This project focuses on developing mathematical methods and algorithms for analyzing and designing optimal control systems.
The project aims to contribute to ongoing research efforts in mathematical control theory and provide new insights into the analysis and design of nonlinear control systems. The project will involve the following research topics:
- Mathematical Control Theory
- Nonlinear Control Systems
- Numerical methods for optimal control problems
This part focuses on developing mathematical methods and algorithms for analyzing and designing nonlinear control systems.
- Developing stability analysis methods for nonlinear systems and systems with uncertainties
Numerical solution to Optimal Control Problem (OPC)
This part contains the following numerical methods for solving optimal control problems:
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Direct methods
- Direct method transformed OCP into finite-dimensional optimization (Nonlinear programming problem (NLP))
- Direct transcription or First-Discretize-then-Optimize
- Reduce optimal control problems to an NLP
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Indirect methods: Indirect Methods or PMP-based Methods or Variational Methods or First-Optimize-then-Discretize
- find an optimal solution with satisfying optimality conditions
- Reduce the optimal control problem to a Boundary Value Problem (BVP)
- Control variable discretization: Shooting methods
- State and Control variables discretization: collocation methods (local and global)
Global collocational methods, so-called Pseudospectral Methods
Feedback-driven machine learning approach for optimal control problems.
-- Model-free RL -- Model-based RL
Generally these methods are based on the following approach:
- Value based method
- Policy based method
- Actor-Critic (combination of value and policy based method)
RL for Control