optimal control

The purpose of this paper is to optimal control a dual-stage cable robot in a predefined path and to determine the maximum load-carrying capacity of this robot as a tower crane. Also, to expand the workspace of the robot two stages are employed. Today, cable robots are extensively used in load handling. Positive cable tension and collision-free cable control are the most important challenges of this type of robot. The high ratio of transposable loads to weight makes these robots very attractive for use as tower cranes. Dynamic Load Carrying Capacity (DLCC) is the maximum load that can be carried along a predefined path without violating the actuators and allowable accuracy constraints. State-Dependent Riccati Equation (SDRE) is employed to control the end-effector within the path to achieve the maximum DLCC. This approach is chosen since it can optimize the required motors' torque which consequently leads us to the maximum DLCC. In addition, the constraint of cables’ collision together is also checked along the predetermined path using the non-interference algorithm. The correctness of modeling is verified by comparing the results with previous research and the efficiency of the proposed optimal controlling strategy toward increasing the DLCC is investigated by conducting some comparative simulations. it is shown that the proposed cable robot by the aid of the designed optimal controller can increase the load carrying capacity successfully along any desired path using the allowable amount of motors' torque.

The supply chain management comprises many uncertain parameters such as the demand value and delivered product rate as the result of an imperfect delivery process. In this article, therefore, a mathematical model in a linear dynamical state-space equation is formulated for an inventory system with uncertain demand value and imperfect delivery process developed from the existing classical model. The new model is used to determine the optimal decision for this inventory system i.e. to calculate the optimal amount of product that should be ordered from the supplier. Moreover, the optimal decision is calculated for the purpose to control the inventory level as the decision-maker wanted to, in this paper, the inventory level is brought to a set point. The robust linear quadratic control, which is an existing model, is employed to this system with a numerical experiment performed to illustrate the controlling responses. From the obtained results, it achieved the optimal decision with the proper control of the inventory level based on the performed set-point control problem. In addition, the performed computational experiment is compared to some related existing works. The analysis showed that the achieved optimal decision is well enough and is not worse than the other results. In conclusion, the proposed model and the method performed in this research are implementable and therefore can be used by practitioners especially in the supply chain management field.

This work considers cooperative advertising in a manufacturer–retailer supply chain. While the manufacturer is the Stackelberg leader, the retailer is the follower. Using Sethi model it models the dynamic effect of the manufacturer and retailer’s advertising efforts on sale. It uses optimal control technique and stochastic differential game theory to obtain the players’ advertising strategies and the long-run value of the awareness share. Further, it models the relationship between the payoffs of both players and the awareness share. The work shows that with the provision of subsidy the retail advertising effort increases while the manufacturer’s advertising effort reduces. It further shows that the total channel payoff is higher for subsidised retail advertising. However, the subsidy can only be possible if the rate of growth of the manufacturer’s payoff is twice higher than that of the retailer.