Cooperative Control Of A Class Of Lower-Triangle Multi-Agent Systems Based On Active Disturbance Rejection Technique

For a class of typical lower-triangular multi-agent systems(MASs)with uncertainties,we take output consensus,output feedback containment control and formation tracking control into account in this thesis,and propsoe distributed cooperative control strategies by active disturbance rejection control(ADRC)and backstepping techniques.The main research work includes the following three aspects.1.For the output consensus control problem of a class of non-affine nonlinear MASs with input saturation,a distributed output consensus control strategy with predefined performance is proposed.The non-affine nonlinear MASs are transformed into affine nonlinear ones with uncertainties via the idea of equivalent transformation.The uncertainties in the MASs are approximated and compensated by extended state observers(ESOs)in real time,and tracking differentiators(TDs)are introduced to avoid the problem of explosion of complexity when computing the derivative of the desired signal and virtual control variables.The control input limitation is handled with the auxiliary system.Moreover,the prescribed performance functions are employed to guarantee the consensus tracking errors stay inside of the desired ranges,and this improves the control performance of the closed-loop system.Furthermore,it is proved that all the signals in the closed-loop system are ultimately bounded in the case of bounded initial conditions by a Lyapunov function.2.For the observer-based containment control problem of a class of uncertain nonlinear MASs connected by directed communications,a distributed containment control strategy based on ESOs is proposed.A kind of nonlinear ESOs based on fractional power functions is developed,and the estimations of extended states are utilized to compensate uncertain dynamics in real time.Compared with linear ESOs,the advantages of the ESOs in this section lie in peaking reduction and better tolerance of measurement noise for the closed-loop system.Moreover,this section presents an output-based containment control strategy for a class of non-affine nonlinear MASs with uncertainies in the case of a directed topology.With the help of differential homeomorphism transform and the idea of equivalent transformation,a non-affine nonlinear MAS is transformed into an affine nonlinear MAS with uncertainties.Two filters with extended states in each follower are designed with the idea of ESO to reconstruct the states of the transformed MAS.Then,uncertainties of the MAS are compensated with the help of the estimations of the extended states.Both of them use the TD to estimate the derivative of the virtual control signal in the backstepping technique to avoid the so-called ‘explosion of complexity' problem.The proposed output feedback containment control strategy only depends on the output and input signals of the follower,and all the signals in the closed-loop system are ultimately bounded in the case of bounded initial conditions.3.For the time-varying formation tracking control problem of a class of non-affine nonlinear MASs,a distributed time-varying formation tracking control strategy with predefined performance is proposed.The strategy transforms non-affine nonlinear MASs into affine nonlinear MASs with uncertainties by the idea of equivalent transformation.The uncertainties in the MASs are approximated and compensated by ESOs in real time,and TDs are introduced to avoid the problem of explosion of complexity when computing the derivative of the desired signal and virtual control variables.The strategy can improve the control performance of the closed-loop system by using the predefined performance function.Furthermore,it is proved that all the signals in the closed-loop system are ultimately bounded in the case of bounded initial conditions by a Lyapunov function.