This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

This article presents a new cascaded extended state observer (CESO)-based sliding-mode control (SMC) for an underactuated flexible joint robot (FJR). The control of the FJR has many challenges, including coupling, underactuation, nonlinearity, uncertainties and external disturbances, and the noise amplification especially in the high-order systems. The proposed control integrates the CESO and SMC, in which the CESO estimates the states and disturbances, and the SMC provides the system robustness to the uncertainty and disturbance estimation errors. First, a dynamic model of the FJR is derived and converted from an underactuated form to a canonical form via the Olfati transformation and a flatness approach, which reduces the complexity of th

Nowadays, Wheeled Mobile Robots (WMRs) have found many applications as industry, transportation, inspection, and other fields. Therefore, the trajectory tracking control of the nonholonomic wheeled mobile robots have an important problem. This work focus on the application of model-based on Fractional Order  PI^aD^b (FOPID) controller for trajectory tracking problem. The control algorithm based on the errors in postures of mobile robot which feed to FOPID controller to generate correction signals that transport to  torque for each driven wheel, and by means of dynamics model of mobile robot these torques used to compute the linear and angular speed to reach the desired pose. In this work a dynamics model of

     In this research, our aim is to study the optimal control problem (OCP) for triple nonlinear elliptic boundary value problem (TNLEBVP). The Mint-Browder theorem is used to prove the existence and uniqueness theorem of the solution of the state vector for fixed control vector. The existence theorem for the triple continuous classical optimal control vector (TCCOCV) related to the TNLEBVP is also proved. After studying the existence of a unique solution for the triple adjoint equations (TAEqs) related to the triple of the state equations, we derive The Fréchet derivative (FD) of the cost function using Hamiltonian function. Then the theorems of necessity conditions and the sufficient condition for optimality of

An adaptive nonlinear neural controller to reduce the nonlinear flutter in 2-D wing is proposed in the paper. The nonlinearities in the system come from the quasi steady aerodynamic model and torsional spring in pitch direction. Time domain simulations are used to examine the dynamic aero elastic instabilities of the system (e.g. the onset of flutter and limit cycle oscillation, LCO). The structure of the controller consists of two models :the modified Elman neural network (MENN) and the feed forward multi-layer Perceptron (MLP). The MENN model is trained with off-line and on-line stages to guarantee that the outputs of the model accurately represent the plunge and pitch motion of the wing and this neural model acts as the identifier. Th

Objectives: The purpose of the study is to ascertain the relationship between the training program and the socio-demographic features of patients with peptic ulcers in order to assess the efficiency of the program on patients' nutritional habits.

Methodology: Between January 17 and October 30 of 2022, The Center of Gastrointestinal Medicine and Surgery at Al-Diwanyiah Teaching Hospital conducted "a quasi-experimental study". A non-probability sample of 30 patients for the case group and 30 patients for the control group was selected based on the study's criteria. The study instrument was divided into 4 sections: the first portion contained 7 questions about demographic information, the second sect

Trajectory tracking and vibration suppression are essential objectives in a flexible joint manipulator control. The flexible joint manipulator is an under-actuated system, in which the number of control actions is less than the degree of freedom to be controlled. It is very challenging to control the underactuated nonlinear system with two degree of freedom. This paper presents a hierarchical sliding mode control (HSMC) for a rotary flexible joint manipulator (RFJM). Firstly, the rotary flexible joint manipulator is modeled by two subsystems. Secondly, the sliding surfaces for both subsystems are constructed. Finally, the control action is designed based on the Lyapunov function. Computer simulation results demonstrate the effectiveness of

The research deals with solar energy as one of the sources of renewable energies available in Iraq, which can be utilized. The research aims to identify the design pillars of the use of solar energy in street furniture and its relationship to formal variables. The research limits included street furniture manufactured by JCDecaux in Boston during the period 2015-2016, and included the theoretical framework which consists of two sections: solar energy (its beginnings and uses), and solar energy and its uses in Street furniture design.

As far as the research procedures and methodology are concerned, it adopted the descriptive approach in describing and analyzing the sample models in addition to describing and analyzing the sample i