A Simple Tube Controller for Efficient Robust Model Predictive Control of Constrained Linear Discrete Time Systems Subject to Bounded Disturbances

Abstract

We present a simple tube controller for efficient robust model predictive control of constrained linear, discrete-time systems in the presence of bounded disturbances. The proposed control policy ensures that controlled trajectories are confined to a given tube despite uncertainty. The robust optimal control problem that is solved on-line is a standard quadratic programming problem of marginally increased complexity compared with that required for model predictive control in the deterministic case. We show how to optimize the tube cross section, how to construct an adequate tube terminal set and we establish robust exponential stability of a suitable robust control invariant set (the 'origin' for uncertain system) with enlarged domain of attraction. Copyright

Design of plug-and-play model predictive control: An approach based on linear programming

“…In the spirit of tube-based control [10], we treat w [i] as a disturbance and define the nominal systemΣ [i] aŝ…”

“…In [1] the most critical step in the design of local MPC controllers requires to solve a nonlinear optimization problem. In this paper, using local tube MPC regulators based on Robust Control Invariant (RCI) sets [10], [11], we guarantee overall stability and constraints satisfaction solving Linear Programming (LP) problems only. Another difference is that in [1] stability requirements are fulfilled imposing an aggregate sufficient small-gain condition for networks.…”

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“Flyable” Guidance and Control Algorithms for Orbital Rendezvous Maneuver

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