feedback law, to prove that the system under consideration decays exponentially to zero at least as fast as the function e - 2 ω t for some ω > 0 . [ABSTRACT FROM AUTHOR]

We establish sufficient conditions for the exponential stability of nonsingular impulsive delayed integro‐differential systems. Our approach to addressing nonsingular differential problems involves the application of permutable matrices and their associated delayed exponential. Furthermore, we investigate the controllability of a nonlinear impulsive and delayed problem by employing the corresponding Gramian matrix. Finally, to illustrate the theoretical outcomes, we provide examples and graphical representations for each situation. [ABSTRACT FROM AUTHOR]

The aging process of proton exchange membrane fuel cell (PEMFC) is affected by different operating factors, and its practical application scenarios involve multiple operation conditions. To improve the accuracy and controllability of aging prediction, a mixed recurrent neural network (RNN) model based on Gated Recurrent Unit (GRU) and Minimal Gated Unit (MGU) is proposed. The model dynamically adjusts the mixed weights of GRU and MGU throughout the entire training process to obtain the optimal prediction network structure throughout the entire lifecycle. Furthermore, an attention mechanism is incorporated into the mixed gated unit (MIXGU) model. The effectiveness of the MIXGU model is evaluated by utilizing experimental data from static condition, quasi-dynamic condition, and dynamic load cycling conditions. The predictive performance of MGU, GRU, MIXGU, and MIXGU model with attention mechanism (AT-MIXGU) are compared under different operating conditions. The validation results indicate that MIXGU model exhibits superior predictive performance compared to single gated unit, the attention mechanism enhances prediction accuracy. And the AT-MIXGU model demonstrates strong generalization capabilities, and well-suited for accurately predicting PEMFC aging under diverse operating conditions. • An adaptive weight-adjusted mixed gated unit recurrent neural network is proposed. • The attention mechanism is introduced into the mixed gated unit model. • Excellent prediction accuracy is proved under multiple operating conditions. • Validating generalization ability of the model for various application scenarios. [ABSTRACT FROM AUTHOR]

This paper is devoted to analyzing a kind of fractional stochastic neutral system (FSNS). Firstly, by introducing the notion of newly defined two-parameter Mittag-Leffler matrix function, we derive the solution of the corresponding linear stochastic system. Subsequently, for the linear case, by virtue of the Grammian matrix, we give a suffcient and necessary condition to guarantee the relatively exact controllability for the addressed case. Furthermore, for the nonlinear one, the relatively exact controllability is obtained by fixed point and explore it via Banach contraction principle. Finally, two examples are provided to intensify our theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the approximate controllability of fractional stochastic Sobolev-type hemivariational differential systems of order r ∈ (1, 2) with sectorial operators. Firstly, by using stochastic analysis, fractional calculus, sine and cosine family operators, sectorial operators, and the fixed-point theorems of multivalued maps, we show the existence of mild solutions for the fractional stochastic evolution systems. Then, we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution systems. Next, our results cover problems involving nonlocal conditions. Finally, we present theoretical and practical applications to support the validity of the study. [ABSTRACT FROM AUTHOR]

For uncertain multiple‐inputs multi‐outputs nonlinear systems, it is nontrivial to achieve asymptotic tracking due to the intrinsic coupling among inputs, while the controllability conditions in most existing methods are rather restrictive or even impractical especially when unexpected actuator faults are involved. In this article, we focus on extending such controllability condition by resorting to the existence (instead of a priori knowledge) of some feasible auxiliary matrix, upon which a robust adaptive control scheme is first presented in the absence of actuator faults that is not only able to achieve asymptotic tracking even in the presence of non‐parametric uncertainties with all the closed‐loop signals globally ultimately uniformly bounded, but also able to deal with a larger class of system models. Furthermore, for the case with intermittent actuator faults, we develop a fault‐tolerant control scheme with extended condition for controllability that is able to accommodate such faults automatically without using any fault detection or fault diagnosis unit. The effectiveness and benefits of the proposed method are verified via simulation on robotic systems. [ABSTRACT FROM AUTHOR]

