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<p>This paper is concerned with sufficient optimality conditions for a Mayer problem with control-affine state equation and state constraints. Assuming that we are given an extremal constituted by the concatenation of a bang arc, a singular internal arc, a single boundary arc and a final bang arc, we provide a set of conditions that guarantee its strong local optimality. These conditions consists of a set of inequalities plus the coercivity of a suitable infinite-dimensional quadratic form (extended second variation).</p>

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Optimality Conditions for Control Problems Under Pure State Constraints

  • 期刊论文

  • 发表日期：

    2025年9月15日

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  • Francesca Carlotta Chittaro,
  • Laura Poggiolini

摘要

This paper is concerned with sufficient optimality conditions for a Mayer problem with control-affine state equation and state constraints. Assuming that we are given an extremal constituted by the concatenation of a bang arc, a singular internal arc, a single boundary arc and a final bang arc, we provide a set of conditions that guarantee its strong local optimality. These conditions consists of a set of inequalities plus the coercivity of a suitable infinite-dimensional quadratic form (extended second variation).