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The purpose of this paper is to study the controllability in the α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach space. To do this, we give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained by using the Schauder fixed-point theorem. [ABSTRACT FROM AUTHOR]

This paper introduces a novel design method that enhances the force/torque, bendability, and controllability of soft pneumatic actuators (SPAs). The complex structure of the soft actuator is simplified by approximating it as a cantilever beam. This allows us to derive approximated nonlinear kinematic models and a dynamical model, which is explored to understand the correlation between natural frequency and dimensional parameters of SPA. The design problem is then transformed into an optimization problem, using kinematic equations as the objective function and the dynamical equation as a constraint. By solving this optimization problem, the optimal dimensional parameters are determined. Six prototypes are manufactured to validate the proposed approach. The optimal actuator successfully generates the desired force/torque and bending angle, while its natural frequency remains within the constrained range. This work highlights the potential of using optimization formulation and approximated nonlinear models to boost the performance and dynamical properties of soft pneumatic actuators. [ABSTRACT FROM AUTHOR]

The present work is a successor of Ilchmann and Kirchhoff (Math Control Signals Syst 33:359–377, 2021. https://doi.org/10.1007/s00498-021-00287-x), Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) on (relative) generic controllability of unstructured linear differential-algebraic systems and of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) on (relative) generic controllability of port-Hamiltonian descriptor systems. We extend their results to (relative) genericity of observability. For unstructured differential-algebraic systems, criteria for (relative) generic observability are derived from Ilchmann and Kirchhoff (Math Control Signals Syst 35:45–76, 2023. https://doi.org/10.1007/s00498-021-00287-x) using duality. This is not possible for port-Hamiltonian systems. Hence, we tweak the results of Ilchmann et al. (Port-Hamiltonian descriptor systems are generically controllable and stabilizable. Submitted to Mathematics of Control, Signals and Systems, 2023. https://arxiv.org/abs/2302.05156) and derive similar criteria as for the unstructured case. Additionally, we consider certain rank constraints on the system matrices. [ABSTRACT FROM AUTHOR]

This paper presents the controllability and optimal control results for a structure with quasi-linear evolution in abstract spaces. First, the analytic semigroup theory was used to prove the existence and uniqueness of the quasilinear system. Additionally, the same system's controllability outcome was examined. The latter uses fixed-point theorems to determine the best control for the quasi-linear system. Two specific examples are then provided to demonstrate the usefulness of our primary findings. [ABSTRACT FROM AUTHOR]

In this article we consider diffeomorphism groups of manifolds with smooth boundary. We show that the diffeomorphism groups of the manifold and its boundary fit into a short exact sequence which admits local sections. In other words, they form an infinite-dimensional fibre bundle. Manifolds with boundary are of interest in numerical analysis and with a view towards applications in machine learning we establish controllability results for families of vector fields. This generalises older results due to Agrachev and Caponigro in the boundary-less case. Our results show in particular that the diffeomorphism group of a manifold with smooth boundary is generated by the image of the exponential map. [ABSTRACT FROM AUTHOR]

We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple bounds. When the intersection of these two sets is empty, typically because the bounds on the control variables are too tight, the problem becomes infeasible. In this paper, we prove that, under a controllability assumption, the "best approximation" optimal control minimizing the distance (and thus finding the "gap") between the two sets is of bang–bang type, with the "gap function" playing the role of a switching function. The critically feasible control solution (the case when one has the smallest control bound for which the problem is feasible) is also shown to be of bang–bang type. We present the full analytical solution for the critically feasible problem involving the (simple but rich enough) double integrator. We illustrate the overall results numerically on various challenging example problems. [ABSTRACT FROM AUTHOR]

The utilization of quaternions in nonlinear systems with input delays is presented in this paper, aiming to investigate the controllability of nonlinear quaternion-valued systems (QVSs). In view of the non-commutativity of quaternion multiplication, the system is decomposed into four real-valued subsystems. The existence and uniqueness of solutions for QVSs with input delays are demonstrated using the contraction mapping principle and Laplace transform. To achieve system controllability amidst distinct input delays, two categories of Gram matrices along with their respective control functions are established, and their feasibility are demonstrated by Arzela-Ascoli theorem and the Schaefer fixed point theorem. Finally, numerical simulations are conducted to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

