I am doing a Linear MPC and I still don't get why we need to throw the rest of the control inputs that we get from solving OCP inside the MPC.
In my opinion, why don't we use the second and so on control input, which is still probably relevant for the next time step control inputs? could someone explain the detailed reason to me?
Thanks!
In Model Predictive Control (MPC), the control problem is typically formulated as an optimization problem over a finite horizon. This optimization problem aims to find the optimal control input sequence over the prediction horizon, which minimizes a certain cost function subject to system dynamics and constraints.
In MPC, only the first control input from the optimal control sequence is applied to the system, and the optimization problem is resolved at the next time step using updated measurements. This process is repeated at every sampling time to compute the next control input.
The reason for only applying the first control input from the optimal control sequence is that the optimization problem is solved in a receding horizon fashion. The optimization problem is solved over a finite horizon, but only the first control input is applied to the system, and the optimization is repeated at the next time step. This allows the controller to adjust the control input in real time based on the current state of the system and the latest measurements.
Additionally, solving an optimization problem over a finite horizon requires significant computational resources, especially for large-scale systems. By only applying the first control input, the computational burden is significantly reduced, allowing for faster computation times and better real-time performance.
Therefore, by using only the first control input from the MPC, we can achieve a balance between real-time performance and computational efficiency while still ensuring good closed-loop performance and satisfying system constraints.
Because only the first element of the control input sequence is designed based on the closed loop dynamics. The others elements are designed based on the prediction.
Maria's answer is the best.
In addition, the state is always evolving with respect to time.
The prediction in the MPC assumes (not general) the state is undisturbed or the model dynamics is perfect.
However, this is almost not true in practice.
If the model dynamics is the same as the physical dynamics, and there is no disturbance, then it is arguable (assuming that the integration error is very small) that you can also use all of the control inputs: re-simulating the prediction that you have done in the MPC (whatever transcription you used).
Jadi begitu, Mas, misal Masnya pakai yang pertama, terus vehicle kena angin, jadi bergeser sedikit dari yang diprediksi di MPC karena di MPC tidak ada prediksi angin apapun. Makanya perlu diupdate terus dan hanya pakai yang pertama saja. Yang kedua dan seterusnya itu tidak perhatikan kondisi aktual vehicle (instantenous state). Kalau tidak angin, dan model Mas sama persis dengan fisiknya vehicle, baru Mas bisa pakai semua itu control inputs.
Semoga bisa membantu, Vivat. Brilian Putra Amiruddin
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