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Plants for Which Model Predictive Control Admits an Analytical Solution

Model predictive control (MPC) provides an optimal control sequence that is the solution to a moving horizon, constrained optimization problem. This problem is usually solved numerically on-line. A question that often process control engineers face is for what class of plants, MPC admits an analytical solution, in which case the optimal control sequence takes significantly less time to calculate. This paper presents an answer to this question. A class of nonlinear and linear plants for which MPC admits an analytical solution, is characterized. It is shown that for plants without directionality, constrained MPC can be identical to unconstrained MPC with saturation. Structural information on the characteristic (decoupling) matrix of a plant is often adequate for the characterization. Two input-constrained plant examples are considered. On the basis of structural information on the characteristic (decoupling) matrices of the two plants, the plan(s) for which constrained MPC admits an analytical solution is (are) specified. Simulated closed-loop responses are then presented to validate the characterization numerically.