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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]

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]

This paper is dedicated towards the inspection of impulsive nonlinear fractional evolution equations (NFEEs) for existence and uniqueness results in Banach spaces. The concerned NFEEs involves Riemann–Liouville higher-order time derivative operators with fixed lower limits along with non-instantaneous impulses. Motive of the paper is to set sufficient conditions to guarantee the existence of mild solution in Banach spaces. Firstly, appropriate integral type initial conditions depending on the impulsive functions are chosen at suitable points. A mild solution of the concerned system is constructed using Riemann–Liouville fractional resolvent operator R γ (t) . Subsequently, existence and uniqueness results are established under sufficient assumptions utilising fixed point approach. An example integrating specific input parameters is presented at the end to demonstrate and validate the methodology proposed. [ABSTRACT FROM AUTHOR]

This work studies the approximate controllability of a class of second-order retarded semilinear differential equations with nonlocal conditions and with delays in control. First, we deduce the existence of mild solutions using cosine family and fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz. Controllability of the system is shown using an approximate and iterative technique. The results are illustrated using an example. [ABSTRACT FROM AUTHOR]

In this paper computation of control for an approximately controllable semilinear system with state delay is studied using Tikhonov regularization. Depending on the state delay occurred in the time interval, approximate controllability of the semilinear control system is proved under the assumption of approximate controllability of the corresponding linear system without state delay under some assumptions on the system constraints.Computing control for a given target state for the aforesaid system is ill-posed in the sense of Hadamard. Regularized control is computed using Tikhonov regularization for a given target state. Under some assumptions on system and nonlinear function f, it is proved that the target state corresponding to the regularized control is very close to the actual state to be attained by the system. Proposed Theory is corroborated with an example of diffusion system. [ABSTRACT FROM AUTHOR]

This work studies the approximate controllability of a class of first-order retarded semilinear differential equations with delays in control and nonlocal conditions. First we deduce the existence of mild solutions using fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz, which is a weaker condition than Lipschitz continuity. Controllability results of the system are shown by using the approximate and iterative technique. The results are illustrated by providing an example. [ABSTRACT FROM AUTHOR]

This article is concerned with the second-order nonlocal retarded semilinear differential systems with fixed delay in control. Utilizing the theory of fixed point as well as cosine family, we establish the existence and uniqueness of the mild solution of the system. Then a set of new sufficient conditions are established for the controllability of the semilinear system. The theory is illustrated by providing an example. [ABSTRACT FROM AUTHOR]

Human action localization in any long, untrimmed video can be determined from where and what action takes place in a given video segment. The main hurdles in human action localization are the spatiotemporal randomnesses of their happening in a parallel mode which means the location (a particular set of frames containing action instances) and duration of any particular action in real-life video sequences generally are not fixed. At another end, the uncontrolled conditions such as occlusions, viewpoints and motions at the crisp boundary of the action sequences demand to develop a fast deep network which can be easily trained from unlabeled samples of complex video sequences. Motivated from the facts, we proposed a weakly supervised deep network model for human action localization. The model is trained from unlabeled action samples from UCF50 action benchmark. The five-channel data obtained from the concatenation of RGB (three-channel) and optical flow vectors (two-channel) are fed to the proposed convolutional neural network. LSTM network is used to yield the region of action happening area. The performance of the model is tested on UCF-sports dataset. The observation and comparative results reflect that our model can localize any action from annotation-free data samples captured in uncontrolled conditions. [ABSTRACT FROM AUTHOR]

This paper presents a trajectory generation algorithm for robots which can walk like human with movable foot and active toe. The proposed algorithm allows smooth transition between walking phases namely, single and double support phases. A neural network approach is used for solving inverse kinematics so that the biped robot follows the ankle and hip trajectories to walk. Zero moment point (ZMP) stability is ensured by taking into account the upper body movements along with the planned motion trajectories. Here, we analyze the effect of lateral upper body motion on ZMP stability. Different types of trajectories for upper body are generated, and the one which ensured the most stable locomotion is identified. [ABSTRACT FROM AUTHOR]

