Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In this paper, we extend this result to the class of discrete-time single-input single-output flat nonlinear systems. We propose a data-based parametrization of all trajectories using only input-output data. Further, we use this parametrization to solve the data-based simulation and output-matching control problems for the unknown system without explicitly identifying a model. Finally, we illustrate the main results with numerical examples.
Scalable Distributed Nonlinear Control Under Flatness-Preserving Coupling
GRASP Laboratory, University of Pennsylvania（宾夕法尼亚大学 GRASP 实验室）；Sibley School of Mechanical and Aerospace Engineering, Cornell University（康奈尔大学 Sibley 机械与航空航天工程学院）
This chapter presents an approach to embed the input/state/output constraints in a unified manner into the trajectory design for differentially flat systems. To that purpose, we specialize the flat outputs (or the reference trajectories) as Bezier curves. Using the flatness property, the system's inputs/states can be expressed as a combination of Bezier curved flat outputs and their derivatives. Consequently, we explicitly obtain the expressions of the control points of the inputs/states Bezier curves as a combination of the control points of the flat outputs. By applying desired constraints t…
Trajectory Tracking Control with Flat Inputs and a Dynamic Compensator
Institute of Control Engineering, Universität der Bundeswehr München（德国联邦国防军慕尼黑大学控制工程系）；Institute of Electrical Drive Systems and Power Electronics, Technische Universität München（慕尼黑工业大学电气驱动系统与电力电子研究所）
Differentially Flat Learning-based Model Predictive Control Using a Stability, State, and Input Constraining Safety Filter
Vector Institute for Artificial Intelligence（矢量人工智能研究所）；University of Toronto Institute for Aerospace Studies (UTIAS)（多伦多大学航空航天研究所）；Queen’s University（女王大学）；Technical University of Munich（慕尼黑工业大学）；University of Toronto（多伦多大学）；Munich Institute for Robotics and Machine Intelligence (MIRMI)（慕尼黑机器人与机器智能研究所）
This article addresses the design of a discrete-time flatness-based tracking control for a gantry crane and demonstrates the practical applicability of the approach by measurement results. The required sampled-data model is derived by an Euler-discretization with a prior state transformation in such a way that the flatness of the continuous-time system is preserved. Like in the continuous-time case, the flatness-based controller design is performed in two steps. First, the sampled-data system is exactly linearized by a discrete-time quasi-static state feedback. Subsequently, a further feedback…
Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems
Learning Systems and Robotics Lab at the Technical University of Munich（慕尼黑技术大学学习系统与机器人实验室）；Learning Systems and Robotics Lab at the University of Toronto Institute for Aerospace Studies (UTIAS) and the Vector Institute for Artificial Intelligence（多伦多航空航天研究所（UTIAS）和向量人工智能研究所的学习系统与机器人实验室）
Active Queue Management (AQM) for mitigating Internet congestion has been addressed via various feedback control syntheses, especially P, PI, and PID regulators, by using a linear approximation where the ``round trip time'', i.e., the delay, is assumed to be constant. This constraint is lifted here by using a nonlinear modeling with a variable delay, introduced more than 20 years ago. This delay, intimately linked to the congestion phenomenon, may be viewed as a ``flat output.'' All other system variables, especially the control variable, i.e., the packet loss ratio, are expressed as a functio…
