This paper addresses the problem of finite-time stability (FTS) in nonlinear systems subject to impulsive disturbances. It extends and builds upon previous research on impulsive systems. The system under consideration is affected by impulsive disturbances, and is constrained within a more general continuous-time dynamic framework. Based on Lyapunov approach, several <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FTS</i> conditions with the corresponding settling-time estimations are proposed, where a relationship between the strength of impulsive disturbances, the impulsive interval, and the continuous dynamic is established. Compared with the existing results, the results presented here not only offer broader applicability but also provide more accurate settling-time estimations. Two numerical examples, including one related to finite-time control of spacecraft experiencing impulsive disturbances, are provided together with simulations to show the effectiveness of the presented solutions.

Safety filters provide a lightweight mechanism for enforcing state and input safety in learningenabled control. However, common Euclidean projections onto the safe set disregard long-term performance, while directly optimizing the action-value function within the safe set can be nonconvex and computationally prohibitive. This paper proposes a state-dependent, Hessian-guided projection for safety filtering that preserves convexity while improving performance. The key idea is to select a weighted projection matrix from the curvature of the action-value function, thereby biasing the correction toward action directions with higher value sensitivity. We establish (i) a uniform bound on the performance gap between the weighted projection and the safe value-optimal action, and (ii) a condition under which the weighted projection outperforms the Euclidean projection in long-term value. To support black-box controllers, we further present a data-driven construction of the weighted projection matrix via an iterative Q-function learning algorithm with quadratic feature blocks and regularization that enforces curvature dominance and bounded higher-order terms. Simulations on a quadrotor tracking-and-avoidance task indicate that the proposed filter maintains safety while reducing value degradation relative to Euclidean projection, with computational overhead compatible with real-time operation.

Timed reach-avoid specifications, a subset of Signal Temporal Logic (STL), provide an expressive framework for specifying complex tasks in dynamic systems. This letter introduces a novel framework that encodes these specifications into a quadratic programming (QP) controller using backup control barrier functions (backup CBFs). Unlike existing approaches that rely on predefined safe sets, we utilize a backup control strategy within a prediction horizon to construct time-varying implicit sets online. Specifically, we address the limitation of standard backup CBFs regarding finite-time convergence by introducing contractive implicit sets. Rigorous analysis of the time-varying properties confirms that backup CBFs enforce system forward invariance within these contractive sets, driving real-time trajectories to satisfy given specifications. Our method unifies high-level planning with continuous control, while does not require explicit safe set computation for Eventually formulas or predefined performance functions. Numerical simulations validate the performance of our approach in safe planning and control of mobile robots.

A reinforcement learning (RL)-based robust model predictive control (MPC) approach is proposed to achieve learning and control for unknown autoregressive exogenous (ARX) systems with bounded noises. We leverage the uniqueness of the ARX model to separately learn unknown coefficients and the corresponding augmented noise interval. A temporal difference (TD) RL algorithm is utilized to learn unknown coefficients by incorporating input-output data information, and both analytical update and empirical update methods are employed to learn the augmented noise interval at specific learning steps. With the learned coefficients of RL, a robust MPC optimization problem is formulated to provide safe control actions for RL, facilitating effective control and learning for the unknown ARX system. The convergence of learning unknown coefficients and input-to-state stability of the unknown system are analyzed. Simulation results are presented to illustrate the effectiveness of the proposed approach.

Consensus control of multiagent systems arises in various applications such as rendezvous and formation control. The input to these algorithms, e.g., the (relative) positions of neighboring agents need to be measured using various sensors. Recent works aim to reconstruct these positions, i.e., achieve localization using Euclidean distance measurements instead of displacements, for cost efficiency and scalability. However, this approach inherently introduces ambiguities, such as a rotation or a reflection, which can cause stability issues in practice without corrections by some anchors. In this letter, we conduct a thorough analysis of the stability of consensus control in the presence of localization-induced rotational ambiguities, in several scenarios including, e.g., proper and improper rotation, and the homogeneity of rotations. We give stability criteria and stability margin on the rotations, which are numerically verified with two traditional examples of consensus control.

This paper investigates distributed constrained optimization over directed networks, where multiple agents collaborate to minimize the sum of local convex cost functions subject to individual constraints. We propose an efficient directed distributed proximal-tracking (DDPT) algorithm that combines the push-sum algorithm for directed networks with an asymptotic operator for local feasibility constraints. Unlike existing approaches that either assume undirected networks or ignore constraints, the DDPT algorithm ensures convergence over directed networks while maintaining constraint satisfaction. Numerical experiments on ridge regression and image deblurring tasks demonstrate its effectiveness and show that it consistently outperforms baseline algorithms in terms of convergence speed, stability, and solution accuracy.

A Bayesian knowledge transfer mechanism that leverages external information to improve the performance of the Kalman fixed-lag interval smoother (FLIS) is proposed. Exact knowledge of the external observation model is assumed to be missing, which hinders the direct application of Bayes’ rule in traditional transfer learning approaches. This limitation is overcome by the fully probabilistic design, conditioning the targeted task of state estimation on external information. To mitigate the negative impact of inaccurate external data while leveraging precise information, a latent variable is introduced. Favorably, in contrast to a filter, FLIS retrospectively refines past decisions up to a fixed time horizon, reducing the accumulation of estimation error and consequently improving the performance of state inference. Simulations indicate that the proposed algorithm better exploits precise external knowledge compared to a similar technique and achieves comparable results when the information is imprecise.

Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent’s feasible set. This convex reformulation enables a solution to be identified efficiently via a branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios.