Multiobjective PID control design in uncertain robotic systems using neural network elimination scheme

A PID-type controller incorporating neural network elimination scheme and sliding-mode control action for different objectives including H₂ tracking performance, H_∞ tracking performance, and regional pole constraints is developed in robotic systems under plant uncertainties and external disturbances. The adaptive neural networks are used to compensate the plant uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via neural network approximation. The sufficient conditions are developed for different objectives in terms of linear matrix inequality (LMI) formulations. The interesting combinations of different objectives are considered in this paper, which include H_∞ PID tracking control design with regional pole constraints and mixed H₂/H_∞ PID tracking control design with regional pole constraints. These multiobjective PID control problems are characterized in terms of eigenvalue problem (EVP). The EVP can be efficiently solved by the LMI toolbox in Matlab. The proposed methods are simple and the PID control gain for different objectives can be obtained systematically