Control of Constrained Uncertain Discrete-Time Linear Systems
Control of Constrained Uncertain Discrete-Time Linear Systems
复制标题
约束不确定离散时间线性系统的控制
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Morari
中科院分区：
文献类型：
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作者：
A. Bemporad;F. Borrelli;M. Morari
对于输入和状态都有约束的离散不确定线性系统，我们提出了一种基于最小最大控制公式的状态反馈控制器设计方法。鲁棒性实现对添加剂范数有界输入干扰和/或多面体参数不确定性的状态空间矩阵。我们证明了有限时域鲁棒最优控制律是状态向量的连续分段仿射函数，并且可以通过求解一系列多参数线性规划来计算。当最优控制律采用滚动时域法时，只需在每一时间步在线计算一个分段仿射函数。该技术计算的鲁棒最优反馈控制器，而不需要诉诸网格的状态空间的一个相当一般的一类系统与适度的计算工作量。
For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min–max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state–space.