arXiv subjects

Xiangru Xu

Publications and source records attributed to Xiangru Xu.

At least 19 recordsLinked to original sources

arXiv2026

Computing the Maximal Controlled Invariant Set for Neural Network Control Systems

This article studies the computation of the maximal controlled invariant set (MCIS) for neural network control systems (NNCSs) with a nominal plant model and a neural network residual model. An interval-based method is developed to construct a control-affine inclusion function for the NNCS dynamics and to exploit the induced hyperplane arrangement in the input space, which reduces the verification of controlled invariance from an infinite control search to a finite set of representative evaluations. Based on this finite characterization, verification-guided algorithms iteratively construct inner and outer approximations of the the MCIS, which are naturally parallelizable. Numerical examples demonstrate the effectiveness of the proposed approach.

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arXiv2026

DASH Robot: Minimalistic Design and Optimal Aerial-Terrestrial Locomotion via Contact-Implicit Control

We present a novel and minimalistic design of an aerial-terrestrial robot DASH: Ducted Aerial Spring Hopper. The goal is to enable both aerial and ground locomotion capabilities on a unified mobile robot that is mechanically-minimalistic, locomotion-versatile, and energy-efficient. We propose an organic integration of ducted fan co-axial body with a springy leg at the bottom for realization. The ducted fan module provides thrust-vectoring as the main actuation for agile flying; when it is combined with the light-weight spring leg, the robot realizes highly efficient ground hopping with energy circulation. Moreover, to realize optimal locomotion with two modes, we employ a contact-implicit model predictive controller to automatically choose locomotion modes and actuation. We successfully validated the design and control of DASH through a range of tasks, including periodic hopping, aerial flight, and mode-free locomotion with autonomous mode transitions during obstacle traversal.

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arXiv2026

Forward and Backward Reachability Analysis of Closed-loop Recurrent Neural Networks via Hybrid Zonotopes

Recurrent neural networks (RNNs) are widely employed to model complex dynamical systems due to their hidden-state structure, which inherently captures temporal dependencies. This work presents a hybrid zonotope-based approach for computing exact forward and backward reachable sets of closed-loop RNN systems with ReLU activation functions. The method formulates state-pair sets to compute reachable sets as hybrid zonotopes without requiring unrolling. To improve scalability, a tunable relaxation scheme is proposed that ranks unstable ReLU units across all layers using a triangle-area score and selectively applies convex relaxations within a fixed binary limit in the hybrid zonotopes. This scheme enables an explicit tradeoff between computational complexity and approximation accuracy, with exact reachability as a special case. In addition, a sufficient condition is derived to certify the safety of closed-loop RNN systems. Numerical examples demonstrate the effectiveness of the proposed approach.

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arXiv2025

Efficient Reachability Analysis for Convolutional Neural Networks Using Hybrid Zonotopes

Feedforward neural networks are widely used in autonomous systems, particularly for control and perception tasks within the system loop. However, their vulnerability to adversarial attacks necessitates formal verification before deployment in safety-critical applications. Existing set propagation-based reachability analysis methods for feedforward neural networks often struggle to achieve both scalability and accuracy. This work presents a novel set-based approach for computing the reachable sets of convolutional neural networks. The proposed method leverages a hybrid zonotope representation and an efficient neural network reduction technique, providing a flexible trade-off between computational complexity and approximation accuracy. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.

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arXiv2025

Robust Stability of Neural Network Control Systems with Interval Matrix Uncertainties

Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties. This work addresses the problem of certifying robust stability in neural network control systems with interval matrix uncertainties. Leveraging classical robust stability techniques and the quadratic constraint-based method to characterize the input-output behavior of neural networks, we derive novel robust stability certificates formulated as linear matrix inequalities. To reduce computational complexity, we introduce three relaxed sufficient conditions and establish their equivalence in terms of feasibility. Additionally, we explore their connections to existing robust stability results. The effectiveness of the proposed approach is demonstrated through inverted pendulum and mass-spring-damper examples.

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arXiv2025

Proxy Control Barrier Functions: Integrating Barrier-Based and Lyapunov-Based Safety-Critical Control Design

This work introduces a novel Proxy Control Barrier Function (PCBF) scheme that integrates barrier-based and Lyapunov-based safety-critical control strategies for strict-feedback systems with potentially unknown dynamics. The proposed method employs a modular design procedure, decomposing the original system into a proxy subsystem and a virtual tracking subsystem that are controlled by the control barrier function (CBF)-based and Lyapunov-based controllers, respectively. By integrating these separately designed controllers, the overall system's safety is ensured. Moreover, a new filter-based disturbance observer is utilized to design a PCBF-based safe controller for strict-feedback systems subject to mismatched disturbances. This approach broadens the class of systems to which CBF-based methods can be applied and significantly simplifies CBF construction by requiring only the model of the proxy subsystem. The effectiveness of the proposed method is demonstrated through numerical simulations.

