This paper is concerned with the stabilization of discrete-time linear systems with quantization of the input and output spaces, i.e., when available values of inputs and outputs are discrete. Unlike most of the existing literature, we assume that how the input and output spaces are quantized is a datum of the problem, rather than a degree of freedom in design. Our focus is hence on the existence and synthesis of symbolic feedback controllers, mapping output words into the input alphabet, to steer a quantized I/O system to within small invariant neighborhoods of the equilibrium starting from large attraction basins. We provide a detailed analysis of the practical stabilizability of systems in terms of the size of hypercubes bounding the initial conditions, the state transient and the steady state evolution. We also provide an explicit construction of a practically stabilizing controller for the quantized I/O case
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.
In this paper, the problem of the stabilization of a discrete-time linear system subject to a fixed and uniformly quantized control set is considered. It is well known that, working with quantized inputs, the states of the system (except for a negligible set of initial conditions) cannot reach asymptotically the equilibrium point. Our aim is then to find an invariant and attractive neighborhood of the equilibrium and provide with a controller which steers the system into it. We construct a continuous and increasing family of invariant sets including one which is, in a specific sense, minimal. The invariance and attractivity properties of such sets are revised in the finite control set case: we propose a family of controllers taking on a finite number of values and ensuring the system convergence to the minimal invariant set. Some consequences of our technique axe underlined with particular regard to the usage of model predictive control tools. In the last section an example which shows the effectiveness of our results is presented
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