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This paper presents an iterative data-driven algorithm for solving dynamicmulti-objective (MO) optimal control problems arising in control of nonlinearcontinuous-time systems. It is first shown that the Hamiltonian functionalcorresponding to each objective can be leveraged to compare the performance ofadmissible policies. Hamiltonian-inequalities are then used for which theirsatisfaction guarantees satisfying the objectives' aspirations. Anaspiration-satisfying dynamic optimization framework is then presented tooptimize the main objective while satisfying the aspiration of otherobjectives. Relation to satisficing (good enough) decision-making framework isshown. A Sum-of-Square (SOS) based iterative algorithm is developed to solvethe formulated aspiration-satisfying MO optimization. To obviate therequirement of complete knowledge of the system dynamics, a data-drivensatisficing reinforcement learning approach is proposed to solve the SOSoptimization problem in real-time using only the information of the systemtrajectories measured during a time interval without having full knowledge ofthe system dynamics. Finally, two simulation examples are provided to show theeffectiveness of the proposed algorithm.

Data-driven Dynamic Multi-objective Optimal Control: An Aspiration-satisfying Reinforcement Learning Approach