This paper presents a novel Model Predictive Control (MPC) algorithm for linear systems subject to stochastic noise and probabilistic constraints on the state and control variables. The method is based on the reformulation of these constraints in terms of deterministic ones, on the use of terminal constraints on the mean value and on the covariance of the state, and on a binary strategy for the selection of the initial conditions to be considered at any time instant in the MPC optimization problem. The proposed algorithm is characterized by a computational burden similar to the one required by stabilizing MPC methods for deterministic systems, by the possibility to consider unbounded noises, and by guaranteed recursive feasibility and convergence
In this paper we propose an output-feedback Model Predictive Control (MPC) algorithm for linear discrete-time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints. In case the noise distribution is unknown, the probabilistic constraints on the input and state variables are reformulated by means of the Chebyshev -Cantelli inequality. The recursive feasibility is guaranteed, the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions, and the implementation issues are thoroughly addressed. Two examples are discussed in details, with the aim of providing an insight into the performance achievable by the proposed control scheme.
A two-layer control scheme based on Model Predictive Control (MPC) operating at two different timescales is proposed for the energy management of a grid-connected microgrid (MG), including a battery, a microturbine, a photovoltaic system, a partially non predictable load, and the input from the electrical network. The high-level optimizer runs at a slow timescale, relies on a simplified model of the system, and is in charge of computing the nominal operating conditions for each MG component over a long time horizon, typically one day, with sampling period of 15 minutes, so as to optimize an economic performance index on the basis of available predictions for the PV generation and load request. The low-level controller runs at higher frequency, typically 1 minute, relies on a stochastic MPC (sMPC) algorithm, and adjusts the MG operation to minimize the difference, over each interval of 15 minutes, between the planned energy exchange and the real one, so avoiding penalties. The sMPC method is implemented according to a shrinking horizon strategy and ensures probabilistic constraints satisfaction. Detailed models and simulations of the overall control system are presented.
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