This study investigates the controllability of a Volterra evolution equation with impulsive terms and nonlocal initial conditions. With the aid of the resolvent operator generated by the linear part of the equation, mild solutions can be defined. Notably, the resolvent operator lacks compactness and equicontinuity. Additionally, the compactness of the impulsive and nonlocal functions is not required. Sufficient conditions for controllability are obtained through measures of noncompactness in Banach spaces. Functional differential equations and hyperbolic partial differential equations can be solved with these results. An example is given to illustrate the validity of the presented results. [ABSTRACT FROM AUTHOR]

We have classified in [7] all linear control systems and studied their controllability and control sets on the homogeneous spaces L ﹨ H of the 3-dimensional Heisenberg group H through its closed subgroups L. In this paper, we characterize the controllability and control sets of the induced linear control systems in the homogeneous spaces left. In particular, we focus on the singularity of the induced drift vector fields. Quite a technical analysis with many cases reveals the control sets. We give some geometric illustrations. [ABSTRACT FROM AUTHOR]

The study of this article deals with the controllability results for time‐varying fractional dynamical systems in terms of Caputo‐type fractional derivatives having a prescribed or predetermined control. We demonstrate the controllability results for time‐varying linear fractional dynamical systems using Gramian technique and fractional calculus. Additionally, we explore the controllability results for semi‐linear and nonlinear fractional dynamical systems through the fixed point techniques. Several numerical examples are illustrated to validate the theoretical results. [ABSTRACT FROM AUTHOR]

The two‐way propagation of a certain class of long‐crested water waves is governed approximately by systems of equations of the Boussinesq type. These equations have been put forward in various forms by many authors and their higher‐order generalizations arise when modeling the propagation of waves on large lakes, ocean, and in other contexts. Considered here is a class of such system which couple two higher‐order Korteweg–de‐Vries type equations. Our aim is to investigate the controllability properties of the linearized model posed on a periodic interval. By using the classical duality approach and some theorems on nonharmonic Fourier series, we prove that the system is exactly controllable in certain well‐chosen Sobolev spaces by means of suitable boundary controls. [ABSTRACT FROM AUTHOR]

Objectives. There is a significant correlation between EEG microstate and the neurophysiological basis of mental illness, brain state, and cognitive function. Given that the unclear relationship between network dynamics and different microstates, this paper utilized microstate, brain network, and control theories to understand the microstate characteristics of short-term memory task, aiming to mechanistically explain the most influential microstates and brain regions driving the abnormal changes in brain state transitions in patients with schizophrenia. Methods. We identified each microstate and analyzed the microstate abnormalities in schizophrenia patients during short-term memory tasks. Subsequently, the network dynamics underlying the primary microstates were studied to reveal the relationships between network dynamics and microstates. Finally, using control theory, we confirmed that the abnormal changes in brain state transitions in schizophrenia patients are driven by specific microstates and brain regions. Results. The frontal-occipital lobes activity of microstate D decreased significantly, but the left frontal lobe of microstate B increased significantly in schizophrenia, when the brain was moving toward the easy-to-reach states. However, the frontal-occipital lobes activity of microstate D decreased significantly in schizophrenia, when the brain was moving toward the hard-to-reach states. Microstate D showed that the right-frontal activity had a higher priority than the left-frontal, but microstate B showed that the left-frontal priority decreased significantly in schizophrenia, when changes occur in the synchronization state of the brain. Conclusions. In conclusion, microstate D may be a biomarker candidate of brain abnormal activity during the states transitions in schizophrenia, and microstate B may represent a compensatory mechanism that maintains brain function and exchanges information with other brain regions. Microstate and brain network provide complementary perspectives on the neurodynamics, offering potential insights into brain function in health and disease. [ABSTRACT FROM AUTHOR]

According to SAMHSA (2023), approximately 16,600,000 American adults and teens reported having serious thoughts of suicide in 2022. While suicide prevention has primarily focused on suicide deaths and attempts, we contend that suicidal ideation (SI) deserves more in-depth investigation and should be an essential intervention target on its own. In support of this point, we provide three examples of ways to improve specificity in understanding of SI through the study of controllability of SI, the language used to assess SI, and measuring SI in real time. We also consider qualitative work on the content of SI, its treatment, and definitional considerations. We thus call for an increased general focus on SI within research, clinical care, and policy. [ABSTRACT FROM AUTHOR]

The primary goal of this study is to investigate the necessary conditions for the Hilfer–Langevin dynamical system with initial circumstances to be controllable. Using a sequencing technique, we have employed the concept of a bounded integral contractor to reach our results. Unlike previous studies, we do not need to specify the induced inverse of the controllability operator, and the relevant nonlinear function does not have to satisfy a Lipschitz condition to prove our accurate controllability conclusions. We have obtained a theoretical result that is shown to be critically important through an example. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the controllability and optimal control results for a structure with quasi-linear evolution in abstract spaces. First, the analytic semigroup theory was used to prove the existence and uniqueness of the quasilinear system. Additionally, the same system’s controllability outcome was examined. The latter uses fixed-point theorems to determine the best control for the quasi-linear system. Two specific examples are then provided to demonstrate the usefulness of our primary findings.

