We exploit the convexity property of the barrier function to formulate the optimal control synthesis problem asalinear program.

Abstract--This work presents an event-triggered switching control framework for a class of nonlinear underactuated multi-channel systems with input constraints. These systems are inspired by cooperative manipulation tasks involving underactua-tion, where multiple underactuated agents collaboratively push or pull an object to a target pose. T o simultaneously account for channel assignment, input constraints, and stabilization, we formulate the control problem as a Mixed Integer Linear Programming and derive sufficient conditions for its feasibility. T o improve real-time computation efficiency, we introduce an event-triggered control scheme that maintains stability even between switching events through a quadratic programming-based stabilizing controller . We theoretically establish the semi-global exponential stability of the proposed method and the asymptotic stability of its extension to nonprehensile cooperative manipulation under noninstantaneous switching. The proposed framework is further validated through numerical simulations on 2D and 3D free-flyer systems and multi-robot nonprehensile pushing tasks. Cooperative tasks involving objects that are collectively controlled by multiple agents such as drone swarms and robotic arms in manufacturing rely on precise object manipulation.

However, even if a plant has negligible transmission delays, it may still have sizable inertial latencies. For example, if we apply a force to a visco-elastic plant, its peak velocity will be achieved after a certain delay; i.e. the velocity itself will lag the force.

We present a Riccati-based framework for safety-critical nonlinear control that integrates the barrier states (BaS) methodology with the State-Dependent Riccati Equation (SDRE) approach. The BaS formulation embeds safety constraints into the system dynamics via auxiliary states, enabling safety to be treated as a control objective. To overcome the limited region of attraction in linear BaS controllers, we extend the framework to nonlinear systems using SDRE synthesis applied to the barrier-augmented dynamics and derive a matrix inequality condition that certifies forward invariance of a large region of attraction and guarantees asymptotic safe stabilization. The resulting controller is computed online via pointwise Riccati solutions. We validate the method on an unstable constrained system and cluttered quadrotor navigation tasks, demonstrating improved constraint handling, scalability, and robustness near safety boundaries. This framework offers a principled and computationally tractable solution for synthesizing nonlinear safe feedback in safety-critical environments.

This study experimentally validates the principle of large-scale satellite swarm control through learning-aided magnetic field interactions generated by satellite-mounted magnetorquers. This actuation presents a promising solution for the long-term formation maintenance of multiple satellites and has primarily been demonstrated in ground-based testbeds for two-satellite position control. However, as the number of satellites increases beyond three, fundamental challenges coupled with the high nonlinearity arise: 1) nonholonomic constraints, 2) underactuation, 3) scalability, and 4) computational cost. Previous studies have shown that time-integrated current control theoretically solves these problems, where the average actuator outputs align with the desired command, and a learning-based technique further enhances their performance. Through multiple experiments, we validate critical aspects of learning-aided time-integrated current control: (1) enhanced controllability of the averaged system dynamics, with a theoretically guaranteed error bound, and (2) decentralized current management. We design two-axis coils and a ground-based experimental setup utilizing an air-bearing platform, enabling a mathematical replication of orbital dynamics. Based on the effectiveness of the learned interaction model, we introduce NODA-MMH (Neural power-Optimal Dipole Allocation for certified learned Model-based Magnetically swarm control Harness) for model-based power-optimal swarm control. This study complements our tutorial paper on magnetically actuated swarms for the long-term formation maintenance problem.

This paper proposes a unidirectionally connected fully actuated system (UC-FAS) approach for the sub-stabilization and tracking control of 6-DOF quadrotors, tackling limitations both in state-space and FAS framework to some extent. The framework systematically converts underactuated quadrotor dynamics into a UC-FAS model, unifying the existing different FAS transformation ways. By eliminating estimation of the high-order derivatives of control inputs, a drawback of current methods, the UC-FAS model simplifies controller design and enables direct eigenstructure assignment for closed-loop dynamics. Simulations demonstrate precise 6-DOF tracking performance. This work bridges theoretical FAS approach advancements with practical implementation needs, offering a standardized paradigm for nonlinear quadrotor control.

In many robotic systems where dynamics are best modeled as stochastic systems due to factors such as sensing noise and environmental disturbances, it is challenging for conventional methods such as Hamilton-Jacobi reachability and control barrier functions to provide a holistic measure of safety. We derive a linear operator governing the dynamic programming principle for safety probability, and find that its dominant eigenpair provides information about safety for both individual states and the overall closed-loop system. The proposed learning framework, called EigenSafe, jointly learns this dominant eigenpair and a safe backup policy in an offline manner. The learned eigenfunction is then used to construct a safety filter that detects potentially unsafe situations and falls back to the backup policy. The framework is validated in three simulated stochastic safety-critical control tasks.

Artificial intelligence (AI) models are becoming key components in an autonomous vehicle (AV), especially in handling complicated perception tasks. However, closing the loop through AI-based feedback may pose significant risks on reliability of autonomous driving due to very limited understanding about the mechanism of AI-driven perception processes. To overcome it, this paper aims to develop tools for modeling, analysis, and synthesis for a class of AI-based AV; in particular, their closed-loop properties, e.g., stability, robustness, and performance, are rigorously studied in the statistical sense. First, we provide a novel modeling means for the AI-driven perception processes by looking at their error characteristics. Specifically, three fundamental AI-induced perception uncertainties are recognized and modeled by Markov chains, Gaussian processes, and bounded disturbances, respectively. By means of that, the closed-loop stochastic stability (SS) is established in the sense of mean square, and then, an SS control synthesis method is presented within the framework of linear matrix inequalities (LMIs). Besides the SS properties, the robustness and performance of AI-based AVs are discussed in terms of a stochastic guaranteed cost, and criteria are given to test the robustness level of an AV when in the presence of AI-induced uncertainties. Furthermore, the stochastic optimal guaranteed cost control is investigated, and an efficient design procedure is developed innovatively based on LMI techniques and convex optimization. Finally, to illustrate the effectiveness, the developed results are applied to an example of car following control, along with extensive simulation.