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In this paper we propose a constrained guaranteed cost robust model predictive controller (GCMPC) for uncertain discrete time systems. This controller was developed based on a quadratic cost functional and guarantee robustness with respect to quadratically bound uncertainties. Such a class of problems is currently intractable by Min-Max Robust Model Predictive Controllers without polytopic approximations of the uncertainties. The proposed technique is computationally more efficient then an enumeration-based approach and requires only a Quadratically Constrained Quadratic Problem (QCQP) optimization, whereas LMI-based GCMPC approaches require a Semi-Definite Programming (SDP) optimization.

In this paper, we propose state-and static output-feedback generalized guaranteed cost control (GCC) approaches for discrete-time linear systems subject to normbounded structured parametric uncertainties. This method enables the convex synthesis for a more general class of systems, where uncertainties are uncorrelated block diagonal, and no feed-through uncertainty is multiplicative with control input ones. It also provides necessary and sufficient conditions for state-feedback and sufficient conditions for static output-feedback. We also present a comparative study among the proposed controllers, standard Linear Quadratic Regulator, and Guaranteed Cost Controller found in the literature.Corresponding author: Carlos M. Masssera.

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Abstract-Road traffic crashes have been the leading cause of death among young people. Most of these accidents occur when the driver becomes distracted and a loss-of-control situation occurs. Steer-by-Wire systems were recently proposed as an alternative to mitigate such accidents. This technology enables the decoupling of the front wheel steering angles from the driver hand wheel angle and, consequently, the measurement of road/tire friction limits and the development of novel control systems capable of ensuring vehicle stabilization and safety. However, vehicle safety boundaries are highly dependent on tire characteristics which vary significantly with temperature, wear and the tire manufacturing process. Therefore, design of autonomous vehicle and driver assistance controllers cannot assume that these characteristics are constant or known. Thus, this paper proposes a Guaranteed Cost Model Predictive Controller Driver Assistance System able to avoid front and rear tire saturation and to track the drivers intent up to the limits of handling for a vehicle with uncertain tire parameters. Simulation results show the performance of the proposed approach under time-varying uniformly distributed disturbances.