The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and control-theoretic guarantees is of utmost importance, yet difficult to achieve for learning-based control schemes. We present a general framework for learning-enhanced robust control that allows for systematic integration of prior engineering knowledge, is fully compatible with modern robust control and still comes with rigorous and practically meaningful guarantees. Building on the established Linear Fractional Representation and Integral Quadratic Constraints framework, we integrate Gaussian Process Regression as a learning component and state-of-the-art robust controller synthesis. In a concrete robust control example, our approach is demonstrated to yield improved performance with more data, while guarantees are maintained throughout.
Technical University of Munich（慕尼黑工业大学）；University of Pennsylvania（宾夕法尼亚大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；LMU Munich（慕尼黑大学）
This paper focuses on the controller synthesis for unknown, nonlinear systems while ensuring safety constraints. Our approach consists of two steps, a learning step that uses Gaussian processes and a controller synthesis step that is based on control barrier functions. In the learning step, we use a data-driven approach utilizing Gaussian processes to learn the unknown control affine nonlinear dynamics together with a statistical bound on the accuracy of the learned model. In the second controller synthesis steps, we develop a systematic approach to compute control barrier functions that expli…
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric theorems to show that a properly configured deep BNN (1) learns the variable importance effectively in high dimensions, and its learning rate can sometimes "break" the curse of dimensionality. (2) BNN's uncertainty quantification for variable importance is rigorous, in the sense that its 95% credible intervals for variable importance indeed covers the truth…
K. N. Toosi University of Technology（K. N. 图西理工大学）
Assurance of asymptotic trajectory tracking in robotic manipulators with a smooth control law in the presence of unmodeled dynamics or external disturbance is a challenging problem. Recently, it is asserted that it is achieved via a rigorous proof by designing a traditional model-free controller together with time delay estimation (TDE) such that neither dynamical parameters nor conservative assumptions on external disturbance are required. The purpose of this note is to show that this claim is not true and the stability proof of the method is incorrect. Finally, some modified versions of this…
Virtual oscillator control is the latest control technique for grid-forming inverters. Virtual Oscillator based Controllers (VOCs) provide all the steady-state droop functionalities of conventional droop controllers and, in addition, the time-domain synchronization with a connected electrical network. However, existing literature does not consider the aspect of dynamic control over the voltage stiffness of a VOC. Voltage stiffness is a vital parameter for a grid-forming inverter. If the voltage stiffness is too high, the inverter picks up all the reactive power demand of the PCC. In contrast, …
Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers, and investigate the performance of safe-by-const…
A unified virtual oscillator controller (uVOC) is proposed, which enables a unified analysis, design, and implementation framework for both grid-forming (GFM) and grid-following (GFL) voltage source converters (VSCs). Oscillator based GFM controllers, such as dispatchable virtual oscillator control (dVOC), offer rigorous analytical framework with enhanced synchronization, but lack effective fault handling capability which severely limits practical application. The proposed uVOC facilitates synchronization with an arbitrarily low grid voltage and fast over-current limiting; this enables effecti…
In this work, we present a mixed sensorless strategy for Permanent Magnets Synchronous Machines, combining a torque/current controller and an observer for position, speed, flux and stator resistance. The proposed co-design is motivated by the need of an appropriate signal injection technique, in order to guarantee full state observability. Neither the typical constant or slowly-varying speed assumptions, nor a priori mechanical model information are used in the observer design. Instead, the rotor speed is modeled as an unknown input disturbance with constant (unknown) sign and uniformly non-ze…
Control problems are always challenging since they arise from the real-world systems where stochasticity and randomness are of ubiquitous presence. This naturally and urgently calls for developing efficient neural control policies for stabilizing not only the deterministic equations but the stochastic systems as well. Here, in order to meet this paramount call, we propose two types of controllers, viz., the exponential stabilizer (ES) based on the stochastic Lyapunov theory and the asymptotic stabilizer (AS) based on the stochastic asymptotic stability theory. The ES can render the controlled …
We propose a tracking control law for the fully actuated rigid body system in the presence of any unknown constant disturbance by employing quaternions with the stable embedding technique and Lyapunov stability theory. The stable embedding technique extends the attitude dynamics from the set of unit quaternions to the set of quaternions, which is a Euclidean space, such that the set of unit quaternions is an invariant set of the extended dynamics. Such a stable extension of the system dynamics to a Euclidean space allows us to employ well studied Lyapunov techniques in Euclidean spaces such as…
Robust Dynamic CPU Resource Provisioning in Virtualized Servers
Aalto University（阿尔托大学）；Cyprus University of Technology（塞浦路斯科技大学）；University of Cambridge（剑桥大学）；University of Lincoln（林肯大学）
本文提出了一种鲁棒的动态资源分配机制，用于在云服务提供商和客户之间达成的服务级别目标(SLOs)下分配应用程序资源。通过提出两种基于过滤器的鲁棒控制器，即H-infinity滤波器和最大相关性准则卡尔曼滤波器(MCC-KF)，并利用时间窗口内的先前测量值计算过程噪声方差和协方差，实现了自适应控制。在分配过程中，保持了有界客户端平均响应时间(mRT)。两种控制器均在实验测试床上部署并评估，测试平台托管着RUBiS( Rice University Bidding System)拍卖基准网站。所提出的控制器在突发工作负载变化下表现出改进的性能，通过与当前最先进的方法进行严格比较得以验证。在实验设置中，单输入-单输出(SISO)控制器可以在执行资源分配的同一台服务器上运行；而多输入-多输出(MIMO)控制器则在另一台服务器上运行，用于收集所有数据以进行决策。SISO控制器的决策不依赖于其他系统状态（服务器），尽管MIMO控制器具有增加的通信开销和潜在延迟。虽然SISO控制器在性能上优于MIMO控制器，但后者为多层应用的资源分配问题提供了更全面的决策框架。
The paper proposes an algorithm for a discretization (sampled-time implementation) of a homogeneous control preserving the finite-time and nearly fixed-time stability property of the original (sampling-free) system. The sampling period is assumed to be constant. Both single-input and multiple-input cases are considered. The robustness (Input-to-State Stability) of the obtained sampled-time control system is studied as well. Theoretical results are supported by numerical simulations.
