模型预测控制的一个主要优点是能显式并优化处理控制量和状态量的约束。为此，主要围绕非线性预测控制的算法、稳定性和鲁棒性、对偶问题和滚动时域估计的最新研究成果进行综述，并阐述了理论与应用方面有待进一步研究的几个主要问题。

以2自由度1/4车模型为例在鲁棒控制理论的统一框架下讨论H2和H∞主动悬架的设计，并采用结构奇异值法和加权最坏RMS增益法对其鲁棒性能进行分析和比较。

This paper formulates the active suspension control problem as disturbance attenuation problem with output and control constraints. The H∞ performance is used to measure ride comfort such that more general road disturbances can be considered, while timedomain hard constraints are captured using the concept of reachable sets and state-space ellipsoids. Hence, conflicting requirements are specified separately and handled in a nature way. In the framework of Linear Matrix Inequality (LMI) optimization, constrained H∞ active suspensions are designed on half-car models with and without considering actuator dynamics. Analysis and simulation results show a promising improvement on ride comfort, while keeping suspension strokes and control inputs within bounds and ensuring a firm contact of wheels to road.

We introduce in this paper a nonlinear model predictive control scheme for open-loop stable systems subject to input and state constraints. Closed-loop stability is guaranteed by an appropriate choice of the finite prediction horizon, independent of the specification of the desired control performance. In addition, this control scheme is likely to allow 'real time' implementation, because of its computational attractiveness. The theoretical results are demonstrated and discussed with a CSTR control application.

This paper suggests a constrained H∞ control scheme for active suspensions with output and control constraints. The H∞ performance is used to measure ride comfort so that more general road disturbances can be considered. Time-domain constraints, representing requirements for: 1) good road holding which may have an impact on safety; 2) suspension stroke limitation; and 3) avoidance of actuator saturation, are captured using the concept of reachable sets and state-space ellipsoids. The proposed approach can potentially achieve the best possible ride comfort by allowing constrained variables free as long as they remain within given bounds. A state feedback solution to the constrained H∞ active suspension control problem is derived in the framework of linear matrix inequality (LMI) optimization and multiobjective control. Analysis and simulation results for a two-degree-of-freedom (2-DOF) quarter-car model show possible improvements on ride comfort, while respecting time-domain hard constraints.

在LMI优化框架下，讨论有时域硬约束线性系统的H∞控制问题。首先提出了一种基于IN优化的状态反馈方法，并给出了闭环系统保证H二性能和满足时域硬约束的条件。在此基础上，融合预测控制的滚动优化原理讨论了一种滚动时域H二性能控制方法。通过对H，性能指标Y的在线最小化，闭环系统能实时协调控制性能要求和硬约束，并充分利用有限的控制能力提高控制性能。

We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closedloop 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.

融合H∞控制的鲁棒概念和预测控制的滚动优化原理，提出了一种全新的约束动态对策预测控制方法。对有状态和控制约束的不确定线性系统，证明了闭环系统的鲁棒稳定性并给出了鲁棒性条件。该方法同时具有H∞控制和预测控制的优点：鲁棒性和显式处理约束的能力。