Fixed Point, Iteration-based, Adaptive Controller Tuning, Using a Genetic Algorithm

From a control perspective, the exact conditioning of systems with time-varying parameters is still a challenge. Many adaptive control algorithms (Adaptive Inverse Dynamics - AID, Model Reference Adaptive Controllers - MRAC, etc.) exist today. "Fixed Point Iteration Methods" attempt to offer "alternative" control planning methods to circumvent the application of the Lyapunov function technique. The foundations of the method were developed in 2009. RFPT is an iterative control method, based on the fixedpoint theorem of Stefan Banach proved in 1922 [1]. There is usually no specific suggestion for the choice of controller parameters, as the response function also depends on the approximation model parameter used and the actual behavior of the system under control. Adaptive RFPT presupposes strongly nonlinear system models in the first place, so in this case, thinking in frequency image and step inputs is not relevant (it is not advisable to conflict a nonlinear system with step inputs), so it does not have a tuning technique applicable to LTI models. However, there are a number of optimal search methods that can also be used to tune controllers (e.g., PIDs), e.g. the Genetic Algorithm. Using this method, I developed a possible autotuning process for adaptive RFPT controllers.