In recent 20 years, the consensus control for multi-agent systems (MAS) has been an active research topic in many areas. If all the agents in one group can reach an agreement like the same position, velocity, attitude and so on, then the agents are said to reach the consensus. Its main advantage over centralized control is that the distributed consensus controller for each agent only uses its local information, i.e. the single agent does not need all the other agents’ information to reach the global agreement. Some influential work has been done. But preliminarily, most of them assume the model of the multi-agent systems is accurate, and the model usually is linear or has the known nonlinear dynamics. However, the practical multi-agent systems may be more complicated, so their model may have imprecise parts due to actual uncertainty about the plant (e.g., unknown plant parameters), or the purposeful choice of a simplified representation of the system’s dynamics, or the environmental uncertainties. To reflect this practical consideration, the multi-agent systems with unknown nonlinear dynamics are studied in this thesis. As we known, in the leaderless consensus control problem, the final consensus states that the multi-agent systems can reach finally have a specific invariance property, that is, the final consensus states are time-invariant and only depend on all agents’ initial states. But sometimes we also require that the consensus state is time-varying and/or can be designed to achieve some specific objectives. So we discuss the leader-following (L-F) consensus control for multi-agent systems with unknown nonlinear dynamics. The main contents of this thesis are listed as follows: (1) The asymptotic L-F consensus problem and finite-time L-F consensus problem of second-order nonlinear multi-agent systems with directed communication topology are investigated. On the basis of sliding mode control theory, a new distributed asymptotic consensus controller is proposed to ensure that the consensus of MAS can be reached as time goes to infinity. Another finite-time consensus control algorithm is also proposed based on terminal sliding mode ii control. The finite-time consensus controller can force the states of MAS to achieve the designed terminal sliding mode surface in finite time and maintain on it. The authors also can prove the consensus of MAS can be obtained in finite time on the terminal sliding mode surface if the directed topology has a directed spanning tree. (2) The consensus tracking control problem of second-order multi-agent systems with unknown nonlinear dynamics, immeasurable states and disturbances is investigated. The nonlinear dynamics in multi-agent systems do not satisfy the matched condition. Fuzzy logic system is introduced to approximate the unknown nonlinear dynamics and adaptive high-gain observer is designed to estimate the unmeasured states. Based on backstepping approach and Lyapunov theory, a new adaptive fuzzy distributed controller is proposed for each agent. It is proved that all the signals in the multi-agent systems are semiglobally uniformly ultimately bounded (SUUB) and the consensus tracking error converges to a small neighborhood of the origin that can be designed as small as possible. (3) The L-F consensus control problem of multi-agent systems in random vibration environment is investigated. The Ito stochastic systems with heterogeneous non- ˆ linear dynamics and external disturbances are established to describe the agents in random vibration environment. We propose a new consensus controller based on the fuzzy logic systems and adaptive algorithm. It is proved that all the follower agents can keep consensus with the leader even though only a very small part of follower agents can measure or receive the state information of the leader, and the states of all the follower agents are bounded in probability