A class of multi-agent discrete hybrid non linearizable systems: Optimal controller design based on quasi-Newton algorithm for a class of sign-undefinite hessian cost functions

 In the present paper, a class of hybrid, nonlinear and non linearizable dynamic systems is considered. The noted dynamic system is generalized to a multi-agent configuration. The interaction of agents is presented based on graph theory and finally, an interaction tensor defines the multi-agent system in leader-follower consensus in order to design a desirable controller for the noted system. A general undirected, simple and connected graph topology is proposed for the system. Next, a nonlinear controller is designed for the multi-agent system to track a predefined reference trajectory and maintain the formation topology. An optimal controller, based on quasi-Newton optimization method is proposed in order to minimize a nonlinear cost function with indefinite variable sign hessian matrix. The convergence of previous optimization algorithms, namely the Newton optimization algorithm, regarding to variable sign hessian matrices fails. Thus, in the present paper, a quasi-newton optimization method is proposed based on eigenvalue modification to design a controller for the system. Afterward, the controller generalized for the multi-agent system and the performance of the controller is examined in a specific scenario of indefinite, variable hessian matrix problem. Consequently, the innovation of the present paper is proposed by considering the quasi-newton optimization method in order to overcome the disadvantages of traditional optimization methods in the problem of undefined hessian cost function. An example is provided in order to illustrate aforementioned claims and declared propositions.