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<p>Many guidance methods that incorporate stochastic modeling assume that the covariance for the initial state distribution is given. Alternatively, this work reframes the problem as one of solving for the maximum possible initial uncertainty—or minimum required initial information—and the associated open loop control sequence such that constraints are satisfied. The optimization is solved exactly via convex optimization with probabilistic guarantees for linear Gaussian systems. Additionally, a nonlinear extension is proposed that incorporates a novel degree of nonlinearity constraint based on a previously published measure. The method is evaluated on two example scenarios, a linear rendezvous and a nonlinear perilune passage. Monte Carlo analysis verifies that, for linear systems, a feasible optimization results in probabilistic guarantees and that, for nonlinear systems, the degree of nonlinearity constraint is an important tuning parameter to assure statistical performance.</p>

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A Minimum Initial Information Approach for Nominal Guidance via Convex Optimization

  • 期刊论文

  • 发表日期：

    2025年4月23日

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  • William N. Fife,
  • Kyle J. DeMars

摘要

Many guidance methods that incorporate stochastic modeling assume that the covariance for the initial state distribution is given. Alternatively, this work reframes the problem as one of solving for the maximum possible initial uncertainty—or minimum required initial information—and the associated open loop control sequence such that constraints are satisfied. The optimization is solved exactly via convex optimization with probabilistic guarantees for linear Gaussian systems. Additionally, a nonlinear extension is proposed that incorporates a novel degree of nonlinearity constraint based on a previously published measure. The method is evaluated on two example scenarios, a linear rendezvous and a nonlinear perilune passage. Monte Carlo analysis verifies that, for linear systems, a feasible optimization results in probabilistic guarantees and that, for nonlinear systems, the degree of nonlinearity constraint is an important tuning parameter to assure statistical performance.