The article aims to develop a fractional-order proportional integral derivative (PID) controller to monitor insulin and glucose levels in humans under the influences of stress, excitement, and trauma. A novel fractional-order diabetes mellitus model is proposed, incorporating a nonsingular, nonlocal kernel (Mittag-Leffler function) to account for the effect of epinephrine on suppressing insulin secretion and the dynamics of beta-cell mass. As beta-cell mass increases in the presence of adrenaline, the system remains highly responsive to rising blood glucose and falling insulin levels, driven by the hormone’s suppressive effects. The key advantage of this model is its ability to incorporate these physiological stressors and use fractional-order derivatives to describe the nonlocal dynamics within the system. The innovations of this work include a fractional-order diabetes mellitus model that captures the biological memory and hereditary effects of glucose regulation under stress, and a fractional-order PID controller that offers greater stability and robustness compared to conventional controllers, particularly in managing adrenaline-induced hyperglycemia. The model’s positivity, boundedness, and equilibrium solutions are rigorously analyzed to ensure feasibility. Additionally, a new theorem is proven using fixed-point theory, confirming the existence and uniqueness of the fractional-order model. Ulam–Hyers stability analysis further demonstrates the model’s robustness and well-posedness, while qualitative properties are explored. Numerical simulations to explore which is done by solutions with a two-step Lagrange polynomial for generalized Mittag Leffler kernel showed that prolonged and severe hyperglycemia was caused by regular release of adrenaline into the blood at different fractional order values and fractal dimensions by changing initial values for normal and diabetes patients. PID and controller results are analyzed to increase the stability of the system to monitor and assess of glucose–insulin system with beta cell mass to control the hyperglycemia. Lastly, the results are obtained and visually shown using graphical representations, which provide empirical evidence in support of our theoretical findings. At the end comparison of numerical simulations is constructed to show the efficiency, convergence, and accuracy of proposed techniques at different fractional values with power law and exponential kernels. Numerical simulations, mathematical modeling, and analysis work together to shed light on the dynamics of diabetes mellitus and make important advances in the knowledge and treatment of this common disease.

In this study, we examine the controllability of a neutral stochastic fractional equation of motion that incorporates the ψ -Hilfer fractional derivative and the Rosenblatt process. Utilizing the measure of non-compactness and the Banach contraction mapping, we derive insights into the existence and unique characteristics of the mild solution for the system. We establish the prerequisites for controllability for both linear and nonlinear systems and confirm the controllability of nonlinear cases using the Banach contraction principle. To illustrate our theoretical findings, we provide numerical examples that highlight the practical implications of our analysis. This combined theoretical and numerical approach enhances the understanding of controllability in neutral stochastic fractional equations with the ψ -Hilfer fractional derivative and Rosenblatt process. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a new soft‐switching bidirectional multiport DC/DC converter for PV/EV applications. The proposed topology is capable of using several different sources simultaneously. Also, it has some benefits including high voltage gain, bidirectional, soft‐switching technique, and multi‐input multi‐output (MIMO) topology. In addition, all inputs of the proposed converter are separate from each other and it causes control of the outputs to be simple in the wake of the common ground of the inputs and outputs. The proposed converter can work on zero current switching (ZCS) conditions on some power semiconductors (power diode/switch) and decreases the switching and conduction losses. It also makes use of semiconductors with lower resistance on‐state (Rds‐on). Using coupled inductor techniques and working of semiconductors under ZCS conditions eliminates the total loss affected by reverse recovery of the power diodes, and a passive clamp circuit can recover the leakage energy released by the leakage inductance of the used coupled inductor. The proposed topology is built and tested in the laboratory. To confirm the accurate operation of the proposed topology, it is tested by Typhoon HIL‐404 emulator at 12 V–12 V–12 V inputs/270 W with 50 kHz switching frequency.

