A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability
A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability
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DOI：
10.1016/s0005-1098(98)00073-9
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发表时间：
1998-10-01
期刊：
影响因子：
6.4
通讯作者：
Allgower, F
中科院分区：
文献类型：
--
作者：
Chen, H;Allgower, F
本文提出了一种新的非线性模型预测控制方案，保证渐近闭环稳定。该方法适用于具有输入约束的稳定和不稳定系统。要最小化的目标功能包括一个积分平方误差（伊势）的一部分，在有限的时间范围内加上二次终端成本。终端成本项的终端状态惩罚矩阵必须被选择为适当的李雅普诺夫方程的解。此外，该设置包括终端不等式约束，该约束迫使有限预测时域结束时的状态位于规定的终端区域内。如果被控非线性系统的雅可比线性化是可镇定的，我们证明了开环最优控制问题在时间t = 0的可行性意味着闭环系统的渐近稳定性。由于输入和终端不等式约束，吸引区域的大小仅受优化问题的可行性要求的限制，因此在某种意义上是最大的。(C)1998爱思唯尔科技有限公司版权所有。
We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed-loop stability. The scheme can be applied to both stable and unstable systems with input constraints. The objective functional to be minimized consists of an integral square error (ISE) part over a finite time horizon plus a quadratic terminal cost. The terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate Lyapunov equation. Furthermore, the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region. If the Jacobian linearization of the nonlinear system to be controlled is stabilizable, we prove that feasibility of the open-loop optimal control problem at time t = 0 implies asymptotic stability of the closed-loop system. The size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense. (C) 1998 Elsevier Science Ltd. All rights reserved.