This article investigates a safety-critical control problem for a mobile robot navigating cluttered environments. Obstacles are represented as a closed set, and a direction-distance function is used to model the obstacle measurement process. Based on real-time obstacle measurements, a safety-critical controller is expected to maintain a safe distance between the robot and obstacles while ensuring that the robot's velocity, considered as the control input, follows a given velocity command signal as closely as possible. This article contributes a regularization method for the obstacle-measurement model in the body-fixed frame and a systematic design of a Lipschitz continuous safety-critical controller based on the regularized obstacle-measurement model and quadratic programming (QP). Specifically, a novel Lipschitz-truncated regularization term is used to replace the conventional quadratic regularization in Moreau-Yosida regularization. It is guaranteed that, for each local minimum distance given by the original direction-distance function and its corresponding direction, there exists a neighborhood around that direction where the value of the regularized direction-distance function does not exceed the local minimum distance. This property is crucial for constructing a feasible set of control input that ensures safety in all directions using only a finite number of constraints. The QP framework is then employed to integrate these safety constraints with nominal velocity commands. A specific positive basis is employed to meet the linear independence constraint qualification, ensuring the Lipschitz continuity of the QP-based safety-critical controller. The effectiveness of the proposed design is demonstrated through numerical simulations and physical experiments.

This note studies the distributed feedbak optimization for linear multiagent systems without precise knowledge of cost functions and agent dynamics. The goal is to regulate the outputs of the agents toward an unknown minimizer of a sum of local costs. To achieve this, distributed reference signals are combined with an extremum seeking mechanism to search for the minimizer. Meanwhile, each agent steers its output toward the designed reference signal using a learning-based adaptive optimal tracker. The entire process relies only on measurements of local costs and input-state data along the agents' trajectories. Moreover, the overall feedback loop has three time scales: tracking and consensus of the reference signals are the fastest, periodic sinusoidal perturbation is the medium, and optimization of the global cost is the slowest. Through this time-scale separation, the closed-loop system is guaranteed to be practically exponentially stable at an equilibrium of interest, along with the convergence of the output of each agent to a small neighborhood of the desired minimizer. A numerical example of robotic networks demonstrates the efficacy of the proposed method.

This paper studies the safety-critical control problem for Euler–Lagrange (EL) systems subject to multiple ball obstacles and velocity constraints. A key strategy is to exploit the underlying cascade structure of EL systems to design a new safety-critical controller featuring an inner–outer-loop structure. In particular, the outer-loop control law is developed based on quadratic programming (QP) to avoid ball obstacles and generate velocity reference signals fulfilling the velocity limitation. Taking full advantage of the energy conservation property, a nonlinear velocity-tracking control law is designed to form the inner loop. One major difficulty is caused by the possible non-Lipschitz continuity of the standard QP algorithm when there are multiple constraints. To solve this problem, we propose a new feasible-set reshaping technique such that the refined QP algorithm with the reshaped feasible set admits a Lipschitz continuity property. Additionally, inspired by small-gain analysis, we construct a max-type Lyapunov-like function to integrate the safety constraints and the velocity-tracking error, and prove the achievement of the safety-critical control objective. The effectiveness of the proposed design is validated through numerical simulations and experiments on a 2-link planar manipulator. © 2025

Feedback optimization aims at regulating the output of a dynamical system to a value that minimizes a cost function. This problem is beyond the reach of the traditional output regulation theory, because the desired value is generally unknown and the reference signal evolves according to a gradient flow using the system's real-time output. This paper complements the output regulation theory with the nonlinear small-gain theory to address this challenge. Specifically, the authors assume that the cost function is strongly convex and the nonlinear dynamical system is in lower triangular form and is subject to parametric uncertainties and a class of external disturbances. An internal model is used to compensate for the effects of the disturbances while the cyclic small-gain theorem is invoked to address the coupling between the reference signal, the compensators, and the physical system. The proposed solution can guarantee the boundedness of the closed-loop signals and regulate the output of the system towards the desired minimizer in a global sense. Two numerical examples illustrate the effectiveness of the proposed method.

For k-valued (control) networks, two types of (control) invariant subspaces are proposed, namely, the state-invariant and dual-invariant subspaces, which are subspaces of the state space and dual space, respectively. Algorithms are presented to check whether a dual subspace is dual- (control) invariant, and to construct state feedback controls. The bearing space of k-valued (control) networks is introduced. Using the structure of the bearing space, the universal invariant subspace is presented, which is independent of the dynamics of particular networks. Finally, the relation between the state-invariant subspaces and the dual-invariant subspaces of a network is investigated. A duality property shows that if a dual subspace is invariant, then its perpendicular state subspace is also invariant, and vice versa.

