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This paper aims to solve the problem of the robust model predictive control, the contradiction of the system robustness, and the conservative terminal constraint set range. A robust model predictive control (RMPC) method based on an ε-approximation single-tube set is proposed. We construct a single-tube RMPC structure for linear discrete time invariant systems with additive disturbances. To this structure, we add the state estimation and state feedback to improve the convergence rate. Furthermore, we use the ε-approximation to estimate the terminal constraint set with less conservatism, thus improving the robustness. Then, we conduct a stability analysis of the ε-approximation single-tube RMPC system. The simulation results demonstrate the stability and interference allowance advantages of the proposed method.

In accordance with the concept of “exchanging space for time” and relying on the supply method of “near-field pre-positioned inventory + end-to-end direct distribution”, forward warehouses meet the small-batch, high-frequency, and highly time-sensitive material procurement demands in surrounding areas. However, for highly time-sensitive materials, it is necessary to consider that their inventory should approach zero balance at the end of the designated sales period, as well as the involved multi-dimensional costs. Based on this, this paper proposes a multi-category dynamic inventory optimization model for forward warehouses under terminal constraints, and conducts research on initial inventory allocation and in-period scheduling and replenishment. The model aims to effectively balance multi-dimensional costs and provide decision support for the refined inventory management of forward warehouses for highly time-sensitive products.

Based on the terminal constraints system (TCS) and reciprocal screw theory, a novel method is presented to determine the isotropic configurations of limited degree-of-freedom (DOF) parallel manipulators. From the available physical meaning of isotropy, the criteria to determine the isotropic configurations can be transformed to investigate whether the TCS acting on the moving platform works equally well in all directions. From the TCS study, the simplest form of constraints system matrix can be obtained. Then the constraint condition number is defined to measure the isotropy of spatial parallel manipulator based on the TCS. This method not only avoids solving the Jacobian matrix for some complex structural parallel manipulators but also points out the physical meaning of isotropy, which indicates that the TCS acting on the moving platform works equally well in all directions. Three examples are employed to illustrate this method.

This paper proposes a formation control method for gliding aircraft based on backstepping consensus control. The method ensures stable formation maintenance and smooth transitions in both altitude and lateral directions while meeting terminal constraints. The formation dynamics model is established using consensus control theory. The control inputs are the angle of attack and bank angle. A backstepping-based controller is designed to generate guidance commands, ensuring system stability and convergence. To improve flight safety, an artificial potential field-based collision avoidance strategy is introduced. Numerical simulations confirm the proposed method’s effectiveness. The results show that the formation control achieves high accuracy, while the collision avoidance strategy effectively prevents aircraft collisions.

We investigate the exponential turnpike property for finite horizon undiscounted discrete time optimal control problems without any terminal constraints. Considering a class of strictly dissipative systems, we derive a boundedness condition for an auxiliary optimal value function which implies the exponential turnpike property. Two theorems illustrate how this boundedness condition can be concluded from structural properties like controllability and stabilizability of the control system under consideration. [PUBLICATION ABSTRACT]

The article is devoted to the development of a numerical algorithm for finding an approximate solution of an optimal control problem with terminal constraints and control constraints. The algorithm is based on the reduction of the original optimal control problem to a finite-dimensional problem and the use of the penalty method and the differential evolution method to solve the latter. A feature of the proposed approach is that the solution found is independent of the choice of the initial approximation. The operation of the algorithm is illustrated by its application to applied optimal control problems. The results of computational experiments are consistent with the results of calculations based on other methods.

