Synergetic Control Theory Approach for Solving Systems of Nonlinear Equations
نویسندگان
چکیده
This paper presents Synergetic Control Theory (SCT) and discusses how it can be used for solving systems of nonlinear equations. SCT is a new methodology for solving systems of nonlinear equations. The main advantage of SCT is that it maps the original system of equations to a dynamical system such that (1) any trajectory in the state space of the system ends in an attracting point; (2) the attracting point is located at the solution of the original system and (3) the rate at which the dynamical system moves towards the attracting point is controllable. An algorithm based on SCT is discussed. The algorithm has the following advantages: (1) If solutions exist, the algorithm finds one at a controllable rate, independently of initial guesses, (2) If no solutions exist, the algorithm makes such determination quickly, using stability analysis.
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