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arXiv2024

Immersion and Invariance-based Disturbance Observer and Its Application to Safe Control

When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance relative degree, which can pose significant limitations. This note introduces a systematic approach for designing an Immersion and Invariance-based Disturbance Observer (IIDOB) that circumvents these strong assumptions. The proposed IIDOB ensures the disturbance estimation error is globally uniformly ultimately bounded by approximately solving a partial differential equation while compensating for the approximation error. Furthermore, by integrating IIDOB into the framework of control barrier functions, a filter-based safe control design method for control-affine systems with disturbances is established where the filter is used to generate an alternative disturbance estimation signal with a known derivative. Sufficient conditions are established to guarantee the safety of the disturbed systems. Simulation results demonstrate the effectiveness of the proposed method.

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arXiv2024

Adaptive Safety-Critical Control for a Class of Nonlinear Systems with Parametric Uncertainties: A Control Barrier Function Approach

This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control-input matrices. The method combines control barrier functions and adaptive laws to generate a safe controller through a nonlinear program with an explicitly given closed-form solution. The proposed approach verifies the non-emptiness of the admissible control set independently of online parameter estimations, which can ensure the safe controller is singularity-free. A data-driven algorithm is also developed to improve the performance of the proposed controller by tightening the bounds of the unknown parameters. The effectiveness of the control scheme is demonstrated through numerical simulations.

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arXiv2024

Hybrid Zonotope-Based Backward Reachability Analysis for Neural Feedback Systems With Nonlinear Plant Models

The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing hybrid zonotopes to compute the over-approximation of backward reachable sets for neural feedback systems with nonlinear plant models and general activation functions. Closed-form expressions as hybrid zonotopes are provided for the over-approximated backward reachable sets, and a refinement procedure is proposed to alleviate the potential conservatism of the approximation. Two numerical examples are provided to illustrate the effectiveness of the proposed approach.

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arXiv2023

Safe Control of Euler-Lagrange Systems with Limited Model Information

This paper presents a new safe control framework for Euler-Lagrange (EL) systems with limited model information, external disturbances, and measurement uncertainties. The EL system is decomposed into two subsystems called the proxy subsystem and the virtual tracking subsystem. An adaptive safe controller based on barrier Lyapunov functions is designed for the virtual tracking subsystem to ensure the boundedness of the safe velocity tracking error, and a safe controller based on control barrier functions is designed for the proxy subsystem to ensure controlled invariance of the safe set defined either in the joint space or task space. Theorems that guarantee the safety of the proposed controllers are provided. In contrast to existing safe control strategies for EL systems, the proposed method requires much less model information and can ensure safety rather than input-to-state safety. Simulation results are provided to illustrate the effectiveness of the proposed method.

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arXiv2023

Using simulation to design an MPC policy for field navigation using GPS sensing

Modeling a robust control system with a precise GPS-based state estimation capability in simulation can be useful in field navigation applications as it allows for testing and validation in a controlled environment. This testing process would enable navigation systems to be developed and optimized in simulation with direct transferability to real-world scenarios. The multi-physics simulation engine Chrono allows for the creation of scenarios that may be difficult or dangerous to replicate in the field, such as extreme weather or terrain conditions. Autonomy Research Testbed (ART), a specialized robotics algorithm testbed, is operated in conjunction with Chrono to develop an MPC control policy as well as an EKF state estimator. This platform enables users to easily integrate custom algorithms in the autonomy stack. This model is initially developed and used in simulation and then tested on a twin vehicle model in reality, to demonstrate the transferability between simulation and reality (also known as Sim2Real).

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arXiv2023

Backward Reachability Analysis of Neural Feedback Systems Using Hybrid Zonotopes

The proliferation of neural networks in safety-critical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural feedback systems based on hybrid zonotopes. It is shown that the input-output relationship imposed by a ReLU-activated neural network can be exactly described by a hybrid zonotope-represented graph set. Based on that, the one-step exact backward reachable set of a neural feedback system is computed as a hybrid zonotope in the closed form. In addition, a necessary and sufficient condition is formulated as a mixed-integer linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions in finite time. Numerical examples are provided to demonstrate the efficiency of the proposed approach.

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arXiv2023

Disturbance Observer-based Robust Control Barrier Functions

This work presents a safe control design approach that integrates the disturbance observer (DOB) and the control barrier function (CBF) for systems with external disturbances. Different from existing robust CBF results that consider the "worst case" of disturbances, this work utilizes a DOB to estimate and compensate for the disturbances. DOB-CBF-based controllers are constructed with provably safe guarantees by solving convex quadratic programs online, to achieve a better tradeoff between safety and performance. Two types of systems are considered individually depending on the magnitude of the input and disturbance relative degrees. The effectiveness of the proposed methods is illustrated via numerical simulations.