This paper addresses the exact controllability of vibrations in a three-dimensional Cosserat elastic solid body using mathematical techniques such as operator theory and semigroup methods. The verification of exact (shape) controllability is accomplished through the application of the Hilbert Uniqueness Method, which involves investigating the boundary observability for the dual system. In partial differential equations control theory, the concept of exact observability for the dual system is fundamental to achieving exact controllability, although it differs from the common understanding of controllability. While control theory for systems governed by ordinary differential equations (ODEs) has a relatively formal and standardized approach, systems with distributed parameters, such as the Cosserat medium under consideration, involve a multitude of technical inequalities that must be established. Notably, Cosserat media possess six degrees of freedom for microstructures, in contrast to classical media with only three degrees of freedom. Consequently, exact control is required for all six variables, encompassing three translational and three rotational degrees of freedom, while classical media only necessitate the exact control of three translational variables. The paper concludes with a series of numerical studies utilizing the fast Fourier transform (FFT) and various simulations, which serve to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Assessing the strength of complex networks is crucial for evaluating their functionality and monitoring system security. Two primary perspectives for measuring network robustness are connectivity and controllability, which quantify how well a network maintains connectivity and controllability after experiencing complete attacks. However, conventional robustness calculation methods that use simulation attacks can be impractical for large-scale networks. Recent research has explored the use of deep learning methods for network robustness prediction, including PCR (short for predictor of controllability robustness), which uses a VGG (short for visual geometry group)-based convolutional neural network (CNN) and a linear filter. However, PCR has limitations, including inaccurate edge importance differentiation and fluctuating output curves. This paper presents ATTRP, an attention-based robustness predictor, which addresses these limitations. ATTRP uses a novel convolutional neural network with channel and spatial attention mechanisms to improve prediction accuracy and a robustness filter based on Savitzky–Golay smoothing to rectify the robustness curve. Experimental studies demonstrate that ATTRP outperforms other predictors, with much lower errors, while its computational speed is far superior to that of traditional attacking simulation. Overall, our research provides a more effective and efficient means of predicting network robustness, with potential applications in monitoring system security. [ABSTRACT FROM AUTHOR]

In this paper we deal with the problem of strong stabilisation for a class of distributed semilinear systems by means of a nonlinear feedback control. The systems under consideration evolve in a Hilbert space and present periodic time-varying state delay. We first give a proof for the existence and uniqueness of the solution for the considered systems. Then, under a null controllability condition, we establish the stabilisation result and provide an explicit optimal decay rate estimate. The particular case of such systems for which the linear part generates a differentiable semigroup is also investigated. Some illustrating applications to hyperbolic and parabolic equations are displayed. Finally, a conclusion and some perspectives are given. [ABSTRACT FROM AUTHOR]

We use the moment method in order to study the uniform boundary controllability of a semidiscrete 1-d wave equation, when a lower rate numerical vanishing viscosity term is added. The high frequency spurious oscillations introduced by the classical method of space discrete numerical schemes lead to nonuniform controllability properties, which are dumped out using an additional vanishing viscosity term. Our extra numerical viscosity is weaker than the one used in [30] , but enough in order to treat high frequency numerical spurious oscillations. Hence, we are able to prove the convergence of the sequence of discrete controls to a control of the continuous wave equation, when the mesh size tends to zero. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of developing a unified method for quantifying and improving the cyber resilience of large-scale cyber-physical systems (CPSs) against cyber-attacks targeting structural controllability. To this end, we provide necessary and sufficient conditions to extend the concept of structural controllability of single-layer systems to two-layer CPSs comprising of power network as the physical layer and communication network as the cyber layer. Next, in order to assess cyber resilience, we introduce the notion of $ R $ R -resilient CPS as the maximum number of cyber nodes that can be attacked by an adversary while preserving the structural controllability of the entire CPS. Furthermore, we provide an algorithm to find the optimal network reconfiguration matrix to increase the resilience level of CPS from $ R $ R -resilient to $ ({R + 1}) $ (R + 1) -resilient by adding a minimum number of transmission lines to the physical layer or communication links to the cyber layer, or both. Additionally, the proposed methodology is extended to achieve $ ({R + \alpha }) $ (R + α) -resilient CPS, where α>1. The effectiveness of the proposed method is verified through simulations of IEEE 14, IEEE 39, and IEEE 118 power networks with different cyber topologies, considering four scenarios of denial-of-service (DoS) attacks, including targeted and random node attacks. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time. [ABSTRACT FROM AUTHOR]

