Continuous time model predictive control design using orthonormal functions

Model predictive control has received wide attention from researchers in both industry and universities over the last two decades. Most approaches, however, were derived on the basis of discrete time models, and their corresponding continuous counter part is still in a relatively immature state of development because of obstacles in obtaining predictions and imposing constraints on the control variable. This paper shows that by using orthonormal functions to describe the trajectory of the control variable, these obstacles can be readily overcome and continuous time predictive control can be solved in a similar framework to the corresponding discrete time case. In addition, because of the parsimonious representation of the control trajectory, the algorithm developed here is computationally efficient. It is also easy to tune the closed-loop performance using two explicit tuning parameters. For several case studies, less than three parameters are required in the optimization procedure, which suggests that this procedure could offer substantial advantages when used in an on-line environment for both continuous and discrete cases.