Adaptive State-space Control of Under-actuated Systems Using Error-magnitude Dependent Self-tuning of Cost Weighting-factors

This article methodically constructs a novel adaptive self-tuning state-space controller that enhances the robustness of under-actuated systems against bounded exogenous disturbances. The generic Linear-Quadratic-Regulator (LQR) is employed as the baseline controller. The main contribution of this article is the formulation of a hierarchical online gain-adjustment mechanism that adaptively modulates the weighting-factors of LQR’s quadratic-performance-index by using pre-calibrated continuous hyperbolic scaling functions. The hyperbolic scaling functions are driven by the magnitude of system’s state-error variables. This augmentation dynamically updates the solution of the Matrix-Riccati-Equation which modifies the state-feedback gains after every sampling interval. The efficacy of the proposed adaptive controller is validated by conducting hardware-in-the-loop experiments on QNET Rotary Pendulum setup. The experimental outcomes show that the proposed adaptive control scheme yields stronger damping against oscillations and faster error-convergence rate, while maintaining the controller’s asymptotic-stability, under the influence of parametric uncertainties.