Abstract Brain cancer is one of the deadliest diseases, although many efforts have been made to treat it, there is no comprehensive and effective treatment approach yet. In recent years, the use of network-based analysis to identify important biological genes and pathways involved in various complex diseases, including brain cancer, has attracted the attention of researchers. The goal of this manuscript is to perform a comprehensive analysis of the various results presented related to brain cancer. For this purpose, firstly, based on the CORMINE medical database, collected all the genes related to brain cancer with a valid P-value. Then the structural and functional relationships between the above gene sets have been identified based on the STRING database. Next, in the PPI network, hub centrality analysis was performed to determine the proteins that have many connections with other proteins. After the modularization of the network, the module with the most hub vertices is considered as the most relevant module to the formation and progression of brain cancer. Since the driver vertices play an important role in biological systems, the edges of the selected module were oriented, and by analyzing the controllability of complex networks, a set of five proteins with the highest control power has been identified. Finally, based on the drug-gene interaction, a set of drugs effective on each of the driver genes has been obtained, which can potentially be used as new combination drugs. Validation of the hub and driver proteins shows that they are mainly essential proteins in the biological processes related to the various cancers and therefore the drugs that affect them can be considered as new combination therapy. The presented procedure can be used for any other complex disease.

Background: Repetitive transcranial magnetic stimulation (rTMS) has shown therapeutic effects in neurological patients by inducing neural plasticity. In this pilot study, we analyzed the modifying effects of high-frequency (HF-)rTMS applied to the dorsolateral prefrontal cortex (DLPFC) of patients with mild cognitive impairment (MCI) using an advanced approach of functional connectome analysis based on network control theory (NCT). Methods: Using local-to-global functional parcellation, average and modal controllability (AC/MC) were estimated for DLPFC nodes of prefrontal-lateral control networks (R/LH_Cont_PFCl_3/4) from a resting-state fMRI series acquired at three time points (T0 = baseline, T1 = T0 + 4 weeks, T2 = T1 + 20 weeks) in MCI patients receiving regular daily sessions of 10 Hz HF-rTMS (n = 10, 68.00 ± 8.16 y, 4 males) or sham (n = 10, 63.80 ± 9.95 y, 5 males) stimulation, between T0 and T1. Longitudinal (group) effects on AC/MC were assessed with non-parametric statistics. Spearman correlations (ρ) of AC/MC vs. neuropsychological (RBANS) score %change (at T1, T2 vs. T0) were calculated. Results: AC median was reduced in MCI-rTMS, compared to the control group, for RH_Cont_PFCl_3/4 at T1 and T2 (vs. T0). In MCI-rTMS patients, for RH_Cont_PFCl_3, AC % change at T1 (vs. T0) was negatively correlated with semantic fluency (ρ = −0.7939, p = 0.045) and MC % change at T2 (vs. T0) was positively correlated with story memory (ρ = 0.7416, p = 0.045). Conclusions: HF-rTMS stimulation of DLFC nodes significantly affects the controllability of the functional connectome in MCI patients. Emerging correlations between AC/MC controllability and cognitive performance changes, immediately (T1 vs. T0) and six months (T2 vs. T0) after treatment, suggest NCT could help explain the HF-rTMS impact on prefrontal-lateral control network, monitoring induced neural plasticity effects in MCI patients. [ABSTRACT FROM AUTHOR]

This paper proposes a new soft‐switching bidirectional multiport DC/DC converter for PV/EV applications. The proposed topology is capable of using several different sources simultaneously. Also, it has some benefits including high voltage gain, bidirectional, soft‐switching technique, and multi‐input multi‐output (MIMO) topology. In addition, all inputs of the proposed converter are separate from each other and it causes control of the outputs to be simple in the wake of the common ground of the inputs and outputs. The proposed converter can work on zero current switching (ZCS) conditions on some power semiconductors (power diode/switch) and decreases the switching and conduction losses. It also makes use of semiconductors with lower resistance on‐state (Rds‐on). Using coupled inductor techniques and working of semiconductors under ZCS conditions eliminates the total loss affected by reverse recovery of the power diodes, and a passive clamp circuit can recover the leakage energy released by the leakage inductance of the used coupled inductor. The proposed topology is built and tested in the laboratory. To confirm the accurate operation of the proposed topology, it is tested by Typhoon HIL‐404 emulator at 12 V–12 V–12 V inputs/270 W with 50 kHz switching frequency. [ABSTRACT FROM AUTHOR]

