We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. Moreover, we apply contemporary statistical estimation techniques to certify the system's safety through persistent constraint satisfaction with high probability. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods.
This paper presents a deep learning based model predictive control algorithm for control affine nonlinear discrete time systems with matched and bounded state-dependent uncertainties of unknown structure. Since the structure of uncertainties is not known, a deep neural network (DNN) is employed to approximate the disturbances. In order to avoid any unwanted behavior during the learning phase, a tube based model predictive controller is employed, which ensures satisfaction of constraints and input-to-state stability of the closed-loop states.
MR-MPCC: Model Predictive Contouring Control for Robotic Manipulator Tracking under Moving Reference Frames
University of Technology Sydney（悉尼科技大学）；Robotics Institute, University of Technology Sydney（悉尼科技大学机器人研究所）；University of Edinburgh（爱丁堡大学）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the paper is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet-Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a …
This paper proposes an adaptive dynamic programming-based adaptive-gain sliding mode control (ADP-ASMC) scheme for a fixed-wing unmanned aerial vehicle (UAV) with matched and unmatched disturbances. Starting from the dynamic of fixed-wing UAV, the control-oriented model composed of attitude subsystem and airspeed subsystem is established. According to the different issues in two subsystems, two novel adaptive-gain generalized super-twisting (AGST) algorithms are developed to eliminate the effects of disturbances in two subsystems and make the system trajectories tend to the designed integral s…
The fundamental problem of stabilizing a general nonaffine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding-mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a nonaffine continuous-time nonlinear system equivalently on a compact region containing the origin. A piecewise sliding-mode parallel controller is designed to globally stabilize the PALM and, consequently, to semiglobally stabilize the original nonlinear system. The proposed sch…
