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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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... rest of the paper is organized as follows, see also the flowchart in Figure 1: In Section 2, we recall some useful geometric tools as well as the reduction procedures for general optimal control problems (OCP) and for mechanical systems from literature. We show the equivalence of the two reductions for controlled mechanical systems. ...
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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...
