Finite‐Time Optimal Formation Control for Second‐Order Multiagent Systems

Abstract

This paper studies the problem of finite-time optimal formation control for second-order multiagent systems in situations where the formation time and/or the cost function need to be considered. The finite-time optimal formation control laws are proposed for the cases with or without a leader, respectively. For the case of control being constrained, the time optimal formation problem is considered and an algorithm is designed to derive a feasible solution for the problem concerned. Although the feasible solution may not be optimal, it can provide a lower bound for time for the formation problem with control constraints. Once the given formation time is lower than this bound, the control constraints cannot be ensured. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.

Guaranteed cost formation control for multi-agent systems: Consensus approach

“…[21][22][23][24][25], formation problems for multi-agent systems were extensively investigated. However, those conclusions did not consider the formation performance and the energy consumption simultaneously.…”

Distributed finite‐time control for systems interconnected over an undirected graph

“…However, the finite-time stability (FTS) is more practical and applicable than the classical stability (Lyapunov stability) in many practical applications, no expect for the class of systems interconnected over an undirected graph. For example, it is necessary to consider the stability of a number of missiles and satellite systems within a limited time interval, or maintain the states of these systems not exceed the given boundaries in a certain time interval [11,12], such as the existence of saturation of the system ridicule [13], the spacecraft's trajectory control [14], and multi-spacecraft formation [15]. Moreover, we have considered the classical Lyapunov stability and distributed control problems for systems interconnected over an undirected graph under the time delay and Markovian jump situation in other studies [16][17][18].…”

Cooperative tracking of vessel trajectories based on curved dynamic coordinates

“…In these conventional sliding mode controls, a linear sliding manifold is usually selected, but system tracking errors will not be convergent to zero for a limited time. To solve this problem, Liu et al [27] proposed mechanisms based on the terminal sliding mode control method, where the system state can completely track the desired state at a specified limited time by designing dynamic nonlinear equations of the sliding surface. However, the introduction of a nonlinear function increases the difficulty of physical implementation, and the TSM control effectiveness is restricted, especially as the initial state of the control system greatly deviates from the target state or in the complex external disturbance conditions.…”