Implementing Receding Horizon Control with GEKKO in Python

Learn how to effectively implement `Receding Horizon Control (RHC)` using GEKKO in Python. This guide offers a deep dive into the process, ensuring you get every detail right.
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Introduction to Receding Horizon Control

Receding Horizon Control (RHC), also known as Model Predictive Control (MPC), is a powerful technique used in control systems and robotics. The main objective is to compute future control actions by solving an optimization problem at each time step. This approach is particularly useful when dealing with dynamic systems that require adaptive and real-time decision-making.

In this guide, we'll walk through implementing an RHC scheme using GEKKO, a popular optimization library in Python. We'll not only provide the code but also clarify the common pitfalls, specifically addressing the issues related to state resetting during the control process.

Problem Statement

When implementing an RHC scheme, it's essential to ensure that the control solution from each optimization horizon is applied correctly in the subsequent iterations. A reader encountered an error while attempting to reset state variables in their GEKKO formulation. They aimed to check the correctness of their implementation, particularly focusing on the state values and transitioning smoothly from one optimization horizon to another.

Understanding the Solution

Upon reviewing the reader's implementation and the encountered issues, we can clarify a few key points to help establish a robust foundation for using GEKKO in an RHC context.

Key Concepts in GEKKO

State Variables: In GEKKO, state variables can be defined using m.SV(), which allows you to model variables that need to be controlled over time.

Manipulated Variables: These are your control inputs, defined using m.MV(). In the provided code, u is used as the control input.

Model Equations: The system dynamics must be captured using the .Equation() function, detailing how the state variables relate to each other and the control inputs.

Common Mistakes

The primary error noted was in attempting to reset state variables in a way that was not necessary, leading to errors like TypeError: 'float' object is not subscriptable.

The Correct Approach

In GEKKO, the state values are automatically handled, which simplifies the coding process. Therefore, there’s no need to manually update the states after each optimization step. Here’s an overview of how to do it properly:

Code Explanation

Here’s a segment of the code from the reader's implementation that highlights the part that caused confusion:

[[See Video to Reveal this Text or Code Snippet]]

Best Practices

Do Not Manually Update States: Automatic state updates simplify your control strategy.

Using MEAS or VALUE: If you need to override the initial conditions for some specific scenarios, you can utilize:

Conclusion

Successfully implementing Receding Horizon Control using GEKKO in Python can greatly enhance your control systems, providing more adaptive and efficient solutions. By understanding the automatic handling of state variables and optimizing the setup of equations and manipulations, you can avoid common pitfalls encountered in MPC frameworks.

We hope this guide clarifies the essentials of your implementation and helps you navigate any challenges that may arise during your project. Happy coding!