In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

This paper investigates the H_∞ consensus control problem of nonlinear multiagent systems under an arbitrary topological structure. A novel Takagi-Sukeno (T-S) fuzzy modeling method is proposed to describe the problem of nonlinear follower agents approaching a time-varying leader, i.e., the error dynamics between the follower agents and the leader, whose dynamics is evolving according to an isolated unforced nonlinear agent model, is described as a set of T-S fuzzy models. Based on the model, a leader-following consensus algorithm is designed so that, under an arbitrary network topology, all the follower agents reach consensus with the leader subject to external disturbances, preserving a guaranteed H_∞ performance level. In addition, we obtain a sufficient condition for choosing the pinned nodes to make the entire multiagent network reach consensus. Moreover, the fuzzy modeling method is extended to solve the synchronization problem of nonlinear systems, and a fuzzy H_∞ controller is designed so that two nonlinear systems reach synchronization with a prescribed H_∞ performance level. The controller design procedure is greatly simplified by utilization of the proposed fuzzy modeling method. Finally, numerical simulations on chaotic systems and arbitrary nonlinear functions are provided to illustrate the effectiveness of the obtained theoretical results.

For a class of nonspherical-wrist manipulators, i.e., redundant or nonredundant, we propose unified singularity analysis and computation-effective avoidance methods. First, we construct a unified model to describe this class of manipulators and derive the kinematics equation and its modified form. Second, the Jacobian matrix of an $n$ -degree-of-freedom (DOF) manipulator is partitioned into block triangle form, and the singularity conditions are isolated and collected in a $3\times(n-3)$ submatrix. By analyzing the rank degeneracy conditions of the submatrix, singularity configurations are identified. Third, based on the partitioned Jacobian matrix, the kinematics equation is decomposed into two smaller dimension subequations, only one of which (called singular subequation, as determined by the $3\times(n-3)$ submatrix) contains singularities. Finally, reduced-order approaches and the singularity parameter optimization (SPO) method are presented to plan the singularity-free trajectories by handling the singular subequation. Theoretical analysis shows that the computation costs of the reduced-order approaches are only 1/3–1/2 of the traditional methods. The SPO method is even more efficient than the reduced-order methods. Simulation results verify the proposed methods.