In this paper, we propose a novel method to solve the model predictive control (MPC) problem for linear time-invariant (LTI) systems with input and output constraints. We establish an algebraic control rule to solve the MPC problem to overcome the computational time of online optimization methods. For this purpose, we express system constraints as a continuous function through the tangent-hyperbolic function, hence the optimization problem is reformulated. There are two steps for the solution of the optimization problem. In the first step, the optimal control signal is determined by the use of the necessary condition for optimality, assuming that there is only input constraint. In the latter, the solution obtained in the first step is revised to keep the system states in a feasible region. It is shown that the solution is suboptimal. The proposed solution method is simulated for three different sample systems, and the results are compared with the classical MPC, which show that the new algebraic method dramatically reduces the computational time of MPC.

中文翻译：

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基于正切双曲函数的约束模型预测控制的代数次优解

在本文中，我们提出了一种新方法来解决具有输入和输出约束的线性时不变 (LTI) 系统的模型预测控制 (MPC) 问题。我们建立了代数控制规则来解决 MPC 问题，以克服在线优化方法的计算时间。为此，我们通过切线双曲函数将系统约束表示为连续函数，因此优化问题被重新表述。求解优化问题有两个步骤。第一步，假设只有输入约束，利用最优性的必要条件来确定最优控制信号。后者对第一步得到的解进行修正，使系统状态保持在可行域内。结果表明该解决方案是次优的。