In this paper, a unique multi-agent control problem is defined --- all the elements of all the agent states reaching consensus at the same time, i.e., the multi-agent system achieves time-synchronized consensus; and fixed-time-synchronized consensus, where the upper bound of the synchronized settling time is independent of the initial states of multi-agent systems. To articulate this (fixed-) time-synchronized consensus problem, we first propose Time-Synchronized Stability and Fixed-Time-Synchronized Stability, a special kind of fixed/finite-time stability, where all the elements of the system state synchronously arrive at the equilibrium at the same time, with the upper bound of the synchronized settling time-dependent/independent of initial conditions. Based on fixed-time-synchronized stability, a singularity-free sliding mode control law is designed to solve the fixed-time-synchronized consensus problem. Finally, numerical simulations are conducted to showcase the effectiveness, and further exploration of the merit of the proposed controller is provided.

Previous research on finite-time control focuses on forcing a system state (vector) to converge within a certain time moment, regardless of how each state element converges. In the present work, we introduce a control problem with unique finite/fixed-time stability considerations, namely time-synchronized stability (TSS), where at the same time , all the system state elements converge to the origin, and fixed-TSS, where the upper bound of the synchronized settling time is invariant with any initial state. Accordingly, sufficient conditions for (fixed-) TSS are presented. On the basis of these formulations of the time-synchronized convergence property, the classical sign function, and also a norm-normalized sign function , are first revisited. Then in terms of this notion of TSS, we investigate their differences with applications in control system design for first-order systems (to illustrate the key concepts and outcomes), paying special attention to their convergence performance. It is found that while both these sign functions contribute to system stability, nevertheless an important result can be drawn that norm-normalized sign functions help a system to additionally achieve TSS. Furthermore, we propose a fixed-time-synchronized sliding-mode controller for second-order systems; and we also consider the important related matters of singularity avoidance there. Finally, numerical simulations are conducted to present the (fixed-) time-synchronized features attained; and further explorations of the merits of the proposed (fixed-) TSS are described.

This paper addresses the distributed formation-containment (DFC) problem for multiple Euler-Lagrange systems with model uncertainties via output feedback in both constant and time-varying formation cases. First, a novel definition of the DFC problem is proposed using a two-layer framework. Since only parts of the followers can acquire the states of the dynamic leader, we design a distributed finite-time sliding-mode estimator to obtain accurate estimations of the desired position and velocity for each agent. Next, to deal with the absence of velocity sensors, we propose two DFC control laws combined with the high-gain observer for the leaders and the followers, respectively, while the time-varying formation in the first layer and the leader-based containment in the second layer can be achieved. Further, the adaptive neural networks are applied to deal with the model uncertainties due to their superior approximation capability. The uniform ultimate boundedness of all the state errors can be guaranteed by Lyapunov stability theory. In addition, a unified framework is given which can be transformed to four other basic distributed problems. Finally, simulation examples are presented to illustrate the feasibility of the theoretical results.

In this note, simultaneous-arrival-to-origin (SATO) convergence is defined --- all the elements of the system state arriving at the origin at the same time. Accordingly, a relevant sufficient condition is proposed for SATO convergence. Based on this formulation of SATO convergence, the classical sign function and the norm-normalized sign function are revisited. We investigate their differences with applications in sliding-mode control design, paying special attention to their convergence performance. It is found that both functions (expectedly when properly invoked) contribute to system stability, while the norm-normalized sign function additionally enables the system to achieve SATO convergence. This finding shows the distinctive merit of the norm-normalized sign function in achieving more than finite-time stability for a sliding-mode control system. Extensions to the scenario with a networked system are studied, where with the utilization of the norm-normalized sign function, the networked system (now with the SATO convergence property) drives all the agents to reach consensus simultaneously. Additionally, for double integrator systems and Euler-Lagrange systems, singularity-fr

Guaranteed safety and performance under various circumstances remain technically critical and practically challenging for the wide deployment of autonomous vehicles. Safety-critical systems in general, require safe performance even during the reinforcement learning (RL) period. To address this issue, a Barrier Lyapunov Function-based safe RL (BLF-SRL) algorithm is proposed here for the formulated nonlinear system in strict-feedback form. This approach appropriately arranges and incorporates the BLF items into the optimized backstepping control method to constrain the state-variables in the designed safety region during learning. Wherein, thus, the optimal virtual/actual control in every backstepping subsystem is decomposed with BLF items and also with an adaptive uncertain item to be learned, which achieves safe exploration during the learning process. Then, the principle of Bellman optimality of continuous-time Hamilton–Jacobi–Bellman equation in every backstepping subsystem is satisfied with independently approximated actor and critic under the framework of actor-critic through the designed iterative updating. Eventually, the overall system control is optimized with the proposed BLF-SRL method. It is furthermore noteworthy that the variance of the attained control performance under uncertainty is also reduced with the proposed method. The effectiveness of the proposed method is verified with two motion control problems for autonomous vehicles through appropriate comparison simulations.

This paper addresses the distributed attitude coordinated tracking problem for multiple constrained spacecraft by state and output feedback. Since only parts of the followers can acquire the states of the dynamic leader, a distributed finite-time sliding-mode estimator is firstly proposed to reconstruct the information of the leader's attitude and angular velocity accurately. Then, to guarantee the attitude constraints of spacecraft systems, we use the integral barrier Lyapunov function (BLF) technique to propose a distributed state feedback attitude tracking control algorithm. Next, in the case without angular velocity sensors, we design a distributed attitude tracking control law via output feedback using high-gain observers. In the two proposed control schemes, the adaptive neural networks (NNs) are introduced to tackle the model uncertainties. The uniform ultimate boundedness of all the state errors can be guaranteed by Lyapunov stability theory. Finally, numerical results are given to show the feasibility of the proposed schemes.