  This letter is devoted to the concept of ``instant'' model predictive control
(iMPC) for linear systems. An optimization problem is formulated to express the
finite-time constrained optimal regulation control, like conventional MPC.
Then, iMPC determines the control action based on the optimization process
rather than the optimizer, unlike MPC. The iMPC concept is realized by a
continuous-time dynamic algorithm of solving the optimization; the primal-dual
gradient algorithm is directly implemented as a dynamic controller. On the
basis of the dissipativity evaluation of the algorithm, the stability of the
control system is analyzed. Finally, a numerical experiment is performed in
order to demonstrate that iMPC emulates MPC and to show its less computational
burden.

Systems and Control;Optimization and Control