In this paper we study the controllability for the 1D-Heat equation with a Dirichlet boundary condition, in the presence of a scale-invariant parameter. First, we construct the scale-invariant solutions for the one-dimensional heat equation. Then we present our problem statement. We finally prove the Dirichlet boundary controllability. [ABSTRACT FROM AUTHOR]

To achieve optoelectronic devices with high resolution and efficiency, there is a pressing need for optical structural units that possess an ultrasmall footprint yet exhibit strong controllability in both the frequency and spatial domains. For dielectric nanoparticles, the overlap of electric and magnetic dipole moments can scatter light completely forward or backward, which is called Kerker theory. This effect can expand to any multipoles and any directions, re‐named as generalized Kerker effect, and realize controllable light manipulation at full space and full spectrum using well‐designed dielectric structures. However, the complex situations of multipole couplings make it difficult to achieve structural design. Here, generative artificial intelligence (AI) is utilized to facilitate multi‐objective‐oriented structural design, wherein the study leverages the concept of "combined spectra" that consider both spectra and direction ratios as labels. The proposed generative adversarial network (GAN) is named as DDGAN (double‐discriminator GAN) that discriminates both images and spectral labels. Using trained networks, the simultaneous design for scattering color and directivities, RGB color routers, as well as narrowband light routers is achieved. Notably, all generated structures possess a footprint <600 × 600 nm indicating their potential applications in optoelectronic devices with ultrahigh resolution. [ABSTRACT FROM AUTHOR]

In biological systems, impulses are often used to model mutations in gene expression. In order to describe the instantaneity of the impulse, this paper employs a hybrid‐index model of impulsive Boolean networks with state‐triggered impulses. Based on this model, the time‐domain output controllability is investigated. Using the quotient mapping method, the hybrid‐domain solutions of this model are mapped to the time‐domain solutions, mathematically. Then a necessary and sufficient condition for output controllability in the time domain is presented. Finally, an example is given to demonstrate the correctness and effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This work studies the controllability of a class of Riemann–Liouville fractional differential equations of order 1<ς<2$$ 1<\varsigma <2 $$ in a new Banach space Zς−1$$ {Z}_{\varsigma -1} $$ using fractional cosine family. To derive the existence of solutions, we construct the definition of mild solutions of the system using Laplace transform theory. Then, by assuming the approximate controllability of corresponding linear equation, we prove that the nonlinear dynamical system is approximately controllable using an iterative technique. Lastly, we give an example to illustrate the established theory. [ABSTRACT FROM AUTHOR]

This study uses a delayed matrix exponential to illustrate the solution of both linear and nonlinear delay problems using permutable matrices. We outline several prerequisites that are necessary to ensure the exponential stability of the trivial solution of delay systems. The conditions that are necessary and sufficient for the linear system to possess relative controllability are established by introducing a delayed Grammian matrix‐like criterion. A sufficient condition is obtained by Krasnoselskii's fixed point theorem for the relative controllability of nonlinear systems. Numerical examples provided at the end of the paper demonstrate the validity of our theoretical findings. [ABSTRACT FROM AUTHOR]

This study investigates the controllability problems for linear and nonlinear fractional control systems with multiple control delays in the context of the ψ$$ \psi $$‐Caputo fractional derivative. For the linear case, using the positive definiteness of the Gramian matrix, the necessary and sufficient conditions are obtained. For the nonlinear case, utilizing the iterative technique together with the completeness of the space, sufficient conditions for the existence of a solution are obtained. Just a few examples are included to make theoretical findings easier to grasp, and their respective graphs are plotted. [ABSTRACT FROM AUTHOR]

The purpose of this work is to investigate the exponential stability of a second‐order coupled wave equations by Laplacian with one locally internal viscous damping. The strong stability is established by combining a unique continuation result and a Carleman estimate. Besides, the exponential stability is proved under (PMGC) condition on the damping region without any restriction on wave propagation speed (i.e., whether the two wave equations propagate at the same speed or not). The proof of this result relies on the frequency domain method combined with the multiplier techniques. [ABSTRACT FROM AUTHOR]

This paper studies the exact controllability of semilinear q ∈ (1 , 2) -order fractional evolution systems with a weighted delay initial condition in abstract spaces. Firstly, with the aid of properties of the strongly continuous cosine family, the expression of mild solutions of the concerned problem is presented. Exact controllability results are achieved under essential conditions on f. An example as an application is also given. [ABSTRACT FROM AUTHOR]

