Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An algorithm for hybrid optimal control is proposed that varies the discrete state sequence based on gradient information during the search for an optimal trajectory. The algorithm is developed for hybrid systems with partitioned state space. It uses a version of the hybrid minimum principle that allows optimal trajectories to pass through intersections of switching manifolds, which enables the algorithm to vary the sequence. Consequently, the combinatorial complexity of former algorithms can be avoided, since not each possible sequence has to be investigated separately anymore. The convergence of the algorithm is proven and a numerical example demonstrates the efficiency of the algorithm.
['Benjamin Passenberg', 'M. Sobotka', 'Olaf Stursberg', 'Martin Buss', 'Peter E. Caines']
I am writing a research paper on a idea An algorithm for discrete state sequence and trajectory optimization for hybrid systems with partitioned state space
[{"from": "human", "value": "I am writing a research paper on a idea An algorithm for discrete state sequence and trajectory optimization for hybrid systems with partitioned state space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An algorithm for hybrid optimal control is proposed that varies the discrete state sequence based on gradient information during the search for an optimal trajectory. The algorithm is developed for hybrid systems with partitioned state space. It uses a version of the hybrid minimum principle that allows optimal trajectories to pass through intersections of switching manifolds, which enables the algorithm to vary the sequence. Consequently, the combinatorial complexity of former algorithms can be avoided, since not each possible sequence has to be investigated separately anymore. The convergence of the algorithm is proven and a numerical example demonstrates the efficiency of the algorithm."}]