arXiv subjects

Riccardo Scattolini

Publications and source records attributed to Riccardo Scattolini.

36 records · Page 2Linked to original sources

arXiv2021

Stability of discrete-time feed-forward neural networks in NARX configuration

The idea of using Feed-Forward Neural Networks (FFNNs) as regression functions for Nonlinear AutoRegressive eXogenous (NARX) models, leading to models herein named Neural NARXs (NNARXs), has been quite popular in the early days of machine learning applied to nonlinear system identification, owing to their simple structure and ease of application to control design. Nonetheless, few theoretical results are available concerning the stability properties of these models. In this paper we address this problem, providing a sufficient condition under which NNARX models are guaranteed to enjoy the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) properties. This condition, which is an inequality on the weights of the underlying FFNN, can be enforced during the training procedure to ensure the stability of the model. The proposed model, along with this stability condition, are tested on the pH neutralization process benchmark, showing satisfactory results.

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arXiv2021

Robust multi-rate predictive control using multi-step prediction models learned from data

This note extends a recently proposed algorithm for model identification and robust MPC of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different steps ahead are estimated with Set Membership methods. It is here shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach.

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arXiv2020

Hierarchical routing control in discrete manufacturing plants via model predictive path allocation and greedy path following

The problem of real-time control and optimization of components' routing in discrete manufacturing plants, where distinct items must undergo a sequence of jobs, is considered. This problem features a large number of discrete control inputs and the presence of temporal-logic constraints. A new approach is proposed, adopting a shift of perspective with respect to previous contributions, from a Eulerian system model that tracks the state of plant nodes, to a Lagrangian model that tracks the state of each part being processed. The approach features a hierarchical structure. At a higher level, a predictive receding horizon strategy allocates a path across the plant to each part in order to minimize a chosen cost criterion. At a lower level, a path following logic computes the control inputs in order to follow the assigned path, while satisfying all constraints. The approach is tested here in simulations, reporting extremely good performance as measured by closed-loop cost function values and computational efficiency, also with very large prediction horizon values. These features pave the way to a number of subsequent research steps, which will culminate with the experimental testing on a pilot plant.

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arXiv2020

Model predictive control design for dynamical systems learned by Long Short-Term Memory Networks

This paper analyzes the stability-related properties of Long Short-Term Memory (LSTM) networks and investigates their use as the model of the plant in the design of Model Predictive Controllers (MPC). First, sufficient conditions guaranteeing the Input-to-State stability (ISS) and Incremental Input-to-State stability (dISS) of LSTM are derived. These properties are then exploited to design an observer with guaranteed convergence of the state estimate to the true one. Such observer is then embedded in a MPC scheme solving the tracking problem. The resulting closed-loop scheme is proved to be asymptotically stable. The training algorithm and control scheme are tested numerically on the simulator of a pH reactor, and the reported results confirm the effectiveness of the proposed approach.

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arXiv2020

Hierarchical Control in Islanded DC Microgrids with Flexible Structures

Hierarchical architectures stacking primary, secondary, and tertiary layers are widely employed for the operation and control of islanded DC microgrids (DCmGs), composed of Distribution Generation Units (DGUs), loads, and power lines. However, a comprehensive analysis of all the layers put together is often missing. In this work, we remedy this limitation by setting out a top-to-bottom hierarchical control architecture. Decentralized voltage controllers attached to DGUs form our primary layer. Governed by an MPC--based Energy Management System (EMS), our tertiary layer generates optimal power references and decision variables for DGUs. In particular, decision variables can turn DGUs ON/OFF and select their operation modes. An intermediary secondary layer translates EMS power references into appropriate voltage signals required by the primary layer. More specifically, to provide a voltage solution, the secondary layer solves an optimization problem embedding power-flow equations shown to be always solvable. Since load voltages are not directly enforced, their uniqueness is necessary for DGUs to produce reference powers handed down by the EMS. To this aim, we deduce a novel uniqueness condition based only on local load parameters. Our control framework, besides being applicable for generic DCmG topologies, can accommodate topological changes caused by EMS commands. Its functioning is validated via simulations on a modified 16-bus DC system.

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arXiv2020

LSTM Neural Networks: Input to State Stability and Probabilistic Safety Verification

The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a time-invariant nonlinear dynamical system. A sufficient condition guaranteeing the Input-to-State (ISS) stability property of this class of systems is provided. The ISS property entails the boundedness of the output reachable set of the LSTM. In light of this result, a novel approach for the safety verification of the network, based on the Scenario Approach, is devised. The proposed method is eventually tested on a pH neutralization process.