The main objective of this article is to provide sufficient conditions for the exact controllability of fractional order semilinear system of order |$\rho\in (1,2]$| when the nonlinear term is not Lipschitz continuous. Here the nonlinear term is assumed to have an integral contractor which is a weaker condition than Lipschitz condition. The existence and uniqueness of the mild solution for the fractional order semilinear system is proved using an iterative approach. Finally, controllability results are established under the assumption that the corresponding linear system is exactly controllable. [ABSTRACT FROM AUTHOR]

In this article, sufficient conditions have been obtained for the controllability of retarded semilinear fractional system with non-local conditions using the compactness of the non-linear function. The Nussbaum fixed point theorem combined with the theory of strongly continuous semigroup and fractional calculus are the main tools used in this problem. Finally, some examples have been provided to illustrate the application of the obtained results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present some sufficient conditions for approximate and exact controllability of semilinear stochastic control system with finite delay. Sufficient conditions for approximate controllability are obtained by separating the given semilinear system into two systems namely a semilinear deterministic system and a linear stochastic system using Schauder fixed point theorem. For obtaining the sufficient conditions for exact controllability of assumed system, Banach fixed point theorem is applied. Instead of a C0-semigroup associated with the mild solution of the system we use the so-called fundamental solution. At the end, examples are given to illustrate the theory. [ABSTRACT FROM AUTHOR]

Computation of control for a controlled partial differential equation is a difficult task, especially when the control problem is ill posed. In this paper, we propose a method of computing the regularized control of a diffusion control system using Tikhonov regularization approach when the system is approximately controllable. The method proposed here for choosing regularization parameter guarantees the convergence of the proposed control. [ABSTRACT FROM PUBLISHER]

A family of dynamical control systems described by nonlinear fractional of order (1,2] stochastic differential equations in L spaces is considered. We discussed the approximate controllability of stochastic semilinear fractional control system of order α∈(1,2] under the assumption that the corresponding linear system is approximately controllable. A new set of sufficient conditions for approximate controllability of system are obtained by the theory of strongly continuous α-order cosine family, fixed point theorem, and stochastic analysis techniques. At the end, an example is given to illustrate the theory. [ABSTRACT FROM AUTHOR]

For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial state x0 to an ϵ neighbourhood of the target state xτ at time τ>0 under the assumption that the nonlinear function f is Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that the target state corresponding to the regularized control is close to the actual state to be attained. [ABSTRACT FROM AUTHOR]

In this paper, approximate controllability of an abstract semilinear control system is proved under simple sufficient conditions in Hilbert spaces. The results are obtained when nonlinearity satisfy Lipschitz condition. At the end one example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

For an approximately controllable nonlinear system, the task of finding a control for a given target state is ill-posed. By finding a regularized control of a linear approximately controllable system using Tikhonov regularization, we compute a regularized control for the nonlinear system under the assumption of Lipschitz continuity of the nonlinear function. The theory is substantiated with numerical experiments. [ABSTRACT FROM AUTHOR]

This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approximate controllability of semilinear deterministic system, Schauder fixed point theorem has been used. At the end, an example has been presented to illustrate the feasibility of the proposed result. [ABSTRACT FROM AUTHOR]

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process that can be modeled by impulsive differential equations. This article studies the approximate controllability of impulsive semilinear stochastic system with delay in state in Hilbert spaces. Assuming the conditions for the approximate controllability of the corresponding deterministic linear system, we obtain the sufficient conditions for the approximate controllability of the impulsive semilinear stochastic system with delay in state. The results are obtained by using Banach fixed point theorem. Finally, two examples are given to illustrate the developed theory. [ABSTRACT FROM AUTHOR]

This paper deals with the approximate controllability of second-order semilinear control system in Hilbert spaces under the assumption that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed, and the sufficient conditions for the approximate controllability of the proposed problem in Hilbert spaces are established. The results are obtained when the nonlinearity satisfying the monotone condition and integral contractor condition. Finally, an example is provided to illustrate the application of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonlinear fractional order control system with delay in state variable. Existence and uniqueness of solution are shown by using method of steps. The sensitivity of the state and control with respect to the parameters of the system is shown. Finally, analytical results are substantiated by numerical examples. [ABSTRACT FROM AUTHOR]

