This article deals with an improved scheme of tube-based robust economic model predictive control (TEMPC). The controller is robust to unknown but bounded disturbances where guarantees recursive feasibility, robust stability, and convergence to the economically optimal operating point. Time-varying economic criteria are considered in the stage cost function of the control design. Initial states of the nominal-nondisturbed-system are considered as decision variables. It lets the controller know more information about the real-disturbance affected-system to take advantage of the recursive horizon approach. It also increases the control degree of freedom and enlarges the region of attraction. Making the closed-loop system work at the economically optimal operating point contradicts with the economic behavior. A convex optimization
In this article, three-dimensional (3D) stacking problem, as a mandatory task in the warehouse distribution centers, is smartly represented by a new mathematical formulation. A model predictive control (MPC) scheme is proposed to optimally solve the problem. The MPC cost function consists of several sequential criteria to suitably put the incoming packages on the dedicated cart and fully use up the cart capacity as much as possible. The practical and hard constraints are taken into consideration without confronting with a complicated optimization problem. A theorem is presented to guarantee the constraints satisfaction. Regarding the burden of computations, the proposed strategy is efficiently applicable to large carts by introducing the adaptive window (AW) idea. The efficacy of the proposed AW-MPC framework is shown by a numerical case study.
INDEX TERMSAdaptive window, matrix representation, model predictive control, stacking problem.
This paper proposes a tube‐based robust model predictive control (TMPC) scheme with an optimal tube for disturbance‐affected linear systems. In the literature on TMPC, there is no proper methodology to handle the considerable effects of the tube size on the closed‐loop system performance. There is usually a trade‐off between the disturbance rejection level and the amount of control effort available for the MPC problem. In some applications, it is nearly impossible to find a feasible TMPC to have a sufficient amount of states and inputs feasible sets for the MPC optimization problem. It would be a vital contribution to the TMPC designs if an algorithm is demonstrated which can investigate the suitability of TMPC for a specific system. This paper provides a solution for the mentioned challenges by introducing the concept of Quasi‐H∞ criterion and proposing a constrained optimization problem. The optimization problem is then reformulated and simplified to present an efficient methodology for the TMPC designers. The proposed TMPC scheme could benefit from a larger terminal region and result in a larger region of attraction. The achievements in TMPC designs are shown by simulations and comparisons with the previously used techniquesover numerical case studies.
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