For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here, a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere, one obtains a compactification of the state space allowing us to describe the behavior "near infinity" of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior. [ABSTRACT FROM AUTHOR]

In our manuscript, we investigate the interior approximate controllability for the subsequent semilinear second-order system in $ L_2(\Omega) $ L 2 (Ω) $$\begin{align*} s''(\sigma)+A_0s(\sigma)&=B_0u(\sigma)+\xi(\sigma,s(\sigma)), \quad 0\le \sigma\leq \varrho\\ s(0)&=s_0, \quad s'(0)=s_1, \end{align*} $$ s ″ (σ) + A 0 s (σ) = B 0 u (σ) + ξ (σ , s (σ)) , 0 ≤ σ ≤ ϱ s (0) = s 0 , s ′ (0) = s 1 , where $ A_0 $ A 0 is the linear and unbounded operator, $ B_0 $ B 0 is a bounded linear operator and ξ is a nonlinear operator defined on appropriate spaces. The proposed problem can be converted into an equivalent first-order semilinear control system, then the approximate controllability results for the proposed system are obtained from the study of the approximate controllability of the reduced first-order system. The Leray–Schauder alternative theorem and principle of contraction are used in the proof of our main theorems. [ABSTRACT FROM AUTHOR]

We consider an optimal control problem on the fixed interval of time with the right endpoint constraint. We introduce the concept of controllability for this problem. The main result of the paper states that if for the optimal control problem the Pontryagin maximum principle fails on the given admissible process then this process satisfies the controllability condition. [ABSTRACT FROM AUTHOR]

The focus of this work is on the absolute controllability of Hilfer impulsive non-instantaneous neutral derivative (HINND) with integral boundary condition of any order. Total controllability refers to the system's ability to be controlled during the impulse time. Kuratowski measure and semigroup theory in Banach space yield the results. Furthermore, we talked about optimal controllability in conjunction with appropriate limitations. Our established outcomes are described using an example. [ABSTRACT FROM AUTHOR]

In a prior work the authors proposed a variant on the Impedance Matched Multi-Axis Test (IMMAT) in which a fixture is defined, called the Transmission Simulator (TS), and the desired environment is matched at a set of sensors on the TS. If the motion of the TS is matched then the response of the rest of the component will also match, provided that the attached component has the same dynamics as it did when the environment was measured. Hence, one would like the TS to be flexible so that it reproduces the boundary conditions that the component of interest experiences during flight, but the more flexible the TS, the more shakers might be needed to control its response. This work presents a derivation that gives expressions for these two potential error sources in TS-IMMAT. Then, various case studies are presented, both on simulated and real hardware, to understand the importance of each error term in practical testing. The theory explains the phenomena that were observed when using measurements from a component that flew on a sounding rocket. The environmental response was measured and then various fixtures were attached, each comprising more of the next assembly, or the hardware to which the component was attached in flight. MIMO testing was repeated with each fixture and the results were compared to seek to understand the role of the impedance match in this type of testing. The results show that the number of modes that are active in the transmission simulator is also very important, and so the best solution balances these two considerations. An improved method of simulating the MIMO test is then proposed, so simulations can be used to predict what fixture, or transmission simulator, will give the best results in a TS-IMMAT test. [ABSTRACT FROM AUTHOR]

This paper investigates partial approximate controllability of fractional linear and semi-linear control systems involving the conformable derivative. First, we derive sufficient and necessary conditions for partial approximate controllability of fractional linear systems over a small interval. Then, we apply a new approach, different from typical methods involving complexity inequalities and fixed point theorems, to obtain sufficient conditions for partial approximate controllability of semi-linear fractional control systems, assuming that the linear part is partially approximately controllable. The effectiveness of these results is demonstrated through an illustrative example. [ABSTRACT FROM AUTHOR]

In this study, our main focus is on the analysis of the existence, controllability, and Hyers–Ulam stability of a neutral switched system with impulsive effects on non-uniform time domains. First, we use the Banach fixed point theorem and the time scales calculus to explore the existence, Ulam's type stability, and controllability of a considered switched system. In the end, we examine the controllability results through numerical simulations. This article aims to identify the essential requirements for achieving controllability and stability on different time scales. [ABSTRACT FROM AUTHOR]

