This paper is concerned with the formation control problem of multiple underactuated surface vessels moving in a leader-follower formation. The formation is achieved by the follower to track a virtual target defined relative to the leader. A robust adaptive target tracking law is proposed by using neural network and backstepping techniques. The advantage of the proposed control scheme is that the uncertain nonlinear dynamics caused by Coriolis/centripetal forces, nonlinear damping, unmodeled hydrodynamics and disturbances from the environment can be compensated by on line learning. Based on Lyapunov analysis, the proposed controller guarantees the tracking errors converge to a small neighborhood of the origin. Simulation results demonstrate the effectiveness of the control strategy.
针对一类具有多项式向量场的仿射型不确定非线性系统,给出一种基于多项式平方和(sum of squares,SOS)技术的鲁棒H∞状态反馈控制器设计方法.该方法的优点在于控制器的设计避开了直接求解复杂的哈密尔顿-雅可比不等式(Hamilton Jacobi inequality,HJI)和构造Lyapunov函数带来的困难.将鲁棒稳定性分析和控制器设计问题转化为求解以Lyapunov函数为参数的矩阵不等式,该类不等式可利用SOS技术直接求解.此外,在前文基础上研究了基于SOS规划理论与S-procedure技术的局部稳定鲁棒H∞控制器设计方法.最后以非线性质量弹簧阻尼系统作为仿真算例验证该方法的有效性.
