PI consensus error transformation for adaptive cooperative control of nonlinear multi-agent systems

Abstract

A solution is provided in this note for the adaptive consensus problem of nonlinear multi-agent systems with unknown and non-identical control directions assuming a strongly connected underlying graph topology. This is achieved with the introduction of a novel variable transformation called PI consensus error transformation. The new variables include the position error of each agent from some arbitrary fixed point along with an integral term of the weighted total displacement of the agent's position from all neighbor positions. It is proven that if these new variables are bounded and regulated to zero, then asymptotic consensus among all agents is ensured. The important feature of this transformation is that it provides input decoupling in the dynamics of the new error variables making the consensus control design a simple and direct task. Using classical Nussbaum gain based techniques, distributed controllers are designed to regulate the PI consensus error variables to zero and ultimately solve the agreement problem. The proposed approach also allows for a specific calculation of the final consensus point based on the controller parameter selection and the associated graph topology. Simulation results verify our theoretical derivations.

Leader tracking control for heterogeneous uncertain nonlinear multi-agent systems via a distributed robust adaptive PID strategy

“…Event-triggered approaches have been also adopted as, for example, in [35,39,56], while the problem of unknown and nonidentical control directions has been addressed in [51] by exploiting the Nussbaum functions via a two-layer distributed hierarchical control scheme. The same problem is also dealt with in [38], where the Nussbaum functions are used by mean of a particular transformation, the socalled PI error transformation, for heterogeneous and unknown second-order nonlinear MASs. Classical dif-fusive protocols have been also proposed, as for example in [47], where the aim is to guarantee some leaderfollowing performance in the case of nonlinear Lipschitz heterogeneous MASs by considering the leader as a non-autonomous system with unknown bounded input, and in [37], where the consensus is ensured in finite time.…”

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

“…In previous works, the adaptive consensus problems of nonlinear multiagent systems with unknown identical control directions are solved via introducing novel Nussbaum‐type functions. Later, by requiring unknown control directions of all the agents to be the same, the consensus control problem with nonidentical partially unknown control directions is approached in the work of Chen et al The aforementioned requirement is further relaxed to completely unknown nonidentical control directions, and sub‐Lyapunov functions are employed to design distributed controllers and analyze the closed‐loop stability for multiagent systems . However, these works consider only the distributed control problem of multiagent systems, and the output constraints of the multiagent systems are not taken into account.…”