Deep neural networks have revolutionized many fields, including image processing, inverse problems, text mining and more recently, give very promising results in systems and control. Neural networks with hidden layers have a strong potential as an approximation framework of predictive control laws as they usually yield better approximation quality and smaller memory requirements than existing explicit (multi-parametric) approaches. In this paper, we first show that neural networks with HardTanh activation functions can exactly represent predictive control laws of linear time-invariant systems. We derive theoretical bounds on the minimum number of hidden layers and neurons that a HardTanh neural network should have to exactly represent a given predictive control law. The choice of HardTanh deep neural networks is particularly suited for linear predictive control laws as they usually require less hidden layers and neurons than deep neural networks with ReLU units for representing exactly continuous piecewise affine (or equivalently min-max) maps. In the second part of the paper we bring the physics of the model and standard optimization techniques into the architecture design, in order to eliminate the disadvantages of the black-box HardTanh learning. More specifically, we design trainable unfolded HardTanh deep architectures for learning linear predictive control laws based on two standard iterative optimization algorithms, i.e., projected gradient descent and accelerated projected gradient descent. We also study the performance of the proposed HardTanh type deep neural networks on a linear model predictive control application.
Riccati-ZORO: An efficient algorithm for heuristic online optimization of internal feedback laws in robust and stochastic model predictive control
Department of Microsystems Engineering (IMTEK), University of Freiburg（弗赖堡大学微系统工程学院（IMTEK））；Department of Mathematics, University of Freiburg（弗赖堡大学数学系）
Beyond Pure Sampling: Hybrid Optimization Mechanisms for Non-Convex Model Predictive Control
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA（航空航天工程学院，佐治亚理工学院，美国亚特兰大，GA州）；Development Division, Komatsu Ltd., Tokyo, Japan（Komatsu Ltd.开发部门，日本东京）；Department of Electrical and Computer Engineering, Inha University, Incheon, Republic of Korea（电气与计算机工程系，inha大学，韩国仁川，大韩民国）