This article is concerned with the exact controllability of the semilinear thermoelastic system, which can be written aswith clamped/Dirichlet boundary conditions. Here, a relation between the reachable set of a semilinear thermoelastic system and that of the corresponding linear system is proved using the results given. [ABSTRACT FROM AUTHOR]

In this paper, the approximate controllability of second order semilinear stochastic system involving nonlocal conditions is studied. By using Sadovskii’s Fixed Point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of second order semilinear stochastic system with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable. Finally, an application to a second order semilinear stochastic system with nonlocal initial condition is provided to illustrate the obtained theory. [ABSTRACT FROM AUTHOR]

In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present some sufficient conditions for approximate controllability of fractional order semilinear system of order α ∊ (1,2] in Hilbert spaces. The results are obtained by using Schauder's fixed point theorem. At the end, an example is given to show the effectiveness of the result. [ABSTRACT FROM AUTHOR]

This paper discusses the analytical solution of fractional differential equations involving the Hilfer fractional derivative. The procedure adopted is the modified iterative Laplace transform method which uses simple calculation and has a higher convergence rate. The approach is such that for distinct values of the type of the Hilfer fractional derivative, the study is shifted automatically between the differential system with Riemann–Liouville and Liouville–Caputo fractional order derivative. Examples of one, two, and three-dimensional differential equations with appropriate initial conditions are analyzed in detail using graphical illustrations and as well as through a numerical approach. The comparison plot is investigated in detail from multiple viewpoints. [ABSTRACT FROM AUTHOR]

In this paper, using the Schauder's fixed point theorem, different sufficient conditions to the approximate controllability for a class of retarded semilinear control systems with bounded delay are established. The paper is also concerned with the existence and uniqueness of mild solution. In particular, to obtain desired results it is assumed that the nonlinear function is locally Lipschitz continuous and satisfies linear growth condition. This theory relax the assumptions on nonlinear term of the semilinear system made by earlier authors. Finally, an example is given to show the application of the main result. [ABSTRACT FROM AUTHOR]

In this article, exact controllability of second-order semilinear differential system with nonlocal conditions in Banach spaces is studied. To establish sufficient conditions for exact controllability, Sadovskii's fixed point theorem together with the theory of strongly continuous cosine family is been used. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. An example is given to illustrate the developed theory. [ABSTRACT FROM AUTHOR]

The aim of this paper is to design a robust adaptive neural network-based hybrid position/force control scheme for robot manipulators in the presence of model uncertainties and external disturbance. The feedforward neural network employed to learn a highly nonlinear function requires no preliminary learning. The control purposes are to achieve the stability in the sense of Lyapunov for desired interaction force between the end-effector and the environment and to regulate robot tip position in cartesian space. An adaptive compensator is also developed to eliminate the effect of disturbance term of neural network approximation error and external disturbance or unmodeled dynamics etc. A key feature of this compensator is that the prior information of the disturbance bound is not required. Finally, a comparative simulation study with a model-based robust control scheme for a two-link robot manipulator is presented. [ABSTRACT FROM AUTHOR]

In this paper, we prove the approximate controllability for a class of semilinear delay control systems of fractional order under the natural assumption that the corresponding linear system is approximately controllable. The theory is illustrated with an example. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, sufficient conditions are established for the approximate controllability of a class of semilinear delay control systems of fractional order. The existence and uniqueness of mild solution of the system is also proved. The results are obtained by using contraction principle and the Schauder fixed point theorem. Some examples are given to illustrate the theory. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to design a neural network based adaptive control scheme for redundant manipulators in the presence of model uncertainties and external disturbances together with multiple self-motion criteria. With reference to the paper (N. Kumar, V. Panwar, N. Sukavanam, S.P. Sharma, J.H. Borm, Neural network based nonlinear tracking control of kinematically redundant robot manipulators, Mathematical and Computer Modelling 53 (2011) 1889–1901), an adaptive mechanism is also developed to estimate the uncertain bound of external disturbances and neural network approximation error etc. without requirement of known bounds. By Lyapunov method asymptotic error convergence can be guaranteed for both task-space and sub-task tracking errors. A comparative simulation study with a robust controller and the proposed controller are included for a 3 link planar robot manipulator. [Copyright &y& Elsevier]

