Model predictive control, Multivariable control, Quadratic programming, Hildreth's method, Algorithm-complexity

A significantly important part of model predictive control (MPC) with constraints are algorithms of numerical optimization. Reduction of the computational complexity of the optimization methods has been widely researched. The reason is that in certain cases of predictive control of fast dynamics processes an optimization algorithm may not be feasible within the sampling period time. This situation occurs particularly when requirements on control are more complex, e.g. in the multivariable control. Hildreth’s method based on the dual-problem-optimization-principles has been widely applied and implemented in model predictive control. However, modifications of this method are not widely described in context of model predictive control. This paper proposes a modification of Hildreth’s method, which reduces the computational complexity of the algorithm, and its application in the multivariable predictive control.