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The paper addresses the energy management of a building cooling system comprising a chiller plant with two chillers, a thermal storage unit, and a cooling load representing a building. Uncertainty affects the system since the cooling load depends on the building occupancy. The goal is to minimize the energy consumption of the cooling system, while preserving comfort in the building. This is achieved by optimally distributing the cooling load demand among the chillers and the thermal storage unit, and modulating the building temperature set-point to some (limited) extent. The problem can be decomposed into a static optimization problem, and a dynamic programming problem, which is solved based on the abstraction to a Markov chain of the stochastic hybrid system modeling the cooling system.

In this paper, a simulation-based method for the analysis and design of abstracted models for a stochastic hybrid system is proposed. The accuracy of a model is evaluated in terms of its capability to reproduce the system output for all the realizations of the stochastic input except for a set of (small) probability ε (ε-abstraction). This naturally leads to chance-constrained optimization problems, which are here tackled by means of a recently developed randomized approach. The main thrust of this paper is that, by testing how close the model and system outputs are over a finite number N of input realizations only, conclusions can be drawn about the model capability as an ε-abstraction. The key feature of the proposed method is its high versatility since it does not require specific assumptions on the system to be approximated. The only requirement is that of being able to run multiple simulations of the system behavior for different input realizations.

This paper concerns the design of an energy management system for a building cooling system that includes a chiller plant (with two or more chiller units), a thermal storage unit, and a cooling load. The latter is modeled in a probabilistic framework to account for the uncertainty in the building occupancy. The energy management task essentially consists in the minimization of the energy consumption of the cooling system, while preserving comfort in the building. This is achieved by a twofold strategy. The cooling power request is optimally distributed among the chillers and the thermal storage unit. At the same time, a slight modulation of the temperature set-point of the zone is allowed, trading energy saving for comfort. The problem can be decoupled into a static optimization problem (mainly addressing the chiller plant optimization) and a dynamic programming (DP) problem for a discrete time stochastic hybrid system (SHS) that takes care of the overall energy minimization. The DP problem is solved by abstracting the SHS to a (finite) controlled Markov chain, where costs associated with state transitions are computed by simulating the original model and determining the corresponding energy consumption. A numerical example shows the efficacy of the approach

This paper addresses the design of the inputs to a mixed logical dynamical system so as to satisfy some specification, while maximizing the number of non-influential inputs, i.e., those inputs that can take an arbitrary value within their admissible range without affecting the satisfaction of the specification. The problem can be rephrased as a reachability problem on an enlarged system and formulated as a robust mixed integer linear program. An iterative procedure that relies on the detection of non-influential inputs is proposed to simplify the solution to the problem for cascading systems. A numerical example shows the efficacy of the approach