Abstract: This paper deals with the approximate controllability of a semilinear control system with delay, where the nonlinear term satisfies the linear growth condition. Sufficient conditions for the approximate controllability of a semilinear control system have been established by assuming that the corresponding linear control system with delay is approximately controllable. To prove our results, the Schauder fixed point theorem is applied and instead of a Co-semigroup associated with the mild solution of the system we use the so-called fundamental solution. [Copyright &y& Elsevier]

In this paper, the approximate controllability for a class of semilinear delay control systems of fractional order is proved under the natural assumption that the linear system is approximately controllable. The existence and uniqueness of the mild solution is also proved under suitable assumptions. An example is given to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper presents a computational method for boundary control of controlled heat equation. The proposed method relies upon the function approximation capability of feedforward neural network and global optimization power of genetic algorithm. [ABSTRACT FROM AUTHOR]

The objective of this article is to investigate some sufficient conditions, for S-controllability of an abstract first order semilinear control system of the form [image omitted] Here, A is the closed linear operator, B and C are bounded linear operators defined on suitable Hilbert spaces, ω and ν are suitable wiener processes, and d is the stochastic differentiation. The results are obtained by the separation principle approach. An example is provided to illustrate the technique. [ABSTRACT FROM AUTHOR]

A result concerning the exact controllability of a semilinear thermoelastic system, in which the control term occurs solely in the thermal equation, is derived under the influence of rotational inertia and Lipschitz nonlinearity, subject to the clamped/Dirichlet boundary conditions. In the proof, we make use of the result given by Avalos (Differential and Integral Equations, 2000; 13(4-6):613-630), which states that the corresponding linear system is exact controllable. [ABSTRACT FROM AUTHOR]

In this paper a neural network based controller for robot positioning and tracking using direct monocular visual feedback is proposed. The visual information is provided using a camera mounted on the end-effector of the manipulator. A PI kinematic controller is proposed to achieve motion control objective in the image plane. A Feedforward Neural Network (FFNN) is used to compensate for the robot dynamics. The FFNN computes the required torques to drive the robot manipulator to achieve desired tracking. The stability of combined PI kinematic and FFNN computed torque is proved by Lyapunov theory. Simulation results are carried out for 3 DOF articulated robot manipulator to evaluate the controller performance. [ABSTRACT FROM AUTHOR]

Many natural and man-made objects have planar and curvilinear surfaces. The images of such curves do not usually have sufficient distinctive features to apply conventional feature-based reconstruction algorithms. In this paper, we describe a method for the reconstruction of various kinds of quadratic curves in 3D space as an intersection of two cones containing the respective projected digitized curve images in the presence of Gaussian noise. The advantage of this method is that it overcomes the correspondence problem that occurs in pairs of projections of the curve. Using nonlinear least-squares curve fitting, the parameters of a curve in 2D digitized image planes are determined. From this we reconstruct the 3D quadratic curve. Relevant mathematical formulations and analytical solutions for obtaining the equation of the reconstructed curve are given. Simulation studies have been conducted to observe the effect of noise on errors in the process of reconstruction. Results for various types of quadratic curves are presented using simulation studies. These are the main contributions of this work. The angle between the reconstructed and the original quadratic curves in 3D space has been used as the criterion for the measurement of the error. The results of this study are useful for the design of a stereo-based imaging system (such as the LBW decision in cricket, the path of a missile, robotic vision, path planning, etc.) and for the best reconstruction with minimum error. [ABSTRACT FROM AUTHOR]

