$\mathcal{KL}$ and Lyapunov Approaches for Discrete-time Peak Computation Problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912615037403136 |
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| author | Adjé, Assalé |
| author_facet | Adjé, Assalé |
| contents | In this paper, we propose a method to solve discrete-time peak computation problems (DPCPs for short). DPCPs are optimization problems that consist of maximizing a function over the reachable values set of a discrete-time dynamical system. The optimal value of a DPCP can be rewritten as the supremum of the sequence of optimal values. Previous results provide general techniques for computing the supremum of a real sequence from a well-chosen pair of a strictly increasing continuous function on [0,1] and a positive scalar in (0,1). In this paper, we exploit the specific structure of the optimal value of the DPCP to construct such a pair from classical tools from stability theory: $\mathcal{KL}$ certificate and Lyapunov functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathcal{KL}$ and Lyapunov Approaches for Discrete-time Peak Computation Problems Adjé, Assalé Optimization and Control Dynamical Systems 39A30, 65Q10, 90C26 In this paper, we propose a method to solve discrete-time peak computation problems (DPCPs for short). DPCPs are optimization problems that consist of maximizing a function over the reachable values set of a discrete-time dynamical system. The optimal value of a DPCP can be rewritten as the supremum of the sequence of optimal values. Previous results provide general techniques for computing the supremum of a real sequence from a well-chosen pair of a strictly increasing continuous function on [0,1] and a positive scalar in (0,1). In this paper, we exploit the specific structure of the optimal value of the DPCP to construct such a pair from classical tools from stability theory: $\mathcal{KL}$ certificate and Lyapunov functions. |
| title | $\mathcal{KL}$ and Lyapunov Approaches for Discrete-time Peak Computation Problems |
| topic | Optimization and Control Dynamical Systems 39A30, 65Q10, 90C26 |
| url | https://arxiv.org/abs/2509.24689 |