Purpose

The purpose of this paper is to derive the output predictor for a stationary normal process with rational spectral density and linear stochastic discrete-time state-space model, respectively, as the output predictor is very important in model predictive control. The derivations are only dependent on matrix operations. Based on the output predictor, one quadratic programming problem is constructed to achieve the goal of subspace predictive control. Then an improved ellipsoid optimization algorithm is proposed to solve the optimal control input and the complexity analysis of this improved ellipsoid optimization algorithm is also given to complete the previous work. Finally, by the example of the helicopter, the efficiency of the proposed control strategy can be easily realized.

Design/methodology/approach

First, a stationary normal process with rational spectral density and one stochastic discrete-time state-space model is described. Second, the output predictors for these two forms are derived, respectively, and the derivation processes are dependent on the Diophantine equation and some basic matrix operations. Third, after inserting these two output predictors into the cost function of predictive control, the control input can be solved by using the improved ellipsoid optimization algorithm and the complexity analysis corresponding to this improved ellipsoid optimization algorithm is also provided.

Findings

Subspace predictive control can not only enable automatically tune the parameters in predictive control but also avoids many steps in classical linear Gaussian control. It means that subspace predictive control is independent of any prior knowledge of the controller. An improved ellipsoid optimization algorithm is used to solve the optimal control input and the complexity analysis of this algorithm is also given.

Originality/value

To the best knowledge of the authors, this is the first attempt at deriving the output predictors for stationary normal processes with rational spectral density and one stochastic discrete-time state-space model. Then, the derivation processes are dependent on the Diophantine equation and some basic matrix operations. The complexity analysis corresponding to this improved ellipsoid optimization algorithm is analyzed.

中文翻译：

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一种改进的子空间预测控制椭球优化算法

目的

本文的目的是分别推导出具有合理谱密度和线性随机离散时间状态空间模型的平稳正态过程的输出预测器，因为输出预测器在模型预测控制中非常重要。推导仅依赖于矩阵运算。在输出预测器的基础上，构造了一个二次规划问题，以实现子空间预测控制的目标。然后提出了一种改进的椭球优化算法来求解最优控制输入，并给出了改进椭球优化算法的复杂度分析，以完成前面的工作。最后，通过直升机的例子，可以很容易地实现所提出的控制策略的效率。

设计/方法/方法

首先，描述了具有合理谱密度和一个随机离散时间状态空间模型的平稳正态过程。其次，分别推导出这两种形式的输出预测变量，推导过程依赖于丢番图方程和一些基本矩阵运算。第三，将这两个输出预测器插入预测控制的代价函数后，可以使用改进的椭球优化算法求解控制输入，并给出了与改进的椭球优化算法相对应的复杂度分析。

发现

子空间预测控制不仅可以自动调整预测控制中的参数，而且避免了经典线性高斯控制中的许多步骤。这意味着子空间预测控制独立于控制器的任何先验知识。采用改进的椭球优化算法求解最优控制输入，并给出了该算法的复杂度分析。

原创性/价值

据作者所知，这是第一次尝试为具有合理谱密度和一个随机离散时间状态空间模型的平稳正态过程推导输出预测变量。然后，推导过程依赖于丢番图方程和一些基本的矩阵运算。分析了该改进椭球优化算法对应的复杂度分析。