针对大型密闭空间内部作业且状态受限的移动机器人，基于混合A*算法、图搜索算法、曲线拟合等思想，提出了一种改进混合A*算法，来保证生成的安全路径处处满足此类状态受限移动机器人的约束。提出的算法可改进混合A*的传统六邻居节点选取策略，考虑移动机器人的固有运动和姿态约束并设计新的邻居节点选择策略，能够有效提升路径的灵活性和连续性，减少后续路径优化负担；采用抛物线曲线代替Reeds-Shepp曲线生成节点间的路径，可以在满足移动机器人非完整约束的同时有效避免移动机器人发生危险位姿，极大的减小了移动机器人的路径跟踪难度，易于设计和实现；最后基于MATLAB仿真环境，在多种工作场景下进行仿真实验验证该方法的有效性。

This article studies the problem of data-driven combined longitudinal and lateral control of autonomous vehicles (AVs) such that the AV can stay within a safe but minimum distance from its leading vehicle and, at the same time, in the lane. Most of the existing methods for combined longitudinal and lateral control are either model-based or developed by purely data-driven methods such as reinforcement learning. Traditional model-based control approaches are insufficient to address the adaptive optimal control design issue for AVs in dynamically changing environments and are subject to model uncertainty. Moreover, the conventional reinforcement learning approaches require a large volume of data, and cannot guarantee the stability of the vehicle. These limitations are addressed by integrating the advanced control theory with reinforcement learning techniques. To be more specific, by utilizing adaptive dynamic programming (ADP) techniques and using the motion data collected from the vehicles, a policy iteration algorithm is proposed such that the control policy is iteratively optimized in the absence of the precise knowledge of the AV's dynamical model. Furthermore, the stability of the AV is guaranteed with the control policy generated at each iteration of the algorithm. The efficiency of the proposed approach is validated by the integrated simulation of SUMO and CommonRoad.

This paper proposes a novel learning-based adaptive optimal controller design method for a class of continuous-time linear time-delay systems. A key strategy is to exploit the state-of-the-art reinforcement learning (RL) techniques and adaptive dynamic programming (ADP), and propose a data-driven method to learn the near-optimal controller without the precise knowledge of system dynamics. Specifically, a value iteration (VI) algorithm is proposed to solve the infinite-dimensional Riccati equation for the linear quadratic optimal control problem of time-delay systems using finite samples of input-state trajectory data. It is rigorously proved that the proposed VI algorithm converges to the near-optimal solution. Compared with the previous literature, the nice features of the proposed VI algorithm are that it is directly developed for continuous-time systems without discretization and an initial admissible controller is not required for implementing the algorithm. The efficacy of the proposed methodology is demonstrated by two practical examples of metal cutting and autonomous driving. © 2024 Elsevier Ltd

We consider deterministic nonlinear discrete-time systems whose inputs are generated by policy iteration (PI) for undiscounted cost functions. We first assume that PI is recursively feasible, in the sense that the optimization problems solved at each iteration admit a solution. In this case, we provide novel conditions to establish recursive robust stability properties for a general attractor, meaning that the policies generated at each iteration ensure a robust KL -stability property with respect to a general state measure. We then derive novel explicit bounds on the mismatch between the (suboptimal) value function returned by PI at each iteration and the optimal one. However, we show by a counterexample that PI may fail to be recursively feasible, disallowing the mentioned stability and near-optimality guarantees. We therefore also present a modification of PI so that recursive feasibility is guaranteed a priori under mild conditions. This modified algorithm, called PI+, is shown to preserve the recursive robust stability when the attractor is compact. In addition, PI+ enjoys the same near-optimality properties as its PI counterpart under the same assumptions.

This article proposes a novel robust reinforcement learning framework for discrete-time linear systems with model mismatch that may arise from the sim-to-real gap. A key strategy is to invoke advanced techniques from control theory. Using the formulation of the classical risk-sensitive linear quadratic Gaussian control, a dual-loop policy optimization algorithm is proposed to generate a robust optimal controller. The dual-loop policy optimization algorithm is shown to be globally and uniformly convergent, and robust against disturbances during the learning process. This robustness property is called small-disturbance input-to-state stability and guarantees that the proposed policy optimization algorithm converges to a small neighborhood of the optimal controller as long as the disturbance at each learning step is relatively small. In addition, when the system dynamics is unknown, a novel model-free off-policy policy optimization algorithm is proposed. Finally, numerical examples are provided to illustrate the proposed algorithm.