Research On Tracking Control Algorithm For Multi-agent Systems With State And Input Constraints

Practical systems are almost characterized by complex structures,high-order nonlinearities,and strong couplings.In order to ensure the security and stable operation of the systems,the inputs,states,and outputs of the system will be subject to physical limitations,the external environment and other factors.Currently,the control problems of single systems with constraints have been fully studied.However,the researches on the control problems of constrained multi-agent systems are incomplete.Therefore,it is essential to study the tracking control problem of constrained multi-agent systems with the pure-feedback form.Based on the nonlinear mapping method,this paper studies the distributed control problem of the constrained nonlinear pure-feedback multi-agent systems.The main results are shown as follows:(1)For the pure feedback multi-agent system with full state constraints,the distributed finite-time tracking control algorithm is proposed under the directed graph.By introducing the nonlinear mapping technique,the system with full state constraints is converted into the form without state constraints.Furthermore,by combining the backstepping method and the fractional dynamic surface control method,a novel finitetime adaptive tracking controller is conducted recursively.In light of the finite-time stability theory,it is proven that all signals of multi-agent systems are bounded in finite time and the full states satisfy the constraints.Lastly,numerical simulations are supplied to demonstrate the effectiveness of the proposed control strategy.The nonlinear mapping method is used in this paper,then the design process can employ traditional Lyapunov functions.In comparison,it is needed to redesign the Lyapunov function if the Barrier Lyapunov Functions are applied.As a result,the proposed control design process is very simple.(2)For the uncertain high-order non-affine pure feedback multi-agent system with full state constraints and the input saturation,the consensus tracking control strategies with the known and unknown control direction are developed under the directed graphs.To solve the input saturation and full state constraints,the hyperbolic tangent function,the mean value theorem,and the nonlinear mapping method are applied.Then,the nonaffine pure-feedback system is converted into a strict-feedback system and the controller design process is more convenient.By combining the backstepping method and the dynamic surface control method,the consensus tracking control strategy with the input and states constraints is proposed and the differential explosion problem is avoided.In light of Lyapunov stability theory,it is proven that all signals of multi-agent systems are bounded.In addition,the inputs and states of the pure-feedback systems satisfy the desired constraints.Based on this algorithm,the Nussbaum function is applied to solve the tracking problem with the unknown control direction.Lastly,numerical simulations are supplied to verify the effectiveness of the proposed control strategies.