Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate.  allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which  apply different optimality conditions derived from Pontryagin principle and the Hamilton–Jacobi–Bellman equation.  thus characterise the singular trajectories of our problem as the extremal trajectories keeping the substrate at a constant level.  also establish conditions for which an immediate one impulse (IOI) strategy is optimal. Some numerical experiences are then included in order to illustrate our study and show that those conditions are also necessary to ensure the optimality of the IOI strategy.
['Juan Carlos Rodríguez', 'Hector Ramirez', 'Pedro Gajardo', 'Alain Rapaport']
I am writing a research paper on a idea Optimality of affine control system of several species in competition on a sequential batch reactor
[{"from": "human", "value": "I am writing a research paper on a idea Optimality of affine control system of several species in competition on a sequential batch reactor"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate.  allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics leads to a slightly different optimal control problem, without impulsive controls, for which  apply different optimality conditions derived from Pontryagin principle and the Hamilton\u2013Jacobi\u2013Bellman equation.  thus characterise the singular trajectories of our problem as the extremal trajectories keeping the substrate at a constant level.  also establish conditions for which an immediate one impulse (IOI) strategy is optimal. Some numerical experiences are then included in order to illustrate our study and show that those conditions are also necessary to ensure the optimality of the IOI strategy."}]