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Wei Xiao

Publications and source records attributed to Wei Xiao.

At least 127 records · Page 7Linked to original sources
arXiv2021

Event-Triggered Safety-Critical Control for Systems with Unknown Dynamics

This paper addresses the problem of safety-critical control for systems with unknown dynamics. It has been shown that stabilizing affine control systems to desired (sets of) states while optimizing quadratic costs subject to state and control constraints can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). Our recently proposed High Order CBFs (HOCBFs) can accommodate constraints of arbitrary relative degree. One of the main challenges in this approach is obtaining accurate system dynamics, which is especially difficult for systems that require online model identification given limited computational resources and system data. In order to approximate the real unmodelled system dynamics, we define adaptive affine control dynamics which are updated based on the error states obtained by real-time sensor measurements. We define a HOCBF for a safety requirement on the unmodelled system based on the adaptive dynamics and error states, and reformulate the safety-critical control problem as the above mentioned QP. Then, we determine the events required to solve the QP in order to guarantee safety. We also derive a condition that guarantees the satisfaction of the HOCBF constraint between events. We illustrate the effectiveness of the proposed framework on an adaptive cruise control problem and compare it with the classical time-driven approach.

eess.SY↗
arXiv2021

High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications

Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In our own recent work, we defined High Order CBFs (HOCBFs) for systems and constraints with arbitrary relative degrees. In this paper, in order to accommodate initial states that do not satisfy the state constraints and constraints with arbitrary relative degree, we generalize HOCBFs to High Order Control Lyapunov-Barrier Functions (HOCLBFs). We also show that the proposed HOCLBFs can be used to guarantee the Boolean satisfaction of Signal Temporal Logic (STL) formulae over the state of the system. We illustrate our approach on a safety-critical optimal control problem (OCP) for a unicycle.

eess.SY↗
arXiv2021

Rule-based Optimal Control for Autonomous Driving

We develop optimal control strategies for Autonomous Vehicles (AVs) that are required to meet complex specifications imposed by traffic laws and cultural expectations of reasonable driving behavior. We formulate these specifications as rules, and specify their priorities by constructing a priority structure. We propose a recursive framework, in which the satisfaction of the rules in the priority structure are iteratively relaxed based on their priorities. Central to this framework is an optimal control problem, where convergence to desired states is achieved using Control Lyapunov Functions (CLFs), and safety is enforced through Control Barrier Functions (CBFs). We also show how the proposed framework can be used for after-the-fact, pass / fail evaluation of trajectories - a given trajectory is rejected if we can find a controller producing a trajectory that leads to less violation of the rule priority structure. We present case studies with multiple driving scenarios to demonstrate the effectiveness of the proposed framework.

cs.RO↗
arXiv2020

Sufficient Conditions for Feasibility of Optimal Control Problems Using Control Barrier Functions

It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. In this paper, we provide sufficient conditions for guranteed feasibility. The sufficient conditions are captured by a single constraint that is enforced by a CBF, which is added to the QPs such that their feasibility is always guaranteed. The additional constraint is designed to be always compatible with the existing constraints, therefore, it cannot make a feasible set of constraints infeasible - it can only increase the overall feasibility. We illustrate the effectiveness of the proposed approach on an adaptive cruise control problem.

math.OC↗
arXiv2020

A General Framework for Decentralized Safe Optimal Control of Connected and Automated Vehicles in Multi-Lane Intersections

We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from four multi-lane roads at an intersection where they conflict in terms of safely crossing (including turns) with no collision. The objective is to jointly minimize the travel time and energy consumption of each CAV while ensuring safety. This problem was solved in prior work for single-lane roads. A direct extension to multiple lanes on each road is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that first converts a multi-lane intersection problem into a decentralized optimal control problem for each CAV with less conservative safety constraints than prior work. We then employ a method combining optimal control and control barrier functions, which has been shown to efficiently track tractable unconstrained optimal CAV trajectories while also guaranteeing the satisfaction of all constraints. Simulation examples are included to show the effectiveness of the proposed framework under symmetric and asymmetric intersection geometries and different schemes for CAV sequencing.

