The optimal tracking problem is addressed in the robotics literature by using a variety of robust and adaptive control approaches. However, these schemes are associated with implementation limitations such as applicability in uncertain dynamical environments with complete or partial model-based control structures, complexity and integrity in discrete-time environments, and scalability in complex coupled dynamical systems. An online adaptive learning mechanism is developed to tackle the above limitations and provide a generalized solution platform for a class of tracking control problems. This scheme minimizes the tracking errors and optimizes the overall dynamical behavior using simultaneous linear feedback control strategies. Reinforcement learning approaches based on value iteration processes are adopted to solve the underlying Bellman optimality equations. The resulting control strategies are updated in real time in an interactive manner without requiring any information about the dynamics of the underlying systems. Means of adaptive critics are employed to approximate the optimal solving value functions and the associated control strategies in real time. The proposed adaptive tracking mechanism is illustrated in simulation to control a flexible wing aircraft under uncertain aerodynamic learning environment.
A distributed model predictive control scheme is developed for tracking piecewise constant references where the terminal set is reconfigured online, whereas the terminal controller is computed offline. Unlike many standard existing schemes, this scheme yields large feasible regions without performing offline centralized computations. Although the resulting optimal control problem (OCP) is a semidefinite program (SDP), an SDP scalability method based on diagonal dominance is used to approximate the derived SDP by a second-order cone program. The OCPs of the proposed scheme and its approximation…
We consider the problem of tracking an adversarial state sequence in a linear dynamical system subject to adversarial disturbances and loss functions, generalizing earlier settings in the literature. To this end, we develop three techniques, each of independent interest. First, we propose a comparator-adaptive algorithm for online linear optimization with movement cost. Without tuning, it nearly matches the performance of the optimally tuned gradient descent in hindsight. Next, considering a related problem called online learning with memory, we construct a novel strongly adaptive algorithm th…
In this work, we consider a time-varying stochastic saddle point problem in which the objective is revealed sequentially, and the data distribution depends on the decision variables. Problems of this type express the distributional dependence via a distributional map, and are known to have two distinct types of solutions--saddle points and equilibrium points. We demonstrate that, under suitable conditions, online primal-dual type algorithms are capable of tracking equilibrium points. In contrast, since computing closed-form gradient of the objective requires knowledge of the distributional map…
University of Pennsylvania（宾夕法尼亚大学）；Instituto de Ciencias Matematicas (CSIC-UAM-UCM-UC3M)（数学科学研究所（西班牙国家研究委员会-马德里自治大学-马德里康普顿斯大学-卡洛斯三世大学））；Technical University of Munich（慕尼黑工业大学）
Underactuated vehicles have gained much attention in the recent years due to the increasing amount of aerial and underwater vehicles as well as nanosatellites. Trajectory tracking control of these vehicles is a substantial aspect for an increasing range of application domains. However, external disturbances and parts of the internal dynamics are often unknown or very time-consuming to model. To overcome this issue, we present a tracking control law for underactuated rigid-body dynamics using an online learning-based oracle for the prediction of the unknown dynamics. We show that Gaussian proce…
Slip is a very common phenomena present in wheeled mobile robotic systems. It has undesirable consequences such as wasting energy and impeding system stability. To tackle the challenge of mobile robot trajectory tracking under slippery conditions, we propose a hierarchical framework that learns and adapts gains of the tracking controllers simultaneously online. Concretely, a reinforcement learning (RL) module is used to auto-tune parameters in a lateral predictive controller and a longitudinal speed PID controller. Experiments show the necessity of simultaneous gain tuning, and have demonstrat…
The Australian National University（澳大利亚国立大学）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）
In this paper, we propose and analyze a new method for online linear quadratic regulator (LQR) control with a priori unknown time-varying cost matrices. The cost matrices are revealed sequentially with the potential for future values to be previewed over a short window. Our novel method involves using the available cost matrices to predict the optimal trajectory, and a tracking controller to drive the system towards it. We adopted the notion of dynamic regret to measure the performance of this proposed online LQR control method, with our main result being that the (dynamic) regret of our metho…
The controller of an input-affine system is determined through minimizing a time-varying objective function, where stabilization is ensured via a Lyapunov function decay condition as constraint. This constraint is incorporated into the objective function via a barrier function. The time-varying minimum of the resulting relaxed cost function is determined by a tracking system. This system is constructed using derivatives up to second order of the relaxed cost function and improves the existing approaches in time-varying optimization. Under some mild assumptions, the tracking system yields a sol…
Min-Max Grassmannian Optimization for Online Subspace Tracking
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Microsoft India（微软印度）；Nanyang Technological University（南洋理工大学）；University of British Columbia（不列颠哥伦比亚大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Action-Increment-Constrained Policy Optimization for Smooth Online Adaptive Critic Flight Control with Actuator Rate Constraints and Low Computational Complexity (extended version with Ultimate Uniform Boundedness analysis)
Section Control and Simulation, Faculty of Aerospace Engineering, Delft University of Technology（控制与仿真部门，航空航天工程学院，代尔夫特理工大学）
Virginia Tech（弗吉尼亚理工大学）；US Army Research Laboratory（美国陆军研究实验室）
A key component of cognitive radar is the ability to generalize, or achieve consistent performance across a range of sensing environments, since aspects of the physical scene may vary over time. This presents a challenge for learning-based waveform selection approaches, since transmission policies which are effective in one scene may be highly suboptimal in another. We address this problem by strategically biasing a learning algorithm by exploiting high-level structure across tracking instances, referred to as meta-learning. In this work, we develop an online meta-learning approach for wavefor…
Online Leader Selection for Improved Collective Tracking and Formation Maintenance
CNRS, LAAS（法国国家科学研究中心，系统分析与研究实验室）；Univ de Toulouse, LAAS（图卢兹大学，系统分析与研究实验室）；CNRS at Irisa and Inria Rennes Bretagne Atlantique（法国国家科学研究中心与布列塔尼大西洋雷恩国家信息与自动化研究所，Irisa）
National University of Sciences and Technology（国立科技大学）
We analyze damage propagation modeling of turbo-engines in a data-driven approach. We investigate subspace tracking assuming a low dimensional manifold structure and a static behavior during the healthy state of the machines. Our damage propagation model is based on the deviation of the data from the static behavior and uses the notion of health index as a measure of the condition. Hence, we incorporate condition-based maintenance and estimate the remaining useful life based on the current and previous health indexes. This paper proposes an algorithm that adapts well to the dynamics of the dat…
Online Robust Subspace Tracking from Partial Information
Nanjing University of Information Science and Technology（南京信息工程大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；The Chinese University of Hong Kong（香港中文大学）
We enable efficient and effective coordination in unpredictable environments, i.e., in environments whose future evolution is unknown a priori and even adversarial. We are motivated by the future of autonomy that involves multiple robots coordinating in dynamic, unstructured, and adversarial environments to complete complex tasks such as target tracking, environmental mapping, and area monitoring. Such tasks are often modeled as submodular maximization coordination problems. We introduce the first submodular coordination algorithm with bounded tracking regret, i.e., with bounded suboptimality …
