A branch and bound approach for the design of decentralized supervisors in Petri net models

The paper addresses the design of compact and maximally permissive decentralized supervisors for Petri nets, based on generalized mutual exclusion constraints. Decentralization constraints are formulated with respect to the net transitions, instructing each local supervisor to detect and disable transitions of its own control site only. A solution is characterized in terms of the states it allows and its feasibility is assessed by means of two separate tests, one checking the required behavioral properties (e.g., liveness, reversibility and controllability) of the induced reachability subgraph and the other ensuring the existence of a decentralized supervisor enforcing exactly the considered set of allowed states. The second test employs an integer linear programming formulation. Maximal permissivity is ensured by efficiently exploring the solution space using a branch and bound method that operates on the reachable states. Particular emphasis is posed on the obtainment of the controllability property, both in the structural and the behavioral interpretation

A classification-based approach to the optimal control of affine switched systems

This paper deals with the optimal control of discrete–time switched systems, characterized by a finite set of operating modes, each one associated with given affine dynamics. The objective is the design of the switching law so as to minimize an infinite–horizon expected cost, that penalizes frequent switchings. The optimal switching law is computed off–line, which allows an efficient online operation of the control via a state feedback policy. The latter associates a mode to each state and, as such, can be viewed as a classifier. In order to train such classifier–type controller one needs first to generate a set of training data in the form of optimal state–mode pairs. In the considered setting, this involves solving a Mixed Integer Quadratic Programming (MIQP) problem for each pair. A key feature of the proposed approach is the use of a classification method that provides guarantees on the generalization properties of the classifier. The approach is tested on a multi–room heating control problem

Distributed allocation of a shared energy storage system in a microgrid

The economic management of a microgrid can greatly benefit from energy storage systems (ESSs), which may act as virtual load deferral systems to take advantage of the fluctuations of energy prices and accommodate for demand-production mismatches caused by the scarce predictability of renewable sources. In a distributed energy management scenario, an ESS may serve multiple users, a setting which calls for the development of suitable resource allocation policies for the storage capacity. In particular, distributed control policies are of interest, where each user operates independently with the least exchange of information with the other users. A methodology is developed in the paper for such purpose, based on an iterative resource allocation mechanism, realized by means of a negotiation process among users, resembling stock exchange dynamics. The resulting distributed strategy for the management of the shared resource comes close to optimality at a low computational cost, which is affordable in large scale practical applications. It is also robust to communication failures between users

A randomized algorithm for nonlinear model structure selection

The identification of polynomial Nonlinear Autoregressive [Moving Average] models with eXogenous variables (NAR[MA]X) is typically carried out with incremental model building techniques that progressively select the terms to include in the model. The Model Structure Selection (MSS) turns out to be the hardest task of the identification process due to the difficulty of correctly evaluating the importance of a generic term. As a result, classical MSS methods sometimes yield unsatisfactory models, that are unreliable over long-range prediction horizons. The MSS problem is here recast into a probabilistic framework based on which a randomized algorithm for MSS is derived, denoted RaMSS. The method introduces a tentative probability distribution over models and progressively updates it by extracting useful information on the importance of each term from sampled model structures. The proposed method is validated over models with different characteristics by means of Monte Carlo simulations, which show its advantages over classical and competitor probabilistic MSS methods in terms of both reliability and computational efficiency

A stochastic optimal control solution to the energy management of a microgrid with storage and renewables

The presence of renewable energy generators in a microgrid calls for the usage of storage units so as to smooth the variability in energy production. This work addresses the optimal management of a battery in a microgrid including a wind turbine facility. A Markov chain model is employed to predict the wind power production and the optimal management of the energy storage element is formulated as a stochastic optimal control problem. An approximate dynamic programming approach resting on system abstraction is then proposed for control policy design. Some numerical examples show the effectiveness of the approach

MPC-based Management of Energy Resources in Smart Microgrids

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A randomised approach for NARX model identification based on a multivariate Bernoulli distribution

The identification of polynomial NARX models is typically performed by incremental model building techniques. These methods assess the importance of each regressor based on the evaluation of partial individual models, which may ultimately lead to erroneous model selections. A more robust assessment of the significance of a specific model term can be obtained by considering ensembles of models, as done by the RaMSS algorithm. In that context, the identification task is formulated in a probabilistic fashion and a Bernoulli distribution is employed to represent the probability that a regressor belongs to the target model. Then, samples of the model distribution are collected to gather reliable information to update it, until convergence to a specific model. The basic RaMSS algorithm employs multiple independent univariate Bernoulli distributions associated to the different candidate model terms, thus overlooking the correlations between different terms, which are typically important in the selection process. Here, a multivariate Bernoulli distribution is employed, in which the sampling of a given term is conditioned by the sampling of the others. The added complexity inherent in considering the regressor correlation properties is more than compensated by the achievable improvements in terms of accuracy of the model selection process

Energy Management of a Building Cooling System With Thermal Storage: An Approximate Dynamic Programming Solution

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