https://github.com/ziraddingulumjanly/numeration-dynamic-programming-and-qp

This repository contains descriptive solutions and implementations for optimal control problems using three approaches:
https://github.com/ziraddingulumjanly/numeration-dynamic-programming-and-qp

Last synced: 16 days ago
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This repository contains descriptive solutions and implementations for optimal control problems using three approaches:

• Host: GitHub
• URL: https://github.com/ziraddingulumjanly/numeration-dynamic-programming-and-qp
• Owner: ziraddingulumjanly
• Created: 2025-04-25T15:01:25.000Z (10 months ago)
• Default Branch: main
• Last Pushed: 2025-04-25T15:05:06.000Z (10 months ago)
• Last Synced: 2025-06-28T12:44:31.457Z (8 months ago)
• Size: 175 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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# Optimal Control Methods: Enumeration, Dynamic Programming, and QP

This repository contains descriptive solutions and implementations for optimal control problems using three approaches:

- **Enumeration-Based Optimization**: Explores all possible control sequences from a discretized control grid to find the one that minimizes the cost function. Suitable for small problems but becomes computationally expensive as the grid size increases.

- **Numerical Dynamic Programming**: Uses the principle of optimality and backward recursion over discretized state and control grids. Efficient for low-dimensional systems, but sensitive to grid resolution and interpolation strategy.

- **Quadratic Programming (QP)**: Solves the discrete-time Linear Quadratic Regulator (LQR) problem exactly using matrix algebra. Fast and accurate for linear systems with quadratic cost, and naturally supports state and control constraints.

![image](https://github.com/user-attachments/assets/adc5491e-d14b-4fa6-87d1-a1e43d6e4cd0)

![image](https://github.com/user-attachments/assets/8f6ed83d-2c4a-4a0b-a9ee-356814a9c473)

The methods are applied to linear systems with quadratic cost, highlighting trade-offs in accuracy, efficiency, and constraint handling.