Although most individuals experience expectation violations in their educational years, individuals' coping strategies differ depending on situational and dispositional characteristics with potentially decisive influence on educational outcomes. As a situational characteristic, optimism bias indicates that individuals tend to update their expectations after unexpected positive feedback and to maintain their expectations after unexpected negative feedback. As a dispositional characteristic, a higher need for cognitive closure (NCC) indicates that individuals tend to both update (accommodation) and try to confirm expectations (assimilation) after unexpected negative feedback. To better understand mechanisms behind optimism bias and context-dependent effects of NCC in an educational context, we included controllability (attribution of success/failure to internal or external causes) and self-enhancement (amplifying positive self-relevant aspects) in an experimental case vignettes study. Our sample of n = 249 students was divided into four experimental groups (high/low controllability × positive/negative valence) and read four different case vignettes referring to expectation violations in an educational context. MANCOVA revealed that individuals updated their expectations after unexpected positive feedback only with stronger (vs. weaker) self-enhancement and that individuals maintained their expectations after unexpected negative feedback in controllable (vs. uncontrollable) situations. Furthermore, interindividual differences in NCC interacted with controllability in predicting expectation update. We conclude that considering the influences of controllability and self-enhancement, we can better understand and evaluate the adaptivity of the optimism bias and context-dependent effects of NCC in an educational context. [ABSTRACT FROM AUTHOR]

The problem of controllability and control of linear discrete-periodic systems is investigated in this paper. The high-order fully-actuated models for linear discrete periodic time-varying systems are constructed, and a controllability criterion based on fully-actuated system models is proposed. On this basis, stabilization as the fundamental issue is studied and periodic state-feedback control laws are designed via fully-actuated systems approach and parametric design, which converted the original problem into the pole assignment problem for linear constant systems. Finally, a numerical example is given to verify the validity and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the controllability of multi-agent systems over finite fields is studied based on the high-order fully actuated (HOFA) system approaches. The concept of HOFA systems over finite fields is introduced. Necessary and sufficient conditions for the controllability of linear systems over finite fields are established. It is proved that a leader–follower multi-agent system over finite fields is controllable if and only if it can be transformed into an HOFA system. Then the stabilisation control protocol is proposed based on the full-actuation property, and the upper bound of settling time for the system can be determined. The uncontrollable leader–follower multi-agent system over finite fields can be transformed into a controllable subsystem and an autonomous subsystem via structural decomposition, the conditions for the system to be stabilisable are provided. Finally, an illustrative example is shown to verify the validity of the main results of this paper. [ABSTRACT FROM AUTHOR]

A thermally coupled distillation technology can bring energy‐saving benefits, but it poses challenges to process control. This article explores dynamic control of different side‐stream quaternary extractive distillation configurations. One the one hand, the open‐loop controllability of these processes is analyzed in terms of various criteria by the control design interface technology of Aspen Plus Dynamics. On the other hand, their control structures are established and examined by introducing large feed flow and composition perturbations. The results show that the triple‐side‐stream distillation still performs the best state and input–output controllability in spite of the strongest nonlinearity, and is also well resistant to large feed perturbations using a simple control structure. [ABSTRACT FROM AUTHOR]

Rudolf Emil Kalman was a Hungarian-American electrical engineer and mathematician who revolutionized the field of control theory by introducing advanced mathematical techniques for studying control systems. In particular, he popularized the "Time-Domain Approach" for studying Linear Time-Invariant (LTI) systems over the traditional "Frequency-Domain Approach" that was typically used before his work. To contrast these approaches briefly, in the former approach, one works with the LTI system directly in the time-domain, whereas in the latter approach, one works with the transfer function, which relates the input of the LTI system to its output in the frequency domain. This was, in fact, one of his major contributions to control theory, since he showed that many fundamental properties of LTI systems can be deduced directly by taking his alternative approach, which otherwise would have been difficult (or maybe even impossible) to establish using the traditional approach. This expository article is an attempt to highlight only a few of his ingenious contributions to control theory. [ABSTRACT FROM AUTHOR]

This paper focuses on two main aspects. Firstly, we introduce a generalized form of conformable fractional derivatives called φ$$ \varphi $$‐conformable fractional derivatives Cδ,φ$$ {C}^{\delta, \varphi } $$ along with their corresponding integrals Iδ,φ$$ {I}^{\delta, \varphi } $$. We also present several theorems related to these derivatives. Secondly, we investigate the observability, controllability, and stability of a fractional dynamical system known as the φ$$ \varphi $$‐conformable fractional dynamical system (φ$$ \varphi $$‐CF‐DS). We establish the connection between controllability, the controllability matrix, and the fractional φ$$ \varphi $$‐conformable fractional differential Lyapunov equation (φ$$ \varphi $$‐CF‐DLE). We prove that the φ$$ \varphi $$‐CF‐DS is stable if and only if all eigenvalues of the matrix M$$ M $$ have negative real parts. Moreover, we provide theorems regarding the observability of an φ$$ \varphi $$‐CF‐DS. To demonstrate the efficacy of our results, we include illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamical behavior of a linear control system on R 2 when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control range can have a strong interference in such dynamics if the matrix is not invertible. In the invertible case, we explicitly construct the unique control set with a nonempty interior. [ABSTRACT FROM AUTHOR]

