Computational Enhancement of the SDRE Scheme: General Theory and Robotic Control System

Abstract

This article presents a new efficient variant of the state-dependent Riccati equation (SDRE) scheme in a general scope, by analytically alleviating the computational burden in solving the pointwise algebraic Riccati equations (AREs). The novel contributions include a more efficient construction of feasible state-dependent coefficients (named alternative SDRE), which is critical at the early design stage, and more efficient solvability check for the classical SDRE scheme. For the selected robotic application-balance control of a two-wheeled robot, the contribution lies in the system-specific analysis that further enhances the computational performance toward an agile mobility. This novelty is with respect to a state-of-the-art ARE solver. An offline/a priori analytical formulation replaces the very first stage of the solving process, which more efficiently integrates the ARE solver into the SDRE design framework. Notably, all the results not only benefit the classical SDRE scheme but, more significantly, favor the proposed alternative SDRE owing to its much better computational efficiency-mainly in terms of time while promisingly for memory saving. In addition, simulations reveal more potential advantages using the variants-such as the control effort efficiency or required regulation time-within and beyond the scope of SDRE.