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arXiv2022

ART/ATK: A research platform for assessing and mitigating the sim-to-real gap in robotics and autonomous vehicle engineering

We discuss a platform that has both software and hardware components, and whose purpose is to support research into characterizing and mitigating the sim-to-real gap in robotics and vehicle autonomy engineering. The software is operating-system independent and has three main components: a simulation engine called Chrono, which supports high-fidelity vehicle and sensor simulation; an autonomy stack for algorithm design and testing; and a development environment that supports visualization and hardware-in-the-loop experimentation. The accompanying hardware platform is a 1/6th scale vehicle augmented with reconfigurable mountings for computing, sensing, and tracking. Since this vehicle platform has a digital twin within the simulation environment, one can test the same autonomy perception, state estimation, or controls algorithms, as well as the processors they run on, in both simulation and reality. A demonstration is provided to show the utilization of this platform for autonomy research. Future work will concentrate on augmenting ART/ATK with support for a full-sized Chevy Bolt EUV, which will be made available to this group in the immediate future.

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arXiv2022

Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes

Artificial neural networks have recently been utilized in many feedback control systems and introduced new challenges regarding the safety of such systems. This paper considers the safe verification problem for a dynamical system with a given feedforward neural network as the feedback controller by using a constrained zonotope-based approach. A novel set-based method is proposed to compute both exact and over-approximated reachable sets for neural feedback systems with linear models, and linear program-based sufficient conditions are presented to verify whether the trajectories of such a system can avoid unsafe regions represented as constrained zonotopes. The results are also extended to neural feedback systems with nonlinear models. The computational efficiency and accuracy of the proposed method are demonstrated by two numerical examples where a comparison with state-of-the-art methods is also provided.

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arXiv2022

Reachability Analysis and Safety Verification of Neural Feedback Systems via Hybrid Zonotopes

Hybrid zonotopes generalize constrained zonotopes by introducing additional binary variables and possess some unique properties that make them convenient to represent nonconvex sets. This paper presents novel hybrid zonotope-based methods for the reachability analysis and safety verification of neural feedback systems. Algorithms are proposed to compute the input-output relationship of each layer of a feedforward neural network, as well as the exact reachable sets of neural feedback systems. In addition, a sufficient and necessary condition is formulated as a mixed-integer linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions. The proposed approach is shown to yield a formulation that provides the tightest convex relaxation for the reachable sets of the neural feedback system. Complexity reduction techniques for the reachable sets are developed to balance the computation efficiency and approximation accuracy. Two numerical examples demonstrate the superior performance of the proposed approach compared to other existing methods.

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arXiv2022

A software toolkit and hardware platform for investigating and comparing robot autonomy algorithms in simulation and reality

We describe a software framework and a hardware platform used in tandem for the design and analysis of robot autonomy algorithms in simulation and reality. The software, which is open source, containerized, and operating system (OS) independent, has three main components: a ROS 2 interface to a C++ vehicle simulation framework (Chrono), which provides high-fidelity wheeled/tracked vehicle and sensor simulation; a basic ROS 2-based autonomy stack for algorithm design and testing; and, a development ecosystem which enables visualization, and hardware-in-the-loop experimentation in perception, state estimation, path planning, and controls. The accompanying hardware platform is a 1/6th scale vehicle augmented with reconfigurable mountings for computing, sensing, and tracking. Its purpose is to allow algorithms and sensor configurations to be physically tested and improved. Since this vehicle platform has a digital twin within the simulation environment, one can test and compare the same algorithms and autonomy stack in simulation and reality. This platform has been built with an eye towards characterizing and managing the simulation-to-reality gap. Herein, we describe how this platform is set up, deployed, and used to improve autonomy for mobility applications.

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arXiv2022

Optimal Control for Kinematic Bicycle Model with Continuous-time Safety Guarantees: A Sequential Second-order Cone Programming Approach

The optimal control problem for the kinematic bicycle model is considered where the trajectories are required to satisfy the safety constraints in the continuous-time sense. Based on the differential flatness property of the model, necessary and sufficient conditions in the flat space are provided to guarantee safety in the state space. The optimal control problem is relaxed to the problem of solving three second-order cone programs (SOCPs) sequentially, which find the safe path, the trajectory duration, and the speed profile, respectively. Solutions of the three SOCPs together provide a sub-optimal solution to the original optimal control problem. Simulation examples and comparisons with state-of-the-art optimal control solvers are presented to demonstrate the effectiveness of the proposed approach.

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