Controllability of nonlinear delayed leader–follower multi-agent system with fixed communication topology is introduced. A solution of a semilinear time-delay control system and Gramian matrix for the linear part which has Kronecker delay perturbation of exponential matrix function are given. The assumptions and conditions under which the nonlinear delay multi-agent system can be controlled are determined thanks to control problem into fixed point problem. A comprehensive example to illustrate given theoretical contents is presented. [ABSTRACT FROM AUTHOR]

The paper deals with the controllability of a degenerate beam equation. In particular, we assume that the left end of the beam is fixed, while a suitable control f$$ f $$ acts on the right end of it. As a first step, we prove the existence of a solution for the homogeneous problem, then we prove some estimates on its energy. Thanks to them, we prove an observability inequality, and using the notion of solution by transposition, we prove that the initial problem is null controllable. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability, controllability, and differential game of pursuit for an infinite system of linear ODEs in ℓ2. The system we consider has a special right-hand side, which is not diagonal and serves as a toy model for controllable system of infinitely many interacting points. We impose integral constraints on the control parameters. We obtain criteria for stability and null controllability of the system. Further, we construct a strategy for the pursuer that guarantees completion of the pursuit problem for the differential game. To prove controllability we use the so called Gramian operators. [ABSTRACT FROM AUTHOR]

This communication presents two new first order universal active filter configurations employing operational transconductance amplifiers (OTA) and use grounded capacitor which is prominently suitable for integrated chip (IC) fabrication. One of the proposed topologies provides voltage mode (VM) and transconductance mode (TCM) of operations while the other circuit provides current mode (CM) in addition with transresistance mode (TRM) filter functions. All three first order filter functions namely low pass filter (LPF), high pass filter (HPF) and all pass filter (APF) are configurable with appropriate choice(s) of input voltage/current signals. An equal transconductor condition (which can be easily achieved) is required for the realization of APF functions. The proposed filter configurations possess high input impedance and high output impedance and also offer independent electronic tunability of pole frequency/cut-off frequency. The gain of filters realized in VM, TCM and TRM has independent electronic tunability feature and can be adjusted through transconductor. For the usability of proposed filters, multi-phase sinusoidal oscillator has also been demonstrated. To assure the workability of the proposed filter structures, PSPICE simulations with CMOS OTA implemented in 0.18 µm TSMC technology parameters has been used. Various simulation results including Monte-Carlo simulations, process corner analysis, total harmonic distortions (%THD) and temperature analysis have also been appended. Experimental results employing off-the-shelf IC LM13700 type OTAs have also been included to verify the theoretical propositions of first order universal filters and multiphase sinusoidal oscillators. [ABSTRACT FROM AUTHOR]

This article is mainly focusing on the approximate controllability of neutral integro‐differential stochastic equations with state‐dependent delay. The main results of this article are proved by applying some ideas about the semigroup theory and resolvent operators. At first, the investigation about the existence of a mild solution and then we discuss the approximate controllability of the considered system. Next, we extend our study to the system with non‐local conditions. Finally, a theoretical application is presented for proving the validity of controllability results obtained. [ABSTRACT FROM AUTHOR]

In our paper, we primarily concentrate on the existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type. By applying the facts related to the measure of noncompactness, fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system. In the end, we present an example to demonstrate the theory. [ABSTRACT FROM AUTHOR]

New possibilities of Gramian computation, by means of canonical transformations into diagonal, controllable, and observable canonical forms, are shown. Using such a technique, the Gramian matrices can be represented as products of the Hadamard matrices of multipliers and the matrices of the transformed right-hand sides of Lyapunov equations. It is shown that these multiplier matrices are invariant under various canonical transformations of linear continuous systems. The modal Lyapunov equations for continuous SISO LTI systems in diagonal form are obtained, and their new solutions based on Hadamard decomposition are proposed. New algorithms for the element-by-element computation of Gramian matrices for stable, continuous MIMO LTI systems are developed. New algorithms for the computation of controllability Gramians in the form of Xiao matrices are developed for continuous SISO LTI systems, given by the equations of state in the controllable and observable canonical forms. The application of transformations to the canonical forms of controllability and observability allowed us to simplify the formulas of the spectral decompositions of the Gramians. In this paper, new spectral expansions in the form of Hadamard products for solutions to the algebraic and differential Sylvester equations of MIMO LTI systems are obtained, including spectral expansions of the finite and infinite cross - Gramians of continuous MIMO LTI systems. Recommendations on the use of the obtained results are given. [ABSTRACT FROM AUTHOR]

