In this paper, the time-optimal Control for point-to-point motion of robotic manipulators, with fixed initial and final states, bounded Control inputs and jerk constraint for entire path is presented. First, the jerk constraint with respect to state variables is derived. Afterwards the dynamic equations of robotic manipulator in state space form and jerk constraints discretized by forward difference technique. Thus the time-optimal Control problem is formulated as a constrained parameter optimization problem. The MATLAB optimization toolbox is used to obtain the solution of the constrained parameter optimization problem. The proposed method can help us to implement the time-optimal Control problem with bounded inputs and jerk constraint. Finally, the above-mentioned method is implemented for a 2R planar robotic manipulator. Simulation results show a smooth trajectory for robot motion when the jerk is limited, which can effectively reduce mechanical wear at joints.

In this paper, the time-optimal Control problem for point-to-point motion of robot manipulators with elastic joints, bounded Control inputs and jerk constraint on entire path is studied. First, The dynamic equations and jerk constraint are derived for a elastic joint manipulator. Then, the jerk constraint and equations of motion in the state space form are discredited by forward difference technique. Thus the time optimal Control problem is formulated as a constrained parameters optimization problem. The MATLAB optimization toolbox is used to obtain the solution of the optimization problem. This method helps to implement the jerk constraint, easily. The above mentioned method is also implemented for a single link with elastic joint, and some of results are presented. The results show a smooth trajectory for robot motion when the jerk is limited, which reduce the vibration and mechanical wear at the joints.

This paper presents a novel method for path planning of redundant manipulators. The idea is to use load distribution as an objective function for resolving kinematic redundancy. The method is based on imposing a set of convenient relation among joint torques as dynamic constraints to system. Two algorithms for path planning of redundant manipulators subject to dynamic constraints are proposed. The first algorithm takes advantage of all necessary dynamic constraint equations which can be approximately solved using a pseudo-inverse technique, whereas the second algorithm is based on finding a good starting point with fair load distribution and generate the path by imposing as many dynamic constraint equations as the number of degrees of redundancy. The results for path planning of a 3-DOF planar manipulator using this method are presenteded.

In this paper an uncertain multi objective closed-loop supply chain is developed. The first objective function is maximizing the total profit. The second objective function is minimizing the use of row materials. In the other word, the second objective function is maximizing the amount of remanufacturing and recycling. Genetic algorithm is used for optimization; and for finding the pareto optimal line, Epsilon-constraint method is used. Finally a numerical example is solved with proposed approach and performance of the model is evaluated in different sizes. The results show that this approach is effective and useful for managerial decisions.

Different optimization methods are available for optimum design of structures including; classical optimization techniques and meta-heuristic optimization algorithms. However, engineers do not generally use optimization techniques to design a structure. They attempt to decrease the structural weight and increase its performance and efficiency, empirically, by changing the variables and Controlling the constraints. Based on this professional engineering design philosophy, in this paper, a simple algorithm, termed the constraint Control Method (CCM), is developed and presented whereby optimum design is achieved gradually by Controlling the problem constraints. Starting with oversized sections, the design is gradually improved by changing sections based on a ‘ Control function’ and Controlling the constraints to be below the target values. As the constraints move towards their targets, the design moves towards an optimum. The general functionality of the proposed algorithm is first demonstrated by solving several linear and nonlinear mathematical problems which have exact answers. The performance of the algorithm is then evaluated through comparing design optimization results of three, 2D steel frame benchmark problems with those from other, metaheuristic optimization solutions. the proposed method leads to the minimum structural weight while performing much smaller number of structural analyses, compared to other optimization methods.

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal Control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the Control is not discreted. Optimal error estimates in L2 are established for the state and the Control variable. As a result, it can be proved that the discrete solutions possess the convergence property of order. Finally, a numerical example is presented which confirms the theoretical results.

A common method for Controlling a group of parallel converters in decentralized Control strategy structure in an island microgrid, the use is the droop-down characteristics of frequency ω-P and voltage E-Q. However, the problem with using this method is that the reactive power is not properly distributed (in proportion to the capacity of the micronutrients) between the micronutrients, which may lead to overload in the converters. Microgrids may also suffer from dynamic stability problems such as power fluctuations, which can be increased by switching between active and reactive power Control. To avoid this problem, the X / R ratio of transmission lines is an important parameter that should be carefully considered in the design of micronutrient Controllers. By linearizing and simplifying conditions, the Control system conversion function model becomes a single input-single output system, which is efficient enough to show the relationship between Control parameters such as slope of droop characteristics and derivative sentences, virtual impedance, and voltage Controllers. Using this model, stability conditions for different parameters are analyzed. Also, to improve power distribution stability, common droop strategies are modified by adjusting the slope as well as adding nonlinear sentence sections. This approach reduces the coupling between active and reactive power Control and reduces the dependence of power distribution on grid parameters such as the X / R ratio. To evaluate the reliability of the proposed model, the simulation results in a sample island microgrid in MATLAB software are presented.

This paper presents distributed training approach for a nonlinear and heterogeneous multi-UAV system to solve a safe and optimal formation Control problem. The objective of Control is to ensure safety while achieving optimal performance. In this regard, the position and attitude Controllers are considered in series. First, the optimal formation Control design is defined as the optimal performance in position Control and is modeled by the cost function. In this article, with the integration of cost functions and local Control barrier functions (CBFs), a novel distributed optimization problems are introduced. Existing the local CBF in the augmented cost function ensures the safety of the position Control, and as a result, collisions do not occur along the path of UAVs. The proposed method considers the safe and optimal position Controllers by solving unconstrained optimization problems instead of constrained ones. In the next stage, the reference attitudes are driven by virtual position Control. The attitude tracking optimal Control is considered the optimal performance in the attitude Control, and the related cost function models it. Finally, the stability and safety of the proposed Controllers are proven. These optimal and safe policies are obtained sequentially using off-policy multi-agent reinforcement learning (MARL) algorithms which do not require knowledge of UAVs' dynamics. The proposed algorithms are validated by simulating the formation Control problem of 6 UAVs with collision avoidance constraints.