eess.SY↗
arXiv2020

Bridging the Gap between Optimal Trajectory Planning and Safety-Critical Control with Applications to Autonomous Vehicles

We address the problem of optimizing the performance of a dynamic system while satisfying hard safety constraints at all times. Implementing an optimal control solution is limited by the computational cost required to derive it in real time, especially when constraints become active, as well as the need to rely on simple linear dynamics, simple objective functions, and ignoring noise. The recently proposed Control Barrier Function (CBF) method may be used for safety-critical control at the expense of sub-optimal performance. In this paper, we develop a real-time control framework that combines optimal trajectories generated through optimal control with the computationally efficient CBF method providing safety guarantees. We use Hamiltonian analysis to obtain a tractable optimal solution for a linear or linearized system, then employ High Order CBFs (HOCBFs) and Control Lyapunov Functions (CLFs) to account for constraints with arbitrary relative degrees and to track the optimal state, respectively. We further show how to deal with noise in arbitrary relative degree systems. The proposed framework is then applied to the optimal traffic merging problem for Connected and Automated Vehicles (CAVs) where the objective is to jointly minimize the travel time and energy consumption of each CAV subject to speed, acceleration, and speed-dependent safety constraints. In addition, when considering more complex objective functions, nonlinear dynamics and passenger comfort requirements for which analytical optimal control solutions are unavailable, we adapt the HOCBF method to such problems. Simulation examples are included to compare the performance of the proposed framework to optimal solutions (when available) and to a baseline provided by human-driven vehicles with results showing significant improvements in all metrics.

eess.SY↗
arXiv2020

Decentralized Optimal Control in Multi-lane Merging for Connected and Automated Vehicles

We address the problem of optimally controlling Connected and Automated Vehicles (CAVs) arriving from two multi-lane roads and merging at multiple points where the objective is to jointly minimize the travel time and energy consumption of each CAV subject to speed-dependent safety constraints, as well as speed and acceleration constraints. This problem was solved in prior work for two single-lane roads. A direct extension to multi-lane roads is limited by the computational complexity required to obtain an explicit optimal control solution. Instead, we propose a general framework that converts a multi-lane merging problem into a decentralized optimal control problem for each CAV in a less-conservative way. To accomplish this, we employ a joint optimal control and barrier function method to efficiently get an optimal control for each CAV with guaranteed satisfaction of all constraints. Simulation examples are included to compare the performance of the proposed framework to a baseline provided by human-driven vehicles with results showing significant improvements in both time and energy metrics.

eess.SY↗
arXiv2020

Herriott-cavity-assisted all-optical atomic vector magnetometer

We report an all-optical atomic vector magnetometer using dual Bell-Bloom optical pumping beams in a Rb vapor cell. This vector magnetometer consists of two orthogonal optical pumping beams, with amplitude modulations at $^{85}$Rb and $^{87}$Rb Larmor frequencies respectively. We simultaneously detect atomic signals excited by these two pumping beams using a single probe beam in the third direction, and extract the field orientation information using the phase delays between the modulated atomic signals and the driving beams. By adding a Herriott cavity inside the vapor cell, we improve the magnetometer sensitivity. We study the performance of this vector magnetometer in a magnetic field ranging from 100~mG to 500~mG, and demonstrate a field angle sensitivity better than 10~$μ$rad/Hz$^{1/2}$ above 10~Hz.

physics.atom-ph↗
arXiv2020

When Dictionary Learning Meets Deep Learning: Deep Dictionary Learning and Coding Network for Image Recognition with Limited Data

