Efficiently tunable real-time implementation of Riccati equation-based designs: general scheme and benchmark study

Abstract

Abstract The article is motivated by extensive Riccati equation (RE)-based designs, where few are efficiently implemented in real-time computing platforms. In particular, the state-dependent Riccati equation (SDRE) scheme is criticized for its computational burden, which is caused by RE solving at each instant. Accordingly, we consider a benchmark problem – thrust vector control (TVC) – and focus on computational efficiency. The analysis efficiently guarantees the applicability and asymptotic stability of the SDRE-based TVC, avoiding the common compromise in practice that resorts to numerical checking routines; however, using the standard applicability-checking routine in MATLAB ® causes substantial computational effort, which accounts for the dominant computational burden in the RE-based design. Practically, we extend a state-of-the-art RE solver “Structure-Preserving Doubling Algorithm” by proposing an FPGA hardware implementation that 1) manifests remarkable computational efficiency in time and accuracy, $$\mathit{simultaneously}$$ ; and 2) provides a tuning flexibility so that practitioners more easily balance the two criteria. To quantify 1) and 2), the computation time (resp., accuracy residual) using the extended solver averagely amounts to $$10\% (\text{resp}., 32\%)$$ of that by the MATLAB $$$\textsuperscript{\textregistered}$$$ benchmark; while the tuning flexibility directly relates to the stopping criterion in the RE-solving process, which adopts the Frobenius norm of the associated RE's residual matrix.