Anchita Dey

Anchita Dey, Shubhendu Bhasin

This paper proposes an adaptive tube framework for model predictive control (MPC) of discrete-time linear time-invariant systems subject to parametric uncertainty and additive disturbances. In contrast to conventional tube-based MPC schemes that employ fixed tube geometry and constraint tightening designed for worst-case uncertainty, the proposed approach incorporates online parameter learning to progressively refine the parametric uncertainty set and update the parameter estimates. These updates are used to adapt the components of the MPC optimization problem, including the prediction model, feedback gain, terminal set, and tube cross-sections. As the uncertainty set contracts, the required amount of constraint tightening reduces and the tube shrinks accordingly, yielding less conservative control actions. Recursive feasibility, robust constraint satisfaction, and closed-loop stability are formally established. Furthermore, the framework does not require the existence of a common quadratically stabilizing linear feedback gain for the entire parametric uncertainty set, thereby relaxing a standard assumption in existing tube-based MPC formulations. Numerical examples illustrate the effectiveness of the proposed approach.

Anchita Dey, Shubhendu Bhasin

An output feedback model predictive control (MPC) framework with adaptive tubes is proposed for linear time-invariant systems subject to parametric and additive uncertainties. An adaptive observer provides point estimates of the system state, model parameters, and initial condition, while jointly updating the corresponding sets containing the true parameters and initial state. These estimates parameterize the constrained optimal control problem, enabling constraint tightening, terminal ingredients, and tube geometry to be updated as the estimates evolve. In contrast to standard robust tube-based MPC formulations, the proposed approach does not require a common quadratically stabilizing linear feedback gain across the parametric uncertainty set. As the available uncertainty information improves, the tube geometry evolves accordingly, resulting in an adaptive tube MPC framework with improved performance over time. Recursive feasibility and robust exponential stability are established, and a numerical example is presented.