Compensation of Nonlinear Uncertain Dynamics of Kalman Filter in Designing Hard-Constrained Feedback Control System Requiring No Operation Parameters Setting-Up

Abstract

In this study, the control design-stage incorporation of the Kalman Filter (KF) dynamic as an optimal predictive element is explored. The control algorithm under investigation exploits the combination of uncertain nonlinear KF dynamic with the main plant model, the impacts of which comprise enhanced trajectory tracking quality, control energy consumption, robustness against parametric uncertainty, and addressing uncertain noise describing covariance, all while guaranteeing the stability of the KF-embedded architecture under the imposition of actuator input and plant input (actuator output) hard limitations. For performance evaluation of the proposed control algorithm, a linear Newtonian system with a 2nd-order oscillatory actuator and uncertain nonlinear KF dynamic was utilized while being subjected to double saturations and process and measurement noise with uncertain covariances. A Gradient Descent (GD)-based optimal dual-mode discrete sliding mode algorithm with search-based self-adjusting feedback loop operating parameters was employed. The simulation results demonstrate the multifaceted superior performance of this architecture in comparison with the scenarios in which the filter dynamic is not embedded into the control strategy. Furthermore, adding a search algorithm to optimize the control and KF parameters not only can reduce the tracking error and the required control energy, but is capable of alleviating the sensitivity to the initial parameter values, preventing initial overshoots and undershoots in the KF-embedded algorithm. Moreover, invoking the search algorithm for the KF parameters also significantly alleviates sensitivity to the search of control parameters, leading to reduced computational cost for the control scheme. This search algorithm enhances the controller's resilience for trajectory redesign to accommodate double saturation bounds. Ultimately, the controller exhibits robustness against noise, parameter uncertainty, and actuator/plant hard constraints, providing fine tracking quality and ensured stability in the face of the aforementioned challenges while keeping an affordable computational burden profile.