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The purpose of this paper is to investigate time-optimal control problems for multiple unmanned aerial vehicle (UAV) systems to achieve predefined flying shape.

Two time-optimal protocols are proposed for the situations with or without human control input, respectively. Then, Pontryagin’s minimum principle approach is applied to deal with the time-optimal control problems for UAV systems, where the cost function, the initial and terminal conditions are given in advance. Moreover, necessary conditions are derived to ensure that the given performance index is optimal.

The effectiveness of the obtained time-optimal control protocols is verified by two contrastive numerical simulation examples. Consequently, the proposed protocols can successfully achieve the prescribed flying shape.

This paper proposes a solution to solve the time-optimal control problems for multiple UAV systems to achieve predefined flying shape.

The purpose of this paper is to propose a precise time-optimal path tracking approach for robots under kinematic and dynamic constraints to improve the work efficiency of robots and guarantee tracking accuracy.

In the proposed approach, the robot path is expressed by a scalar path coordinate and discretized into N points. The motion between two neighbouring points is assumed to be uniformly accelerated motion, so the time-optimal trajectory that satisfies constraints is obtained by using equations of uniformly accelerated motion instead of numerical integration. To improve dynamic model accuracy, the Coulomb and viscous friction are taken into account (while most publications neglect these effects). Furthermore, an iterative learning algorithm is designed to correct model-plant mismatch by adding an iterative compensation item into the dynamic model at each discrete point before trajectory planning.

An experiment shows that compared with the sequential convex log barrier method, the proposed numerical integration-like (NI-like) approach has less computation time and a smoother planning trajectory. Compared with the experimental results before iteration, the torque deviation, tracking error and trajectory execution time are reduced after 10 iterations.

As the proposed approach not only yields a time-optimal solution but also improves tracking performance, this approach can be used for any repetitive robot tasks that require more rapidity and less tracking error, such as assembly.

In this paper the design of a controller for a relay controlled second order nonlinear unstable plant with fourth order nonlinearity is considered. The task of the controller is the simultaneous reduction of output and output derivative to zero with the input being at zero. It is established that, if the initial values of error and error derivative fall in a “controllable region”, it is possible to reduce error and error derivative to zero simultaneously and in the shortest possible time with at most one switching reversal of the relay. It is also shown that, through simple transformation of error and error derivative, the equation of the switching curve can be made independent of the constant gain of the plant, as well as the coefficient of the nonlinear term.

The purpose of this paper is to devise a new approach to synthesize closed‐loop feedback guidance law for online thrust‐insensitive optimal trajectory generation utilizing neural networks.

The proposed methodology utilizes an open‐loop variational formulation that initially determines optimal launch/ascent trajectories for various scenarios of known uncertainties in the thrust profile of typical solid propellant engines. These open‐loop optimized trajectories will then provide the knowledge base needed for the subsequent training of a neural network. The trained network could eventually produce thrust‐insensitive closed‐loop optimal guidance laws and trajectories in flight.

The proposed neuro‐optimal guidance scheme is effective for online closed‐loop optimal path planning through some measurable and computable engine and flight parameters.

Determination of closed‐loop optimal guidance law for non‐linear dynamic systems with uncertainties in system and environment has been a challenge for researchers and engineers for many years. The problem of steering a solid propellant driven vehicle is one of these challenges. Even though a few researchers have worked in the area of non‐linear optimal control and thrust‐insensitive guidance, this paper proposes a new strategy for the determination of closed‐loop online thrust insensitive guidance laws leading to optimal flight trajectories for solid propellant launch and ascent vehicles.

From practical perspectives and to improve the working efficiency, trolley transportation and payload hoisting/lowering should be simultaneously controlled. Moreover, in practical crane applications, the transportation time is an important criterion for improving transportation efficiency. Based on these requirements, this paper aims to solve positioning and antiswing control problems and shorten the transportation time for underactuated varying-rope-length overhead cranes.

By choosing trolley acceleration and varying-rope-length acceleration as system inputs, the crane system dynamic model is converted into an equivalent model without linearizing/approximating. Then, based on the converted model and system state constraints, a time-optimal problem is formulated. Further, the original problem is converted into an optimization problem with algebraic constraints which can be conveniently solved. Finally, by solving the optimization problem, the optimal trajectories of system states, including displacements, velocities and accelerations, are obtained.

This paper first provides a nonlinear time-optimal trajectory planner for varying-rope-length overhead cranes, which achieves accurate and fast trolley positioning and eliminates payload residual swings. Meanwhile, all system states satisfy the given constraints during the entire process. Hardware experimental results show that the proposed time-optimal planner is effective and has better performance compared with existing methods.

This paper proposes a time-optimal trajectory planner for overhead crane systems with hoisting/lowering motion. The proposed planner achieves fast trolley positioning and eliminates payload residual swing with all the system states being constrained within given scopes. The planner is presented based on the original nonlinear system dynamics without linearization/approximation.

The purpose of this paper is to propose a new smooth online near time‐optimal trajectory planning approach to reduce the consuming time compared to the conventional dynamics trajectory planning methods.