This study presents a learning‐based iterative model predictive control (MPC) scheme for unknown (Lipschitz continuous) nonlinear dynamical systems. The proposed method begins by learning the unknown part of the controlled system using a Gaussian process (GP), which helps derive multi‐step reachable sets that are guaranteed to encompass the actual system states. At each time step in each iteration, the MPC controller calculates a sequence of control inputs that robustly satisfy state and control constraints, as well as terminal constraints based on the GP‐based reachable sets. Then only the first control input is applied to the system. After the iteration, the initial state is reset, and the same procedure is executed with the MPC optimization problem defined by the updated terminal set and cost. As iteration goes on, improvement of the control performance is expected since more data is obtained and the environment is progressively explored. The proposed method provides properties such as recursive feasibility and input to state stability of the goal region under certain assumptions. Moreover, bound on the performance cost in each iteration associated with the implementation of the proposed MPC scheme is also analyzed. The results of the simulation study show that the proposed control scheme can iteratively improve the control performance. This study presents a method to improve the terminal components of the MPC optimization problem with the iterative execution of a control task when a system is nonlinear and initially unknown. The proposed method provides desirable properties such as robust constraint satisfaction, recursive feasibility, and input to state stability of the goal region under certain assumptions, and bound on the performance cost in each iteration is also analyzed. The results of the simulation study show that the proposed control scheme can iteratively improve the control performance.

In order to improve the adaptability and robustness of gliding guidance under complex environments and multiple constraints, this study proposes an intelligent gliding guidance strategy based on the optimal guidance, predictor-corrector technique, and deep reinforcement learning (DRL). Longitudinal optimal guidance was introduced to satisfy the altitude and velocity inclination constraints, and lateral maneuvering was used to control the terminal velocity magnitude and position. The maneuvering amplitude was calculated by the analytical prediction of the terminal velocity, and the direction was learned and determined by the deep Q-learning network (DQN). In the direction decision model construction, the state and action spaces were designed based on the flight status and maneuvering direction, and a reward function was proposed using the terminal predicted state and terminal constraints. For DQN training, initial data samples were generated based on the heading-error corridor, and the experience replay pool was managed according to the terminal guidance error. The simulation results show that the intelligent gliding guidance strategy can satisfy various terminal constraints with high precision and ensure adaptability and robustness under large deviations.

In electric are furnace smelting, electrode regulator system is a key link. A good electrode control algorithm will reduce energy consumption effectively and shorten smelting time greatly. The offline design online synthesis model predictive control algorithm is proposed for electrode regulator system with input and output constraints. On the offline computation, the continuum of terminal constraint sets will be constructed. On the online synthesis, the time-varying terminal constraint sets will be adopted and at least one free control variable will be introduced to solve the min-max optimization control problem. Then Lyapunov method will be adopted to analyze closed-loop system stability. Simulation and field trial results show that the proposed offline design online synthesis model predictive control method is effective.

In this paper, the control problem of multi‐robot systems under temporal logic tasks with limited time and logic constraints is studied, where each robot is required to reach the specified region in a given time and avoid collision all the time. Since the cooperative collision avoidance task of one robot depends on other robots' behaviors, the satisfaction of all the tasks may be conflicting. In this work, a distributed model predictive control (DMPC) strategy is proposed for conflicting temporal logic tasks. First, signal temporal logic (STL) is adopted to formally describe the temporal logic tasks. Based on robust semantics of STL formulas, a reference trajectory for the satisfaction degree of the task is designed to determine the short‐term task in the optimization horizon. In the DMPC optimization problem, the compatibility constraints are introduced to redesign the collision avoidance constraints, such that the collision avoidance tasks can be fulfilled using neighbouring robots' predicted information of the last time instant. Then, the terminal constraint is designed by the short‐term motion task which enforces each robot to move towards the goal region within the specified time interval. For conflicting tasks, a slack parameter is introduced in the terminal set to relax the motion task of each robot. The recursive feasibility of the DMPC algorithm is guaranteed, and the relaxed temporal logic tasks are fulfilled. In the proposed method, the discrete events including limited time and logic requirements are incorporated into the DMPC optimization problem, such that the motion task can be satisfied as much as possible and safety requirements are fulfilled. The effectiveness of the algorithm is illustrated by simulation and experiment results.