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This paper proposes a Robust Safe Control Architecture (RSCA) for safe-decision making. The system to be controlled is a vehicle in the presence of bounded disturbances. The RSCA consists of two parts: a Supervisor MPC and a Controller MPC. Both the Supervisor and the Controller are tube MPCs (TMPCs). The Supervisor MPC provides a safety certificate for an operating controller and a backup control input in every step. After an unsafe action by the operating controller is predicted, the Controller MPC takes over the system. In this paper, a method for the computation of a terminal set is proposed, which is robust against changes in the road curvature and forces the vehicle to reach a safe reference. Moreover, two important proofs are provided in this paper. First, it is shown that the backup control input is safe to be applied to the system to lead the vehicle to a safe state. Next, the recursive feasibility of the RSCA is proven. By simulating some obstacle avoidance scenarios, the effectiveness of the proposed RSCA is confirmed.

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In this paper, a practical model predictive control (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the linear parameter-varying (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single quadratic programming (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of admissible reference, the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality.INDEX TERMS Constrained systems, Linear parameter-varying systems, Model predictive control, Robust stability, Robotic manipulators.