In the proposed method, the robot path is expressed by a scalar path coordinate. The joints torque boundary and speed boundary are transformed into the plane, which can generate the limitation curves of pseudo‐velocity. The maximum pseudo‐velocity curve that meets the limits of torque and speed is built up through the feature points and control points in the plane by using cubic polynomial fitting method. Control points used for cubic polynomial construction are optimized by the Golden‐Section method.

The proposed method can avoid Range's phenomenon and also guarantee the continuity of torque.

The algorithm designed in this paper is used for the controller of a new industrial robot which will be equipped for the welding automatic lines of Chery Automobile Co. Ltd.

Compared to the five‐order polynomial trajectory optimization method proposed by Macfarlane and Croft, the approach described in this paper can effectively take advantage of joints maximum speed, and the calculation time of this method is shorter than conventional dynamics methods.

The purpose of this paper is to use analytical method and optimization tools to suggest time-optimal vaccination program for a basic SIR epidemic model with mass action contact rate when supply is limited.

The Lagrange Multiplier Method and Pontryagin’s Maximum Principle are used to explore optimal control strategy and obtain analytical solution for the control system to minimize the total cost of disease with boundary constraint. The numerical simulation is done with Matlab using the sequential linear programming method to illustrate the impact of parameters.

The result highlighted that the optimal control strategy is Bang-Bang control – to vaccinate with maximal effort until either all of the resources are used up or epidemic is over, and the optimal strategies and total cost of vaccination are usually dependent on whether there is any constraint of resource, however, the optimal strategy is independent on the relative cost of vaccination when the supply is limited.

The research indicate a practical view that the enhancement of daily vaccination rate is critical to make effective initiatives to prevent epidemic from out breaking and reduce the costs of control.

The analysis of the time-optimal application of outbreak control is of clear practical value and the introducing of resource constraint in epidemic control is of realistic sense, these are beneficial for epidemiologists and public health officials.

The purpose of this paper is to investigate the time optimal trajectory of the multi-tethered robot (MTR) on a large spinning net structures in microgravity environment.

The MTR is a small space robot that uses several tethers attached to the corner-fixed satellites of a spinning net platform. The transition of the MTR from a start point to any arbitrary designated points on the platform surface can be achieved by controlling the tethers’ length and tension simultaneously. Numerical analysis of trajectory optimization problem for the MTR is implemented using the pseudospectral (PS) method.

The globally time optimal trajectory for MTR on a free-end spinning net platform can be obtained through the PS method.

The analysis in this paper is limited to a planar trajectory and the effects caused by attitude of the MTR will be neglected. To make the problem simple and to see the feasibility in the general case, in this paper, it is assumed there are no any limitations of mechanical hardware constraints such as the velocity limitation of the robot and tether length changing constraint, while only geometrical constraints are considered.

The optimal solution derived from numerical analysis can be used for a path planning, guidance and navigation control. This method can be used for more efficient on-orbit autonomous self-assembly system or extravehicular activities supports which using a tether-controlled robot.

This approach for a locomotion mechanism has the capability to solve problems of conventional crawling type robots on a loose net in microgravity.

This paper aims to present a continuous-time workforce planning model in which workforce flow occurs in terms of internal and external recruitment considering human resource strategies (HRS). The proposed model is a linear optimal control model in which promotions occur by inside appointment and outside employment of the system considering a cost leadership or a differentiation strategy and whether organizations have an internal or an external recruitment orientation. In other words, in the model and its solution procedure, this paper could determine any arbitrary function for the demand of the workforce with each HRS.

The proposed model contains five main sections, namely, applicants, newcomers, workforce who are doing sensitive-simple jobs, expert workforce and supervisors (or managers) that have a different orientation in different HRS. Each of these sections has a target value that this paper tries to attain it by applying appropriate control variables, such as recruitment, layoff, degradation, promotion and retirement. To reach this purpose, this paper formulated an optimal control problem using a linear system transition equation with a quadratic cost function.

Based on the proposed model, it was found that the optimal control model can interpret the managerial aspects. This model could be useful for different firms with different types of workforce demands. This paper has tried to have a comprehensive view of different flows of the workforce in an organization that concern to workforce planning.

Despite the considerable amount of research published, and the importance of following a human resources strategy from organizational strategy, in the knowledge, there is no comprehensive study dedicated to human resources strategy and workforce planning by optimal control models for workforce planning.

The purpose of this paper is to maximize the speed of industrial robots by obtaining the minimum‐time trajectories that satisfy various constraints commonly given in the application of industrial robots.

The method utilizes the dynamic model of the robot manipulators to find the maximum kinematic constraints that are used with conventional trajectory patterns, such as trapezoidal velocity profiles and cubic polynomial functions.

The experimental results demonstrate that the proposed method can decrease the motion times substantially compared with the conventional kinematic method.

Although the method used a dynamic model, the computational burden is minimized by calculating dynamics only at certain points, enabling implementation of the method online. The proposed method is tested on more than 40 different types of robots made by Hyundai Heavy Industries Co. Ltd (HHI). The method is successfully implemented in Hi5, a new generation of HHI robot controller.

The paper shows that the method is computationally very simple compared with other minimum‐time trajectory‐planning methods, thus making it suitable for online implementation.