Fast Constrained LQR Based on MPC With Linear Decomposition

A technique is presented to solve the linear quadratic optimal control problem with state and control constraints. The control law, called LD-MPC, has both implicit and explicit forms. Compared to conventional model predictive control (MPC), with the same feasible region, the implicit LD-MPC has fewer decision variables, and hence may reduce online computational time. One numerical example with comparison to MPC shows the main benefits of the proposed method.