In this article, we completely describe the control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups. We show that, if the restriction of the associate derivation to the nilradical is nontrivial, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior. Moreover, such a control set is unique and, up to conjugations, given as a cylinder of the state space. On the other hand, if such a restriction is trivial, one can obtain an infinite number of control sets with empty interiors or even controllability, depending on the group considered. [ABSTRACT FROM AUTHOR]

In this paper, we study the thermal entanglement and geometric quantum discord in Heisenberg XXZ Hamiltonian with nonuniform magnetic field and Dzyaloshinskii–Moriya (DM) interaction. Here, we consider primarily the effect of different factors such as nonuniform magnetic field, exchange interaction J , Dzyaloshinskii–Moriya interaction D on the thermal entanglement and the geometric quantum discord for the antiferromagnetic in Heisenberg qubit system. The results indicate that strong DM interaction plays the essential role in the conservation of quantum correlation. For any J , D and T quantum correlation indicates the exact symmetry about the inversion of nonuniform part of magnetic field. Also, these results indicate robustness of the thermal entanglement and the geometric quantum discord against the increasing J and D . On the other hand, the geometric quantum discord is more robust for temperature than thermal entanglement. Thus, the results indicate that Quantum correlation can be appreciably manipulated according to the exchange interaction and DM interaction, uniform part and nonuniform part of magnetic field. [ABSTRACT FROM AUTHOR]

In this paper, we present a lemma that allows us to characterize a broad class of C0-semigroups on time scales, which can be applied to prove existence and uniqueness of solutions of systems of partial differential equations where the time domain is a time scale. The result obtained is applied to study the controllability of the heat equation on time scales. The lemma presented in this paper can be seen as a unification of the one proved by H. Leiva in [28], for semigroups in [0,∞). [ABSTRACT FROM AUTHOR]

The paper deals with the boundary controllability of a family of nonlinear Boussinesq systems introduced by J. L. Bona, M. Chen and J.-C. Saut to describe the two-way propagation of small amplitude gravity waves on the surface of water in a canal. By combining the classical duality approach and a careful spectral analysis of the operator associated with the state equations, we first obtain the exact controllability of the linearized system in suitable Hilbert spaces. Then, by means of a contraction mapping principle, we establish the local exact controllability for the original nonlinear system. [ABSTRACT FROM AUTHOR]

Brain cancer is one of the deadliest diseases, although many efforts have been made to treat it, there is no comprehensive and effective treatment approach yet. In recent years, the use of network-based analysis to identify important biological genes and pathways involved in various complex diseases, including brain cancer, has attracted the attention of researchers. The goal of this manuscript is to perform a comprehensive analysis of the various results presented related to brain cancer. For this purpose, firstly, based on the CORMINE medical database, collected all the genes related to brain cancer with a valid P-value. Then the structural and functional relationships between the above gene sets have been identified based on the STRING database. Next, in the PPI network, hub centrality analysis was performed to determine the proteins that have many connections with other proteins. After the modularization of the network, the module with the most hub vertices is considered as the most relevant module to the formation and progression of brain cancer. Since the driver vertices play an important role in biological systems, the edges of the selected module were oriented, and by analyzing the controllability of complex networks, a set of five proteins with the highest control power has been identified. Finally, based on the drug-gene interaction, a set of drugs effective on each of the driver genes has been obtained, which can potentially be used as new combination drugs. Validation of the hub and driver proteins shows that they are mainly essential proteins in the biological processes related to the various cancers and therefore the drugs that affect them can be considered as new combination therapy. The presented procedure can be used for any other complex disease. [ABSTRACT FROM AUTHOR]

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In this article, we study the controllability of dynamical systems with (k , ψ) -Hilfer fractional derivative. The Gramian matrix is used to get a necessary and sufficient controllability requirement for linear systems, which are characterized by the Mittag–Leffler (M–L) functions, while the fixed point approach is used to arrive at adequate controllability criteria for nonlinear systems. The novel feature of this study is to inquire into the controllability notion by using (k , ψ) -Hilfer fractional derivative, the most generalized variant of the Hilfer derivative. The advantage of this type of fractional derivative is that it recovers the majority of earlier studies on fractional differential equations (FDEs). Finally, we provide numerical examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

