LMPC

LMPC is an acronym used in control theory that can refer to two related but distinct approaches: Linear Model Predictive Control and Learning Model Predictive Control.

Linear Model Predictive Control describes an MPC framework in which the process dynamics are modeled as a linear system x_{k+1} = A x_k + B u_k with state and input constraints, and a quadratic cost over a finite horizon. At each time step, an optimization problem is solved to determine a control sequence that minimizes the cost while respecting the constraints. Only the first control input is applied, and the horizon is rolled forward (receding horizon). Stability and constraint satisfaction are typically ensured through standard MPC techniques, including appropriate terminal penalties or terminal constraints. Linear MPC is widely used in process control, chemical engineering, aerospace, automotive, and robotics.

Learning Model Predictive Control describes a data-driven extension of MPC in which past state and input data are used to improve model accuracy or to guarantee safety and feasibility when the system model is uncertain or unknown. Typical LMPC frameworks construct a data-driven terminal set and a terminal cost from stored trajectories, enabling stable and feasible operation across repeated tasks. LMPC is especially applicable to nonlinear or uncertain systems and in iterative or repetitive tasks such as autonomous driving, robotics, and batch operations. Limitations include computational complexity, memory requirements for data storage, and the need for representative data to ensure performance gains.

See also: Model Predictive Control, Safe set, Iterative Learning Control, Data-driven control.