Abstract
This paper presents robust linear model predictive control (MPC) technique for small scale linear MPC problems. The quadratic programming (QP) problem arising in linear MPC is solved using primal dual interior point method. We present a merit function based on a path following strategyto calculate the step length α, which forces the convergence of feasible iterates . The algorithm globally converges to the optimal solution of the QP problem while strictly followingthe inequality constraints. The linear system in the QP problem is solved using LDL T factorization based linear solver which reduces the computational cost of linear system to a certain extent. We implement this method for a linear MPC problem of undamped oscillator. With the helpof a Kalman filter observer, we show that the MPC design is robust to the external disturbances and integrated white noise.
Highlights
The purpose of the new control input is to ensure that the output signal tracks the reference signal while satisfying the objective function of the model predictive control (MPC) problem without violating the given constraints, see [1]-[3]
We presented a linear model predictive control of an undamped oscillator
The primal dual interior point method has been used to solve the quadratic programming (QP) optimal control problem arising in MPC
Summary
The computational cost of inverting the Hessian is O(n3), Secondly, the barrier method requires two distinct iterations to update primal and dual variables, see [9] This method works only for strictly feasible problems. The primal dual interior point method has several advantages over barrier methods such as updates of primal and dual variables are computed in a single iteration, efficiency in terms of accuracy and ability to work even when problem is not strictly feasible, and inverting the Hessian matrix is not required. Faster convergence of iterates can be achieved by considering new step length strategies in the primal dual algorithm One of such strategies is to measure progress to the solution by monitoring a merit function. This paper discusses the primal dual interior point method to solve linear model predictive control problems with convex quadratic objective function and linear inequality constraints on the control input.
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