Explicit MPC for LPV Systems: Stability and Optimality
Explicit MPC for LPV Systems: Stability and Optimality
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DOI：
10.1109/tac.2012.2187400
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发表时间：
2012-09-01
影响因子：
6.8
通讯作者：
Morari, Manfred
中科院分区：
文献类型：
--
作者：
Besselmann, Thomas;Lofberg, Johan;Morari, Manfred
本文研究了约束线性变参数系统的模型预测控制快速控制问题。现有的模型预测控制方案的约束线性参数变化系统的控制通常需要解决一个半定规划在每个采样实例。近年来，针对线性参数变化系统提出了多胞体表示的显式模型预测控制，使在线计算量减少了几个数量级。根据底层系统的数学结构，约束有限时间最优控制问题可以最优地求解，或者可以计算接近最优的解。通过适当地选择终端状态约束和终端代价，可以先验地保证约束满足、递归可行和渐近稳定。手头的文件收集以前的发展，并提供了新的材料，如证明的最优性的解决方案，或者，在接近最优的解决方案的情况下，一个程序来确定一个边界的次优的解决方案。
This paper considers high-speed control of constrained linear parameter-varying systems using model predictive control. Existing model predictive control schemes for control of constrained linear parameter-varying systems typically require the solution of a semi-definite program at each sampling instance. Recently, variants of explicit model predictive control were proposed for linear parameter-varying systems with polytopic representation, decreasing the online computational effort by orders of magnitude. Depending on the mathematical structure of the underlying system, the constrained finite-time optimal control problem can be solved optimally, or close-to-optimal solutions can be computed. Constraint satisfaction, recursive feasibility and asymptotic stability can be guaranteed a priori by an appropriate selection of the terminal state constraints and terminal cost. The paper at hand gathers previous developments and provides new material such as a proof for the optimality of the solution, or, in the case of close-to-optimal solutions, a procedure to determine a bound on the suboptimality of the solution.