We present a new Deep Dictionary Learning and Coding Network (DDLCN) for image recognition tasks with limited data. The proposed DDLCN has most of the standard deep learning layers (e.g., input/output, pooling, fully connected, etc.), but the fundamental convolutional layers are replaced by our proposed compound dictionary learning and coding layers. The dictionary learning learns an over-complete dictionary for input training data. At the deep coding layer, a locality constraint is added to guarantee that the activated dictionary bases are close to each other. Then the activated dictionary atoms are assembled and passed to the compound dictionary learning and coding layers. In this way, the activated atoms in the first layer can be represented by the deeper atoms in the second dictionary. Intuitively, the second dictionary is designed to learn the fine-grained components shared among the input dictionary atoms, thus a more informative and discriminative low-level representation of the dictionary atoms can be obtained. We empirically compare DDLCN with several leading dictionary learning methods and deep learning models. Experimental results on five popular datasets show that DDLCN achieves competitive results compared with state-of-the-art methods when the training data is limited. Code is available at https://github.com/Ha0Tang/DDLCN.

cs.CV↗
arXiv2020

Jantzen coefficients and simplicity of generalized Verma modules

The main purpose of the paper is to establish new tools in the study of $\mathcal{O}^\mathfrak{p}$. We introduce the Jantzen coefficients of generalized Verma modules. It comes from the Jantzen's simplicity criteria for generalized Verma modules and has a deep relation with the structure of $\mathcal{O}^\mathfrak{p}$. We develop a reduction process to compute those coefficients. For which we need to consider generalized Verma modules induced from maximal parabolic subalgebras having maximal nontrivial singularity, so called basic generalized Verma modules. The classification of such modules is obtained in this paper. As the first application of our results, we give a refinement of Jantzen's simplicity criteria.

math.RT↗
arXiv2020

Janzten coefficients and Blocks of category $\mathcal{O}^\mathfrak{p}$

The BGG category $\mathcal{O}$ and its generalization $\mathcal{O}^\mathfrak{p}$ play essential roles in representation theory and have led to far-reaching work. Some elementary problems remain open for several decades, such as the block decomposition of category $\mathcal{O}^\mathfrak{p}$. In this paper, we solve the problem of blocks by applying the theory of Jantzen coefficients.

math.RT↗
arXiv2020

Jantzen coefficients and radical filtrations for generalized Verma modules

In this paper we give a sum formula for the radical filtration of generalized Verma modules in any (possibly singular) blocks of parabolic BGG category which can be viewed as a generalization of Jantzen sum formula for Verma modules in the usual BGG category $\mathcal{O}$. Combined with Jantzen coefficients, we determine the radical filtrations for all basic generalized Verma modules. The proof makes use of the graded version of parabolic BGG category. Explicit formulae for the graded decomposition numbers and inverse graded decomposition numbers of generalized Verma modules in any (possibly singular) integral blocks of the parabolic BGG category are also given.

math.RT↗
arXiv2020

Adaptive Control Barrier Functions for Safety-Critical Systems

Recent work showed that stabilizing affine control systems to desired (sets of) states while optimizing quadratic costs and observing state and control constraints can be reduced to quadratic programs (QP) by using control barrier functions (CBF) and control Lyapunov functions. In our own recent work, we defined high order CBFs (HOCBFs) to accommodating systems and constraints with arbitrary relative degrees, and a penalty method to increase the feasibility of the corresponding QPs. In this paper, we introduce adaptive CBF (AdaCBFs) that can accommodate time-varying control bounds and dynamics noise, and also address the feasibility problem. Central to our approach is the introduction of penalty functions in the definition of an AdaCBF and the definition of auxiliary dynamics for these penalty functions that are HOCBFs and are stabilized by CLFs. We demonstrate the advantages of the proposed method by applying it to a cruise control problem with different road surfaces, tires slipping, and dynamics noise.

eess.SY↗
arXiv2019

Feasibility-Guided Learning for Robust Control in Constrained Optimal Control Problems