The role of network metrics in exploring brain networks of mental illness is crucial. This study focuses on quantifying a node controllability index (CA-scores) and developing a novel framework for studying the dysfunction of attention deficit hyperactivity disorder (ADHD) brains. By analyzing fMRI data from 143 healthy controls and 102 ADHD patients, the controllability metric reveals distinct differences in nodes (brain regions) and subsystems (functional modules). There are significantly atypical CA-scores in the Rolandic operculum, superior medial orbitofrontal cortex, insula, posterior cingulate gyrus, supramarginal gyrus, angular gyrus, precuneus, heschl gyrus, and superior temporal gyrus of ADHD patients. A comparison with measures of connection strength, eigenvector centrality, and topology entropy suggests that the controllability index may be more effective in identifying abnormal regions in ADHD brains. Furthermore, our controllability index could be extended to investigate functional networks associated with other psychiatric disorders. [ABSTRACT FROM AUTHOR]

Intertemporal decision-making is important for both economy and physical health. Nevertheless, in daily life, individuals tend to prefer immediate and smaller rewards to delayed and larger rewards, which is known as delay discounting (DD). Episodic future thinking (EFT) has been proven to influence DD. However, there is still no inconsistent conclusion on the effect of negative EFT on DD. Considering the perceived controllability of negative EFT may address the issue (Controllability refers to the extent to which progress and result of an event could be controlled by ourselves). In the current study, we manipulated EFT conditions (baseline, neutral EFT, negative-controllable EFT and negative-uncontrollable EFT), delayed time (i.e. 1 week, 1 month, 3 months, 6 months, 1 year and 3 years) and reward magnitude (small, large). We mainly found that when experiencing negative-uncontrollable EFT compared to negative-controllable EFT in the delayed time of 6 months with large rewards, individuals chose more delayed rewards, suggesting that negative-uncontrollable EFT effectively reduced DD under conditions of both large-magnitude reward and longer delayed time. The current study provides new insight for healthy groups on optimising EFT. In that case, individuals are able to gain long-term benefits in financial management and healthcare. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a set of sufficient conditions for the controllability of a class of nonlocal impulsive neutral stochastic integro-differential systems perturbed by a Rosenblatt process in a separable Hilbert space with infinite delay. We obtain our result using stochastic analysis and a fixed-point technique. Lastly, an example is provided to show the validity of the obtained results. [ABSTRACT FROM AUTHOR]

The main objective of this work is to develop algorithms and software solutions for finding optimal control strategies for an unmanned aerial vehicle, the mathematical model of which is represented by a system of ordinary differential equations. Using the maximum principle, an algorithm was developed to determine the optimal control. The presented methods and models are of high practical importance for managing various economic and technical systems. [ABSTRACT FROM AUTHOR]

The aim of this research is to design algorithms and develop software for the automated assessment of stability criteria in the dynamic behavior of unmanned aerial vehicles (UAVs), modeled through systems of ordinary differential equations (ODEs). By employing advanced symbolic computation techniques, an application has been created that facilitates the automatic linearization of nonlinear equation systems and the derivation of the characteristic polynomial for the resulting linearized ODE systems. The introduced methodologies and models provide substantial practical significance in the evaluation of stability across a broad range of both economic and technical systems. [ABSTRACT FROM AUTHOR]

In this paper, we study fractional-order linear, finite-dimensional disturbed systems. The fundamental objective of this work is to study the remediability or compensation problem in linear fractional-order time-invariant perturbed systems. The remediability was introduced with the aim of finding an appropriate control that steers the output of the perturbed system towards normal observation at the final moment. We begin first by giving some characterizations of compensation, and then we prove that a rank condition is sufficient to assure the remediability of our system. The relationship between controllability and compensation is also given, and we provide some examples to illustrate our results. [ABSTRACT FROM AUTHOR]

The deep integration of power grid and information network enhances the controllability of the power system while reducing its ability to resist external interference. Firstly, an interdependent model of cascading failures in the cyber-physical power system (CPPS) was established based on the proposed load redistribution scheme using node load and capacity probabilities. This model was used to investigate the robustness and controllability changes in the CPPS under different coupling strategies. Secondly, the concept of surviving load percentage was utilized to quantify the power grid's ability to withstand cascading failures. The effects of different coupling strategies and capacity parameters on the robustness and controllability of CPPS were analyzed. The assessment method for power node importance was proposed based on network controllability theory and validated in the IEEE39 system. The research results indicate that the coupling of high-betweenness nodes in the power grid and high-betweenness nodes in the information network leads to a stronger resistance to interference in the power information physical network, and the capacity parameters of power grid nodes have a greater impact on the system compared to the capacity parameters of information network nodes. [ABSTRACT FROM AUTHOR]