Human tracking and localization play a crucial role in many applications like accident avoidance, action recognition, safety and security, surveillance and crowd analysis. Inspired by its use and scope, we introduced a novel method for human tracking (one or many) and re-localization in a complex environment with large displacement. The model can handle complex background, variations in illumination, changes in target pose, the presence of similar target and appearance (pose and clothes), the motion of target and camera, occlusion of the target, background variation, and massive displacement of the target. Our model uses three convolutional neural network based deep architecture and cascades their learning such that it improves the overall efficiency of the model. The first network learns the pixel level representation of small regions. The second architecture uses these features and learns the displacement of a region with its category between moved, not-moved, and occluded classes. Whereas, the third network improves the displacement result of the second network by utilizing the previous two learning. We also create a semi-synthetic dataset for training purpose. The model is trained on this dataset first and tested on a subset of CamNeT, VOT2015, LITIV-tracking and Visual Tracker Benchmark database without training with real data. The proposed model yield comparative results with respect to current state-of-the-art methods based on evaluation criteria described in Object Tracking Benchmark, TPAMI 2015, CVPR 2013 and ICCV 2017. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to study the approximate controllability of nonlocal and impulsive neutral integro-differential equations using the resolvent operator theory, the approximating technique, semigroup theory and the theory of fixed point. We also derive a variation of constants formula for representing a solution of the given system by resolvent operators and then study the existence of a mild solution of the system. We prove the main results by taking the impulsive functions to be continuous only and taking the nonlocal initial condition function to be Lipschitz continuous in the first case and continuous only in the second case. Finally, the main results are illustrated using examples. [ABSTRACT FROM AUTHOR]

Computing steering control for an approximately controllable linear system for a given target state is an ill-posed problem. We use a weighted Tikhonov regularization method and compute the regularized control. It is proved that the target state corresponding to the regularized control is close to the actual state to be attained. We also obtained error estimates and convergence rates involved in the regularization procedure using both the a priori and a posteriori parameter choice rule. Theory is substantiated with numerical experiments. [ABSTRACT FROM AUTHOR]

The paper deals with the approximate controllability of a semi-linear stochastic system with multiple delays in control in infinite dimensional spaces. Sufficient conditions for the approximate controllability of the semi-linear control system have been established. The results are obtained using the Banach fixed-point theorem. An example is introduced to show the effectiveness of the result. [ABSTRACT FROM AUTHOR]

The approximate controllability of a fractional impulsive stochastic neutral integro-differential equation with deviating argument and infinite delay is studied. The control parameter being inside the nonlinear term. Only Schauder fixed point theorem and a few fundamental hypotheses are used to prove our result. The assumption of the existence of the inverse of controllability operator is not required. Since its inverse does not exist in infinite dimensional space if the associated semigroup is compact. Lipschitz continuity of the nonlinear function is also not required. We also give an example to illustrate our result. [ABSTRACT FROM AUTHOR]

A mathematical model for bi-directional functionally graded Euler-Bernoulli nanobeams has been developed based on nonlocal strain gradient theory intervened with Gurtin-Murdoch surface elasticity theory. This model estimates the combined effect of nonlocal, strain gradient and surface stresses on natural frequencies of the nanobeams with varying material properties in axial and transverse directions both as per the power-law functions. The governing differential equation of motion and nonclassical boundary conditions for considered nanobeams have been derived with the help of Hamilton's energy principle. For the first time, the problem of bi-directional functionally graded nonlocal strain gradient nanobeam has been well-posed by considering higher-order nonclassical boundary conditions. Differential quadrature rule has been used to solve the governing differential equations for frequency parameters. A parametric study has been performed to analyze the significance of considering the surface effect on the vibration behavior of nonlocal strain gradient nanobeams with varying values of nonlocal parameter, length scale parameter, gradient indices and slenderness ratio for three different boundary conditions. The results reveal that the surface effect has a considerable increase in the frequencies of bi-directional functionally graded nanobeam, especially at lower thicknesses. An additional increase in the effect of material length scale parameter and nonlocal parameter has been noticed in the presence of surface parameters. • Effect of surface stresses has been accounted using Gurtin-Murdoch surface elasticity theory. • Bi-directional variation of material properties has been considered. • The material properties of bulk part are taken to be different from the surface layers. • Analysis of vibration characteristic has been presented using nonlocal strain gradient theory. [ABSTRACT FROM AUTHOR]