What Is Predictive Control?

Predictive control is a class of feedback control strategies that use an explicit mathematical model of the system to forecast its future behavior and compute control actions by solving a finite-horizon optimization problem at each time step. The defining feature is the receding horizon: only the first control action of each computed optimal sequence is applied, after which the horizon shifts forward and the optimization is solved again with updated state information. This online replanning distinguishes predictive control from classical control methods, which rely on fixed feedback gains, and gives the framework a natural ability to handle constraints and multi-objective performance specifications.

The most widely studied formulation is model predictive control (MPC), which minimizes a cost function over a prediction horizon subject to explicit constraints on inputs and outputs. MPC was developed in the process industries during the 1970s and 1980s for multivariable refinery control, where managing constraints between dozens of interacting variables exceeded the capabilities of proportional-integral-derivative controllers. The framework has since spread to autonomous systems, power electronics, chemical processes, and aerospace guidance, driven by increases in embedded computing power that make real-time optimization tractable.

Receding Horizon Optimization

At each sample time, MPC solves an open-loop optimal control problem over a prediction horizon of N steps. The cost function typically penalizes deviations of predicted outputs from a reference trajectory and the magnitude of control actions, trading off setpoint tracking against actuator effort. When the system model is linear and the cost is quadratic, the optimization reduces to a quadratic program that can be solved reliably in milliseconds on embedded processors. For nonlinear systems, the problem becomes a nonlinear program, requiring iterative solvers such as sequential quadratic programming or interior-point methods. Real-time optimization and model predictive control for aerospace and automotive applications documents how active-set and interior-point solvers have been tailored for embedded hardware, achieving solution times compatible with sampling rates of hundreds of hertz in vehicle and aircraft control loops.

Constraint Handling

The ability to enforce hard constraints on states, inputs, and outputs throughout the prediction horizon is the principal advantage of MPC over classical control designs. Constraints arise naturally in every engineering application: actuators have magnitude and rate limits, process variables must stay within safe operating bounds, and multi-variable systems must respect coupling restrictions between channels. In MPC, these are stated directly as inequality constraints in the optimization problem and satisfied by construction at each step. Soft constraints, which relax hard bounds with a penalty when infeasibility would otherwise occur, preserve solvability under disturbances. Stability guarantees for constrained MPC rely on a terminal cost and terminal constraint set that together act as a Lyapunov function for the closed-loop system, a construction detailed in the MPC textbook by Rawlings, Mayne, and Diehl, the standard reference in the field.

Applications in Aerospace and Robotics

Aerospace and robotics present some of the most demanding predictive control scenarios because the plant dynamics are nonlinear, the operating envelope is wide, and safety constraints are hard limits. In spacecraft rendezvous and proximity operations, MPC formulates the docking trajectory as a constrained optimization over orbital mechanics, handling thruster saturation and collision-avoidance zones simultaneously. In autonomous ground robots and quadrotors, nonlinear MPC tracks high-speed reference trajectories while respecting joint torque limits and obstacle constraints. Transformer-based model predictive control for trajectory optimization represents a recent direction in which learned sequence models replace or warm-start the online optimization, reducing solve time for complex nonlinear systems while retaining the constraint-handling structure of classical MPC.

Applications

Predictive control has applications in a range of fields, including:

• Chemical and petroleum refining, where MPC manages multivariable interactions in distillation and reaction systems
• Electric power grids, including frequency regulation and battery energy storage dispatch
• Autonomous vehicles, where MPC plans trajectories subject to road boundaries and collision constraints
• Aerospace guidance and flight control, including attitude control of satellites and hypersonic vehicles
• Robotic manipulation, where real-time MPC generates joint torque commands for dexterous tasks