In this paper, the disjunctive and conjunctive lattice piecewise affine (PWA) approximations of explicit linear model predictive control (MPC) are proposed. The training data is generated uniformly in the domain of interest, consisting of the state samples and corresponding affine control laws, based on which the lattice PWA approximations are constructed. Resampling of data is also proposed to guarantee that the lattice PWA approximations are identical to the explicit MPC control law in unique order (UO) regions containing the sample points as interior points. Besides, under mild assumptions, the equivalence of the 2 lattice PWA approximations guarantees the approximations are error-free in the domain of interest. The algorithms for deriving statistical error-free approximation to the explicit linear MPC is proposed and the complexity of the whole procedure is analyzed, which is polynomial with respect to the number of samples. The performance of the proposed approximation strategy is tested through 2 simulation examples, and the result shows that with a moderate number of sample points, we can construct lattice PWA approximations that are equivalent to optimal control law of the explicit linear MPC.
翻译:在本文中,提出了明确线性模型预测控制(MPC)的脱钩和合合式拉链条形近似值。培训数据是在利益领域统一生成的,包括州样本和相应的松式控制法,据此构建了拉特式PWA近似值。还提议对数据进行重新抽样,以保证拉特式的PWA近似值与以独特的顺序(UO)地区包含作为内点的样本点的明确的MPC控制法(UO)完全相同。此外,在轻度假设下,2拉特式PWA近似值的等值保证了近似值在利益领域无误。提出了得出统计性无误近似于明确的线性MPC的算法,并对整个程序的复杂性进行了分析,该算法与样品的数量是多式的。拟议的近似战略的绩效通过两个模拟示例进行测试,结果显示,如果有少量的样本点,我们就可以构建拉蒂式PWA近值的近似值,相当于直线性MPC的最佳控制法。