Adaptive MPC for Constrained Trajectory Tracking of Uncertain LTI System with Input-Rate Limits

A team of researchers from India — Bishal Dey, Abhishek Dhar, Sumit kr. Pandey, and Anindita Sengupta — has published a new paper on adaptive Model Predictive Control (MPC) for constrained trajectory tracking in uncertain linear time-invariant (LTI) systems. The work tackles a notoriously difficult control problem: ensuring a system follows a desired trajectory when its parameters are unknown, while obeying hard limits on states, control inputs, and the rate at which inputs can change. Existing methods either assume only partial uncertainty, ignore input-rate or state constraints, or focus solely on regulation (keeping a system at a setpoint) rather than tracking a moving reference.

To overcome these challenges, the authors systematically combine online parameter estimation with a reformulated MPC framework. The key innovation is handling the temporal coupling introduced by input-rate limits — because a fast change in control is penalized, the set of admissible control actions becomes time-varying, breaking standard recursive feasibility proofs. The paper rigorously establishes that the proposed adaptive optimization remains feasible at every step, and uses Lyapunov-based analysis to guarantee closed-loop stability and boundedness of all system states. Simulation results confirm that tracking error converges to zero even under full parametric uncertainty. This work advances the theory of safe autonomous control for applications like robotics, drones, and autonomous vehicles where both uncertainty and actuator limits are critical.