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<p>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<sup>®</sup> causes substantial computational effort, which accounts for the <i>dominant</i> 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,<InlineEquation ID="IEq4005"><EquationSource Format="TEX">\(\mathit{simultaneously}\)</EquationSource></InlineEquation>; 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 <InlineEquation ID="IEq401"><EquationSource Format="TEX">\(10\% (\text{resp}., 32\%)\)</EquationSource></InlineEquation> of that by the MATLAB <InlineEquation ID="IEq400"><EquationSource Format="TEX">\($\textsuperscript{\textregistered}\)$</EquationSource></InlineEquation> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月9日

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  • Li-Gang Lin,
  • Shao-An Kuo,
  • Ching-Kai Lin,
  • Chin-Tien Wu,
  • Ming Xin

摘要

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.