This work studies the existence of solutions and approximate controllability of fractional integrodifferential systems with Riemann-Liouville derivatives and with multiple delays in control. We establish suitable assumptions to prove the existence of solutions. Controllability of the system is shown by assuming a range condition on control operators and Lipschitz condition on non-linear functions. We use the concepts of strongly continuous semigroup rather than resolvent operators. Finally, an example is give to illustrate the theory. [ABSTRACT FROM AUTHOR]

The moment method is used to prove the exact controllability of a wide class of bidimensional linear dispersive PDE's posed on the two-dimensional torus T². The control function is considered to be acting on a small vertical and horizontal strip of the torus. Our results apply to several well-known models including some bidimesional extensions of the Benajamin--Ono and Korteweg--de Vries equations. As a by product, the exponential stabilizability with any given decay rate is also established in the Sobolev space Hsp(T²), with s ≥ 0, by constructing an appropriated feedback control law. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. L\"u and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms. [ABSTRACT FROM AUTHOR]

This paper is dedicated to solving a multi-objective control problem for a 2 × 2 system of parabolic equations. Here, we have many objectives, possibly conflictive, and we adopt a concept of hierarchy for the controls. We have the leader control, responsible for objectives of controllability type, and the follower controls which intend to be a Nash-equilibrium with respect to some given cost functionals. The novelty here is that we formulate this problem for systems of parabolic equations, meaning that we have many variables and naturally much more objectives to accomplish. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the controllability conditions of linear control systems involving distinct local fractional derivatives. Sufficient conditions for controllability using Kalman rank conditions and the Gramian matrix are presented. We show that the controllability of the local fractional system can be determined by the invertibility of the Gramian matrix and the full rank of the Kalman matrix. We also show that the local fractional system involving distinct orders is controllable if and only if the Gramian matrix is invertible. Illustrative examples and an application are provided to demonstrate the validity of the theoretical findings. [ABSTRACT FROM AUTHOR]

Controllability is a fundamental issue in the field of fractional complex network control, yet it has not received adequate attention in the past. This paper is dedicated to exploring the controllability of complex networks involving the Caputo fractional derivative. By utilizing the Cayley–Hamilton theorem and Laplace transformation, a concise proof is given to determine the controllability of linear fractional complex networks. Subsequently, leveraging the Schauder Fixed-Point theorem, controllability Gramian matrix, and fractional calculus theory, we derive controllability conditions for nonlinear fractional complex networks with a weighted adjacency matrix and Laplacian matrix, respectively. Finally, a numerical method for the controllability of fractional complex networks is obtained using Matlab (2021a)/Simulink (2021a). Three examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear ν -Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear ν -Caputo fractional evolution equations is established, utilizing resolvent-like operators. Additionally, we identify a control strategy that not only satisfies the approximative controllability property but also ensures exact finite-dimensional controllability. Leveraging the approximative controllability of the corresponding linear ν -Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear ν -Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to ν -Caputo fractional heat equations. [ABSTRACT FROM AUTHOR]

This paper deals with the boundary exact controllability to the trajectories of the one-phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. We prove the local exact controllability to (smooth) trajectories. To this purpose, we first reformulate the problem as the local null controllability of a coupled PDE-ODE system with distributed controls. Then, a new Carleman inequality for the adjoint of the linearized PDE-ODE system, coupled on the boundary through nonlocal in space and memory terms, is presented. This leads to the null controllability of an appropriate linear system. Finally, the result is obtained via local inversion, by using Lyusternik-Graves' Theorem. As a byproduct of our approach, we find that some parabolic equations which contains memory terms located on the boundary are null-controllable. [ABSTRACT FROM AUTHOR]

In this paper, we study the controllability of a nonlinear system of coupled second- and fourth-order parabolic equations. This system can be regarded as a simplification of the well-known stabilized Kuramoto-Sivashinsky system. Using only one control applied on the boundary of the second-order equation, we prove that the local-null controllability of the system holds if the square root of the diffusion coefficient of the second-order equation is an irrational number with finite Liouville-Roth constant. [ABSTRACT FROM AUTHOR]