Data-Driven Dynamic Multiobjective Optimal Control: An Aspiration-Satisfying Reinforcement Learning Approach

Area of Science:

• Control Theory
• Optimization
• Machine Learning

Background:

• Dynamic multiobjective optimal control problems are complex for nonlinear systems.
• Existing methods often require complete knowledge of system dynamics.

Purpose of the Study:

• To develop a data-driven iterative algorithm for solving dynamic multiobjective optimal control problems.
• To enable real-time control without requiring full system dynamics knowledge.

Main Methods:

• Leveraging Hamiltonian functionals and inequalities to satisfy objective aspirations.
• Solving relaxed Hamilton-Jacobi-Bellman (HJB) inequalities for Pareto optimal solutions.
• Developing a sum-of-square (SOS)-based iterative algorithm for aspiration-satisfying optimization.
• Proposing a data-driven satisficing reinforcement learning approach for real-time problem-solving.

Main Results:

• The algorithm effectively finds Pareto optimal solutions for dynamic multiobjective optimal control problems.
• The data-driven approach successfully solves the SOS optimization problem using system trajectory data.
• The method obviates the need for complete knowledge of system dynamics.

Conclusions:

• The proposed iterative data-driven algorithm provides an effective solution for dynamic multiobjective optimal control of nonlinear systems.
• The reinforcement learning approach enables real-time control decisions using limited system information.
• This work contributes to advancing control strategies for complex dynamic systems.