This paper is concerned with the robust $H_{\mathrm{\infty }}$ model predictive control problem for a class of non-linear systems subject to state and input constraints and with norm bounded disturbances. It is well known that the disturbance degrades the control performance remarkably and can cause system instability. As well as, design the $H_{\mathrm{\infty }}$ model predictive control based on the non-linear model is much more challenging, because the control problem changes to a non-convex non-linear problem. The main contribution is the introduction of the novel robust controller to stabilize the perturbed Lipschitz non-linear systems. The objective is to minimize the L2 gain between the disturbance input and the controlled output. The non-convex control problem is formulated as a linear matrix inequality optimization problem. The designed controller guarantees the closed-loop asymptotic stability with a prescribed $H_{\mathrm{\infty }}$ disturbance attenuation level. In order to reduce conservatism, a sum of squares optimization problem is proposed to obtain the optimal value of Lipschitz coefficient. The proposed algorithm is applied to two non-linear systems, a laboratory tank and a DC/AC converter to evaluate its applicability and effectiveness.

本文关注的是稳健的 $H_{\mathrm{\infty }}$一类受状态和输入约束以及范数有界干扰的非线性系统的模型预测控制问题。众所周知，扰动会显着降低控制性能，并可能导致系统不稳定。此外，设计$H_{\mathrm{\infty }}$基于非线性模型的模型预测控制更具挑战性，因为控制问题变为非凸非线性问题。主要贡献是引入了新颖的鲁棒控制器来稳定受扰的 Lipschitz 非线性系统。目标是最小化干扰输入和受控输出之间的 L2 增益。非凸控制问题被表述为线性矩阵不等式优化问题。设计的控制器保证了闭环渐近稳定性$H_{\mathrm{\infty }}$干扰衰减水平。为了减少保守性，提出了平方和优化问题来获得Lipschitz系数的最优值。将所提出的算法应用于两个非线性系统、实验室水箱和 DC/AC 转换器，以评估其适用性和有效性。