The controllability of complex networks is a core issue in network research. Assessing the controllability robustness of networks under destructive attacks holds significant practical importance. This paper studies the controllability of networks from the perspective of malicious attacks. A novel attack model is proposed to evaluate and challenge network controllability. This method disrupts network controllability with high precision by identifying and targeting critical candidate nodes. The model is compared with traditional attack methods, including degree-based, betweenness-based, closeness-based, pagerank-based, and hierarchical attacks. Results show that the model outperforms these methods in both disruption effectiveness and computational efficiency. Extensive experiments on both synthetic and real-world networks validate the superior performance of this approach. This study provides valuable insights for identifying key nodes crucial for maintaining network controllability. It also offers a solid framework for enhancing network resilience against malicious attacks. [ABSTRACT FROM AUTHOR]

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Controllability is a fundamental property of control systems, serving as the prerequisite for controller design. While controllability test is well established in modelic (i.e., model-driven) control systems, extending it to datatic (i.e., data-driven) control systems is still a challenging task due to the absence of system models. In this study, we propose a general controllability test method for nonlinear systems with datatic description, where the system behaviors are merely described by data. In this situation, the state transition information of a dynamic system is available only at a limited number of data points, leaving the behaviors beyond these points unknown. Different from traditional exact controllability, we introduce a new concept called ϵ-controllability, which extends the definition from point-to-point form to point-to-region form. Accordingly, our focus shifts to checking whether the system state can be steered to a closed state ball centered on the target state, rather than exactly at that target state. Given a known state transition sample, the Lipschitz continuity assumption restricts the one-step transition of all the points in a state ball to a small neighborhood of the subsequent state. This property is referred to as one-step controllability backpropagation, i.e., if the states within this neighborhood are ϵ-controllable, those within the state ball are also ϵ-controllable. On its basis, we propose a tree search algorithm called maximum expansion of controllable subset (MECS) to identify controllable states in the dataset. Starting with a specific target state, our algorithm can iteratively propagate controllability from a known state ball to a new one. This iterative process gradually enlarges the ϵ-controllable subset by incorporating new controllable balls until all ϵ-controllable states are searched. Besides, a simplified version of MECS is proposed by solving a special shortest path problem, called Floyd expansion with radius fixed (FERF). FERF maintains a fixed radius of all controllable balls based on a mutual controllability assumption of neighboring states. The effectiveness of our method is validated in three datatic control systems whose dynamic behaviors are described by sampled data.

Identifying beat positions in music recordings, a central task in Music Information Retrieval (MIR), is commonly referred to as beat tracking. Typically, this involves computing an activation function to reveal frame-wise beat likelihood and then conducting post-processing to derive final beat positions. Existing methods often operate offline, requiring access to the entire music track for processing. In this article, we introduce a real-time beat tracking system based on the predominant local pulse (PLP) concept, originally designed for offline use. Our main contribution is the successful transformation of the PLP-based algorithm into a real-time procedure. Unlike traditional offline methods providing static beat positions, our real-time approach dynamically captures changes in local pulse characteristics with each frame of an audio stream. This yields additional insights, including beat context, beat stability, and beat lookahead for predicting beats in advance. In this way, our system not only demonstrates high controllability for real-time applications but also can operate at zero latency. Additionally, we present experiments comparing our real-time beat tracking system with other models and evaluating the accuracy of our lookahead feature. Finally, we showcase two real-world applications for interactive music making and educational music gaming that creatively leverage our system’s output. In summary, our real-time beat tracking system offers a lightweight algorithm that is particularly well-suited for interactive music software development.

An increase in the share of weather-dependent generation at low voltage levels necessitates incorporating the low-voltage network in optimizing a distribution network. Optimization in a multi-voltage network requires significant computation time and effort due to many nodes operating at different voltage levels. This research proposes a decomposition and strategic optimization method to reduce the computation requirements for such large multi-voltage distribution networks. The proposed algorithm reduces the space complexity and the computation time required for solving the optimization routines of these multi-voltage distribution networks. A virtual transformer model incorporates tap-changer as a continuous variable in the semidefinite programming power flow optimization model. The zero-duality gap condition for multiple virtual transformers is proven empirically. Compared to a centralized optimization using the same power flow model, the proposed framework reduced the computation time by 96%.