470597 Proportional State-Feedback Controller Design Using MPC Structure and Carleman Approximation Method
Motivated by the above discussion, this work tunes a proportional state feedback controller employing the nonlinear MPC structure combined with the Carleman approximation method. Therefore, the analytical solution and sensitivity of the objective function with respect to the proportional gain vector are available. This proposed state feedback control in the MPC structure, gives a smoother control law rather than a traditional nonlinear MPC which generates a piecewise constant input. Also, the analytical calculation of the Hessian matrix in addition to the gradient vector, in this work, reduces the online computation efforts even more.
The proposed controller would inherit the same nominal stability properties of the ideal nonlinear MPC, when there exists no Carleman approximation error. However, Carleman approximation method, with a finite dimension, always has a dynamic error which might endanger the stability of the closed-loop system. This work discusses the conditions required to guarantee the input-to-state stability in the presence of the Carleman approximation.
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