We study a trajectory tracking problem for a multi-rotor in the presence of modeling error and external disturbances. The desired trajectory is unknown and generated from a reference system with unknown or partially known dynamics. We assume that only position and orientation measurements for the multi-rotor and position measurements for the reference system can be accessed. We adopt an extended high-gain observer (EHGO) estimation framework to estimate the feed-forward term required for trajectory tracking, the multi-rotor states, as well as modeling error and external disturbances. We design…
ETH AI Center（苏黎世联邦理工学院人工智能中心）；Institute for Automatic Control at ETH Zurich（苏黎世联邦理工学院自动控制研究所）；Department of Electrical and Systems Engineering at the University of Pennsylvania（宾夕法尼亚大学电气与系统工程学院）
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous performance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation …
Distributed Adaptive Fault-Tolerant Control of Uncertain Multi-Agent Systems
Wright State University（赖特州立大学）；University of Cyprus（塞浦路斯大学）；Imperial College London（伦敦帝国学院）；University of Trieste（的里雅斯特大学）；Air Force Research Laboratory（空军研究实验室）
Process control is widely discussed in the manufacturing process, especially for semiconductor manufacturing. Due to unavoidable disturbances in manufacturing, different process controllers are proposed to realize variation reduction. Since reinforcement learning (RL) has shown great advantages in learning actions from interactions with a dynamic system, we introduce RL methods for process control and propose a new controller called RL-based controller. Considering the fact that most existing process controllers mainly rely on a linear model assumption for the process input-output relationship…
Optimal nonlinear damping control was recently introduced for the second-order SISO systems, showing some advantages over a classical PD feedback controller. This paper summarizes the main theoretical developments and properties of the optimal nonlinear damping controller and demonstrates, for the first time, its practical experimental evaluation. An extended analysis and application to more realistic (than solely the double-integrator) motion systems are also given in the theoretical part of the paper. As comparative linear feedback controller, a PD one is taken, with the single tunable gain …
In the past couple of decades, non-quadratic convex penalties have reshaped signal processing and machine learning; in robust control, however, general convex costs break the Riccati and storage function structure that make the design tractable. Practitioners thus default to approximations, heuristics or robust model predictive control that are solved online for short horizons. We close this gap by extending $H_\infty$ control of discrete-time linear systems to strictly convex penalties on state, input, and disturbance, recasting the objective with Bregman divergences that admit a completion-o…
In this study, we propose a novel adaptive control architecture, which provides dramatically better transient response performance compared to conventional adaptive control methods. What makes this architecture unique is the synergistic employment of a traditional, Adaptive Neural Network (ANN) controller and a Long Short-Term Memory (LSTM) network. LSTM structures, unlike the standard feed-forward neural networks, can take advantage of the dependencies in an input sequence, which can contain critical information that can help predict uncertainty. Through a novel training method we introduced,…
There exists a vast amount of literature how dissipativity properties can be exploited to design controllers for stability and performance guarantees for the closed loop. With the rising availability of data, there has therefore been an increasing interest in determining dissipativity properties from data as a means for data-driven systems analysis and control with rigorous guarantees. Most existing approaches, however, consider dissipativity properties that hold only over a finite horizon and mostly only qualitative statements can be made in the presence of noisy data. In this work, we presen…
The problem of controller reduction has a rich history in control theory. Yet, many questions remain open. In particular, there exist very few results on the order reduction of general non-observer based controllers and the subsequent quantification of the closed-loop performance. Recent developments in model-free policy optimization for Linear Quadratic Gaussian (LQG) control have highlighted the importance of this question. In this paper, we first propose a new set of sufficient conditions ensuring that a perturbed controller remains internally stabilizing. Based on this result, we illustrat…
Learning event-triggered controllers for linear parameter-varying systems from data
State Key Laboratory of Robotics and Systems, Harbin Institute of Technology（哈尔滨工业大学机器人技术与系统国家重点实验室）；Nanyang Technological University（南洋理工大学）；The Hong Kong Polytechnic University（香港理工大学）；Adelaide University（阿德莱德大学）
We consider the problem of how to deploy a controller to a (networked) cyber-physical system (CPS). Controlling a CPS is an involved task, and synthesizing a controller to respect sensing, actuation, and communication constraints is only part of the challenge. In addition to controller synthesis, one should also consider how the controller will work in the CPS. Put another way, the cyber layer and its interaction with the physical layer need to be taken into account. In this work, we aim to bridge the gap between theoretical controller synthesis and practical CPS deployment. We adopt the syste…
