Model Predictive Control Parameterized in Terms of Orthogonal Polynomials

In this article, model predictive control was parameterized in terms of orthogonal Legendre and Chebyshev polynomials to minimize the set of free variables of constrained optimization problem that has to be solved at every time step. In this study, these orthogonal polynomials were used to approximate the control signal to represent them by a lower dimensional set of variables; these variables are the unknown coefficients of the truncated series of orthogonal polynomials. It was shown that constrained model predictive control and the associated constrained optimization problem can be recast in terms of these unknown coefficients of the truncated series of orthogonal polynomials. This new constrained optimization problem can be solved in a fraction of the time required for the original constrained model predictive control. This new constrained model predictive control was tested on a four-tank bench-marking problem to demonstrate its performance.