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arXiv2020

Supervised MPC control of large-scale electricity networks via clustering methods

This paper describes a control approach for large-scale electricity networks, with the goal of efficiently coordinating distributed generators to balance unexpected load variations with respect to nominal forecasts. To mitigate the difficulties due to the size of the problem, the proposed methodology is divided in two steps. First, the network is partitioned into clusters, composed of several dispatchable and non dispatchable generators, storage systems, and loads. A clustering algorithm is designed with the aim of obtaining clusters with the following characteristics: (i) they must be compact, keeping the distance between generators and loads as small as possible; (ii) they must be able to internally balance load variations to the maximum possible extent. Once the network clustering has been completed, a two layer control system is designed. At the lower layer, a local Model Predictive Controller is associated to each cluster for managing the available generation and storage elements to compensate local load variations. If the local sources are not sufficient to balance the cluster's load variations, a power request is sent to the supervisory layer, which optimally distributes additional resources available from the other clusters of the network. To enhance the scalability of the approach, the supervisor is implemented relying on a fully distributed optimization algorithm. The IEEE 118-bus system is used to test the proposed design procedure in a non trivial scenario.

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arXiv2019

Scenario optimization for optimal training of Echo State Networks

Echo State Networks (ESNs) are widely-used Recurrent Neural Networks. They are dynamical systems including, in state-space form, a nonlinear state equation and a linear output transformation. The common procedure to train ESNs is to randomly select the parameters of the state equation, and then to estimate those of the output equation via a standard least squares problem. Such a procedure is repeated for different instances of the random parameters characterizing the state equation, until satisfactory results are achieved. However, this trial-and-error procedure is not systematic and does not provide any guarantee about the optimality of the identification results. To solve this problem, we propose to complement the identification procedure of ESNs by applying results in scenario optimization. The resulting training procedure is theoretically sound and allows one to link precisely the number of identification instances to a guaranteed optimality bound on relevant performance indexes, such as the Root Mean Square error and the FIT index of the estimated model evaluated over a validation data-set. The proposed procedure is finally applied to the simulated model of a pH neutralization process: the obtained results confirm the validity of the approach.

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arXiv2019

Tustin neural networks: a class of recurrent nets for adaptive MPC of mechanical systems

The use of recurrent neural networks to represent the dynamics of unstable systems is difficult due to the need to properly initialize their internal states, which in most of the cases do not have any physical meaning, consequent to the non-smoothness of the optimization problem. For this reason, in this paper focus is placed on mechanical systems characterized by a number of degrees of freedom, each one represented by two states, namely position and velocity. For these systems, a new recurrent neural network is proposed: Tustin-Net. Inspired by second-order dynamics, the network hidden states can be straightforwardly estimated, as their differential relationships with the measured states are hardcoded in the forward pass. The proposed structure is used to model a double inverted pendulum and for model-based Reinforcement Learning, where an adaptive Model Predictive Controller scheme using the Unscented Kalman Filter is proposed to deal with parameter changes in the system.

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arXiv2019

Design of aggregators for the day-ahead management of microgrids providing active and reactive power services

The increasing diffusion of distributed energy generation systems requires the development of new control paradigms for the coordination of micro-generators, storage systems, and loads aimed at maintaining the efficiency and the safe operability of the electricity network. MicroGrids (MGs) are an interesting way to locally manage groups of generation devices, but they cannot singularly provide a significant contribution to sustain the main electricity grid in terms of ancillary services, such as the availability of a minimum amount of power reserve for the frequency regulation. For these reasons, in this paper we propose a framework for the aggregation and coordination of interconnected MGs to provide ancillary services to the main utility. The proposed framework is structured in three main phases. In the first one, a distributed optimization algorithm computes the day-ahead profile of the active power production of the MGs based on the available forecasts of the renewable sources production and the loads absorption. In this phase, scalability of the optimization problem and confidentiality requirements are guaranteed. In the second phase, reactive power flows are scheduled and it is ensured that the active power trends planned in the first phase do not compromise the voltage/current limitations. A final third phase is used to schedule the active and reactive power profiles of the generation units of each MG to make them consistent with the requirements and results of the previous two phases. The developed method is used for control of the IEEE 13-bus system network and the results achieved are thoroughly discussed in terms of performance and scalability properties.

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arXiv2019

Echo State Networks: analysis, training and predictive control

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition guaranteeing incremetal global asymptotic stability is devised. Then, a modified training algorithm allowing for dimensionality reduction of ESNs is presented. Eventually, a model predictive controller is designed to solve the tracking problem, relying on ESNs as the model of the system. Numerical results concerning the predictive control of a nonlinear process for pH neutralization confirm the effectiveness of the proposed algorithms for the identification, dimensionality reduction, and the control design for ESNs.

