Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  demonstrates, how an approximation of the costate trajectory can be obtained for switched systems with state jumps, when an optimal control problem with fixed switching sequence is solved using a direct method, i.e. direct shooting or collocation. The obtained trajectories include the jump conditions for the costate given by necessary conditions for optimal control of switched systems.
['Markus Schori', 'Thomas Juergen Boehme', 'Torsten Jeinsch', 'Bernhard P. Lampe']
I am writing a research paper on a idea Costate approximation from direct methods for switched systems with state jumps
[{"from": "human", "value": "I am writing a research paper on a idea Costate approximation from direct methods for switched systems with state jumps"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  demonstrates, how an approximation of the costate trajectory can be obtained for switched systems with state jumps, when an optimal control problem with fixed switching sequence is solved using a direct method, i.e. direct shooting or collocation. The obtained trajectories include the jump conditions for the costate given by necessary conditions for optimal control of switched systems."}]