Hi Chri,
In MATLAB's Nonlinear MPC, defining Jacobians for the cost function and constraints is crucial for several reasons:
- Jacobians provide the necessary gradient information that optimization algorithms use to converge more quickly to a solution. By knowing how the cost function and constraints change with respect to the decision variables, the solver can make informed adjustments.
- Just as you mentioned for the state-space matrices (A, B, C), the Jacobians of the cost function and constraints allow for linearization around the current operating point. This is essential in NMPC, where the control problem is solved at each time step based on a prediction model.
- Jacobians help in understanding how sensitive the cost and constraints are to changes in the decision variables. This is particularly important in NMPC, where the system dynamics can be highly nonlinear.
Therefore, by providing Jacobians, NMPC can effectively optimize the control inputs while respecting the defined constraints.
To know more about NMPC, refer to the following MathWorks documentation link:
