An improved inverse optimal control design for affine-in-Input discrete-time nonlinear systems

This study presents an improved inverse optimal control (IOC) framework for both regulator and tracking control problems in affine-in-input discrete-time nonlinear dynamical systems. The proposed approach introduces state-dependent sigmoid weighting functions in the control input cost, enhancing design flexibility while preserving stability requirements. The effectiveness of the method is evaluated through regulator problems using a discrete-time nonlinear benchmark system and an unstable inverse pendulum, and through tracking problems using a real-time two-tank liquid level control system and an HIV infection dynamics model. Performance is assessed using various performance metrics. Results show that the proposed approach satisfies stability conditions of the IOC framework without requiring structural transformation of the system dynamics. In addition, it provides greater flexibility in controller parameter selection and achieves improved control performance compared with classical IOC methods. These findings demonstrate that the proposed design significantly enhances the applicability and effectiveness of IOC for affine-in-input discrete-time nonlinear systems.