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The turnpike property is depicted for the control u and state variables Ω 1 , Ω 2 , Ω 3 and their adjoints λ 1 , λ 2 , λ 3 . The trim depicted in dashed black and the optimal solution in red. For the representation we consider Ω 0 = Ω T = (0.9, 0.5, 0.5) T , T = 60, I = diag(1, 5, 10).
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Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing symmetries. Following recent works, which generalized the classical concept of static turnpike to manifold turnpike, we extend the exponential turnpike property to the exponential trim turnpike for control systems with symmetries induced by abelian or n...
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Motivated by mechanical systems with symmetries, we focus on optimal control problems possessing certain symmetries. Following recent works (Faulwasser in Math Control Signals Syst 34:759–788 2022; Trélat in Math Control Signals Syst 35:685–739 2023), which generalized the classical concept of static turnpike to manifold turnpike we extend the expo...