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arXiv2018

Learning-based predictive control for linear systems: a unitary approach

A comprehensive approach addressing identification and control for learningbased Model Predictive Control (MPC) for linear systems is presented. The design technique yields a data-driven MPC law, based on a dataset collected from the working plant. The method is indirect, i.e. it relies on a model learning phase and a model-based control design one, devised in an integrated manner. In the model learning phase, a twofold outcome is achieved: first, different optimal p-steps ahead prediction models are obtained, to be used in the MPC cost function; secondly, a perturbed state-space model is derived, to be used for robust constraint satisfaction. Resorting to Set Membership techniques, a characterization of the bounded model uncertainties is obtained, which is a key feature for a successful application of the robust control algorithm. In the control design phase, a robust MPC law is proposed, able to track piece-wise constant reference signals, with guaranteed recursive feasibility and convergence properties. The controller embeds multistep predictors in the cost function, it ensures robust constraints satisfaction thanks to the learnt uncertainty model, and it can deal with possibly unfeasible reference values. The proposed approach is finally tested in a numerical example.

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arXiv2018

On multi-step prediction models for receding horizon control

The derivation of multi-step-ahead prediction models from sampled data of a linear system is considered. A dedicated prediction model is built for each future time step of interest. In addition to a nominal model, the set of all models consistent with data and prior information is derived as well, making the approach suitable for robust control design within a Model Predictive Control framework. The resulting parameter identification problem is solved through a sequence of convex programs, overcoming the non-convexity arising when identifying 1-step prediction models with an output-error criterion. At the same time, the derived models guarantee a worst-case error which is always smaller than the one obtained by iterating models identified with a 1-step prediction error criterion.

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arXiv2017

A hierarchical multirate MPC scheme for interconnected systems - $\textit{extended version}$

This paper presents a hierarchical control scheme for interconnected linear systems. At the higher layer of the control structure a robust centralized Model Predictive Control (MPC) algorithm based on a reduced order dynamic model of the overall system optimizes a long-term performance index penalizing the deviation of the state and the control input from their nominal values. At the lower layer local MPC regulators, possibly working at different rates, are designed for the full order models of the subsystems to refine the control action computed at the higher layer. A simulation experiment is presented to describe the implementation aspects and the potentialities of the proposed approach.

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arXiv2017

A hierarchical MPC scheme for interconnected systems

This paper describes a hierarchical control scheme for interconnected systems. The higher layer of the control structure is designed with robust Model Predictive Control (MPC) based on a reduced order dynamic model of the overall system and is aimed at optimizing long-term performance, while at the lower layer local regulators acting at a higher frequency are designed for the full order models of the subsystems to refine the control action. A simulation experiment concerning the control of the temperature inside a building is reported to witness the potentialities of the proposed approach.

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arXiv2014

An MPC approach to output-feedback control of stochastic linear discrete-time systems

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 chance constraints on the input and state variables are reformulated by means of the Chebyshev - Cantelli inequality. The recursive feasibility of the proposed algorithm is guaranteed and the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions. The implementation issues are thoroughly addressed showing that, with a proper choice of the design parameters, its computational load can be made similar to the one of a standard stabilizing MPC algorithm. Two examples are discussed in details, with the aim of providing an insight on the performance achievable by the proposed control scheme.

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arXiv2013

Model predictive control of voltage profiles in MV networks with distributed generation

The Model Predictive Control (MPC) approach is used in this paper to control the voltage profiles in MV networks with distributed generation. The proposed algorithm lies at the intermediate level of a three-layer hierarchical structure. At the upper level a static Optimal Power Flow (OPF) manager computes the required voltage profiles to be transmitted to the MPC level, while at the lower level local Automatic Voltage Regulators (AVR), one for each Distributed Generator (DG), track the reactive power reference values computed by MPC. The control algorithm is based on an impulse response model of the system, easily obtained by means of a detailed simulator of the network, and allows to cope with constraints on the voltage profiles and/or on the reactive power flows along the network. If these constraints cannot be satisfied by acting on the available DGs, the algorithm acts on the On-Load Tap Changing (OLTC) transformer. A radial rural network with two feeders, eight DGs, and thirty-one loads is used as case study. The model of the network is implemented in DIgSILENT PowerFactory, while the control algorithm runs in Matlab. A number of simulation results is reported to witness the main characteristics and limitations of the proposed approach.

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arXiv2013

Plug-and-play distributed state estimation for linear systems

This paper proposes a state estimator for large-scale linear systems described by the interaction of state-coupled subsystems affected by bounded disturbances. We equip each subsystem with a Local State Estimator (LSE) for the reconstruction of the subsystem states using pieces of information from parent subsystems only. Moreover we provide conditions guaranteeing that the estimation errors are confined into prescribed polyhedral sets and converge to zero in absence of disturbances. Quite remarkably, the design of an LSE is recast into an optimization problem that requires data from the corresponding subsystem and its parents only. This allows one to synthesize LSEs in a Plug-and-Play (PnP) fashion, i.e. when a subsystem gets added, the update of the whole estimator requires at most the design of an LSE for the subsystem and its parents. Theoretical results are backed up by numerical experiments on a mechanical system.

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