Optimal control problems with constraints ensuring safety and convergence to desired states can be mapped onto a sequence of real time optimization problems through the use of Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in these approaches is ensuring the feasibility of the resulting quadratic programs (QPs) if the system is affine in controls. The recently proposed penalty method has the potential to improve the existence of feasible solutions to such problems. In this paper, we further improve the feasibility robustness (i.e., feasibility maintenance in the presence of time-varying and unknown unsafe sets) through the definition of a High Order CBF (HOCBF) that works for arbitrary relative degree constraints; this is achieved by a proposed feasibility-guided learning approach. Specifically, we apply machine learning techniques to classify the parameter space of a HOCBF into feasible and infeasible sets, and get a differentiable classifier that is then added to the learning process. The proposed feasibility-guided learning approach is compared with the gradient-descent method on a robot control problem. The simulation results show an improved ability of the feasibility-guided learning approach over the gradient-decent method to determine the optimal parameters in the definition of a HOCBF for the feasibility robustness, as well as show the potential of the CBF method for robot safe navigation in an unknown environment.

eess.SY↗
arXiv2019

Control Barrier Functions for Systems with High Relative Degree

This paper extends control barrier functions (CBFs) to high order control barrier functions (HOCBFs) that can be used for high relative degree constraints. The proposed HOCBFs are more general than recently proposed (exponential) HOCBFs. We introduce high order barrier functions (HOBF), and show that their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. We then introduce HOCBF, and show that any control input that satisfies the HOCBF constraints renders the intersection of a series of sets forward invariant. We formulate optimal control problems with constraints given by HOCBF and control Lyapunov functions (CLF) and analyze the influence of the choice of the class $\mathcal{K}$ functions used in the definition of the HOCBF on the size of the feasible control region. We also provide a promising method to address the conflict between HOCBF constraints and control limitations by penalizing the class $\mathcal{K}$ functions. We illustrate the proposed method on an adaptive cruise control problem.

eess.SY↗
arXiv2019

Fast and Robust Dynamic Hand Gesture Recognition via Key Frames Extraction and Feature Fusion

Gesture recognition is a hot topic in computer vision and pattern recognition, which plays a vitally important role in natural human-computer interface. Although great progress has been made recently, fast and robust hand gesture recognition remains an open problem, since the existing methods have not well balanced the performance and the efficiency simultaneously. To bridge it, this work combines image entropy and density clustering to exploit the key frames from hand gesture video for further feature extraction, which can improve the efficiency of recognition. Moreover, a feature fusion strategy is also proposed to further improve feature representation, which elevates the performance of recognition. To validate our approach in a "wild" environment, we also introduce two new datasets called HandGesture and Action3D datasets. Experiments consistently demonstrate that our strategy achieves competitive results on Northwestern University, Cambridge, HandGesture and Action3D hand gesture datasets. Our code and datasets will release at https://github.com/Ha0Tang/HandGestureRecognition.

cs.CV↗
arXiv2018

Deep Micro-Dictionary Learning and Coding Network

In this paper, we propose a novel Deep Micro-Dictionary Learning and Coding Network (DDLCN). DDLCN has most of the standard deep learning layers (pooling, fully, connected, input/output, etc.) but the main difference is that the fundamental convolutional layers are replaced by novel compound dictionary learning and coding layers. The dictionary learning layer learns an over-complete dictionary for the input training data. At the deep coding layer, a locality constraint is added to guarantee that the activated dictionary bases are close to each other. Next, the activated dictionary atoms are assembled together and passed to the next compound dictionary learning and coding layers. In this way, the activated atoms in the first layer can be represented by the deeper atoms in the second dictionary. Intuitively, the second dictionary is designed to learn the fine-grained components which are shared among the input dictionary atoms. In this way, a more informative and discriminative low-level representation of the dictionary atoms can be obtained. We empirically compare the proposed DDLCN with several dictionary learning methods and deep learning architectures. The experimental results on four popular benchmark datasets demonstrate that the proposed DDLCN achieves competitive results compared with state-of-the-art approaches.

cs.CV↗