A fast optmization algorithm for Moving Horizon Estimation.

The Moving Horizon Estimation (MHE) is a technique that allows to estimate the states of a system considering constraints, either when they are effected by noise or are not measured. This method can be associated with control techniques such as Model Predictive Control. The core of the mathematics formulation of MHE consists of an optimization problem that can easily become huge as the horizon and the number of states of the system increase. This leads inevitably to a large computational time that makes dicult the implementation of the algorithm for on-line purpose. In this work we show through several simulations on linear random systems that if we assume box constraints on the states and output noises, we can eciently apply the Nesterov's Fast Gradient method for solving the optimization problem faster than using the standard optimization algorithms such as Interior Point Method or Active Set Method

Predictive control for longitudinal beam dynamics in heavy ion synchrotrons

We present a design of a predictive control scheme for longitudinal beam dynamics in heavy ion synchrotrons. Specifically, we consider a linear-quadratic model predictive control (MPC) approach, whereby the quadratic program is solved via a fast gradient method. Furthermore, we investigate whether the fast gradient method allows for real-time feasible implementation of the proposed approach on a field programmable gate array (FPGA). Our results indicate that sampling rates in the order of 1MHz are achievable

Offset-free output feedback predictive control for longitudinal beam dynamics in heavy ion synchrotrons

Control of the longitudinal beam dynamics in heavy ion synchrotrons is a challenging task due primarily to the very fast time constants present in the system. Recently, the authors developed a model predictive controller for this system and demonstrated that solution of the required optimisation problem can be accomplished in about 1 microsecond when implemented on a Field Programmable Gate Array (FPGA). This initial design made several simplifying assumptions and in this paper we extend this initial design to account for known implementation issues relevant to the SIS18 heavy ion synchroton at the GSI Helmholtz Center. In particular, in this paper we present a design of an offset-free output feedback predictive control scheme for longitudindal beam dynamics in heavy ion sychrotons. Furthermore, we demonstrate how to compensate for possible communication delays. The performance of this offset-free output feedback predictive controller is validated in simulation