This paper proposes an optimal approach for state estimation based on the Takagi–Sugeno (TS) Kalman filter using measurement sensors and rough pose obtained from LIDAR scan end-points matching. To obtain stable and optimal TS Kalman gain for estimator design, a linear matrix inequality (LMI) is optimized which is constructed from Lyapunov stability criteria and dual linear quadratic regulator (LQR). The technique utilizes a Takagi–Sugeno (TS) representation of the system, which allows modeling the complex nonlinear dynamics in such a way that linearization is not required for the estimator or controller design. In addition, the TS fuzzy representation is exploited to obtain a real-time Kalman gain, avoiding the expensive optimization of LMIs at every step. The estimation schema is integrated with a nonlinear model-predictive control (NMPC) that is in charge of controlling the vehicle. For the demonstration, the approach is tested in the simulation, and for practical validity, a small-scale autonomous car is used.

This paper presents an optimal approach for state estimation and Simultaneous Localization and Mapping (SLAM) correction using Kalman gain obtained via Linear Matrix Inequality (LMI). The technique utilizes a Linear Parameter Varying (LPV) represention of the system, which allows to model the complex non-linear dynamics in a way that linearization is not required for the estimator or controller design. In addition, the LPV polytopic representation is exploited to obtain a real-time Kalman gain, avoiding expensive optimization of LMIs at every step. The estimation schema is integrated with a Non-linear Model Predictive Control (NMPC) in charge of controlling the vehicle. For the demonstration, the approach is tested in the simulation and for the practical validity, a smallscale autonomous car is used.