Marcello Farina

Distributed predictive control: A non-cooperative algorithm with neighbor-to-neighbor communication for linear systems

This paper presents a novel Distributed Predictive Control (DPC) algorithm for linear discrete-time systems. This method enjoys the following properties: (i) state and input constraints can be considered; (ii) under mild assumptions, convergence of the closed loop control system is proved; (iii) it is not necessary for each subsystem to know the dynamical models of the other subsystems; (iv) the transmission of information is limited, in that each subsystem only needs the reference trajectories of the state variables of its neighbors. A simulation example is reported to illustrate the main characteristics and performance of the algorithm.

Distributed Moving Horizon Estimation for Linear Constrained Systems

This paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation. Under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process. Simulation examples are provided in order to show the main features of the proposed method.

Plug-and-Play Decentralized Model Predictive Control for Linear Systems

In this technical note, we consider a linear system structured into physically coupled subsystems and propose a decentralized control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. The design procedure is totally decentralized, since the synthesis of a local controller uses only information on a subsystem and its neighbors, i.e. subsystems coupled to it. We show how to automatize the design of local controllers so that it can be carried out in parallel by smart actuators equipped with computational resources and capable to exchange information with neighboring subsystems. In particular, local controllers exploit tube-based Model Predictive Control (MPC) in order to guarantee robustness with respect to physical coupling among subsystems. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.

Brief paper: Moving-horizon partition-based state estimation of large-scale systems

This paper presents three novel moving-horizon estimation (MHE) methods for discrete-time partitioned linear systems, i.e., systems decomposed into coupled subsystems with non-overlapping states. The MHE approach is used due to its capability of exploiting physical constraints on states and noise in the estimation process. In the proposed algorithms, each subsystem solves reduced-order MHE problems to estimate its own state and different estimators have different computational complexity, accuracy and transmission requirements among subsystems. In all cases, proper tuning of the design parameters, i.e., the penalties on the states at the beginning of the estimation horizon, guarantees convergence of the estimation error to zero. Numerical simulations demonstrate the viability of the approach.

Forecasting peak air pollution levels using NARX models

Air pollution has a negative impact on human health. For this reason, it is important to correctly forecast over-threshold events to give timely warnings to the population. Nonlinear models of the nonlinear autoregressive with exogenous variable (NARX) class have been extensively used to forecast air pollution time series, mainly using artificial neural networks (NNs) to model the nonlinearities. This work discusses the possible advantages of using polynomial NARX instead, in combination with suitable model structure selection methods. Furthermore, a suitably weighted mean square error (MSE) (one-step-ahead prediction) cost function is used in the identification/learning process to enhance the model performance in peak estimation, which is the final purpose of this application. The proposed approach is applied to ground-level ozone concentration time series. An extended simulation analysis is provided to compare the two classes of models on a selected case study (Milan metropolitan area) and to investigate the effect of different weighting functions in the identification performance index. Results show that polynomial NARX are able to correctly reconstruct ozone concentrations, with performances similar to NN-based NARX models, but providing additional information, as, e.g., the best set of regressors to describe the studied phenomena. The simulation analysis also demonstrates the potential benefits of using the weighted cost function, especially in increasing the reliability in peak estimation.

Distributed moving horizon estimation for nonlinear constrained systems

In this paper we consider a nonlinear constrained system observed by a sensor network and propose a distributed state estimation scheme based on Moving Horizon Estimation (MHE). In order to embrace the case where the whole system state cannot be reconstructed from data available to individual sensors, we resort to the notion of MHE-detectability for nonlinear systems, and add to the MHE problems solved by each sensor a consensus term for propagating information about estimates through the network. Under some suitable assumptions we prove convergence to zero and stability of the state estimation error provided by any sensor.

Plug-and-play model predictive control based on robust control invariant sets ☆

In this paper we consider a linear system represented by a coupling graph between subsystems and propose a distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Most importantly, as in Riverso et al., 2012 our design procedure enables plug-and-play (PnP) operations, meaning that (i) the addition or removal of subsystems triggers the design of local controllers associated to successors to the subsystem only and (ii) the synthesis of a local controller for a subsystem requires information only from predecessors of the subsystem and it can be performed using only local computational resources. Our method hinges on local tube MPC controllers based on robust control invariant sets and it advances the PnP design procedure proposed in Riverso et al., 2012 in several directions. Quite notably, using recent results in the computation of robust control invariant sets, we show how critical steps in the design of a local controller can be solved through linear programming. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.

A Robust MPC Algorithm for Offset-Free Tracking of Constant Reference Signals

A robust model predictive control algorithm solving the tracking and the infeasible reference problems for constrained systems subject to bounded disturbances is presented in this technical note. The proposed solution relies on three main concepts: 1) the reformulation of the system in the so-called velocity form to obtain offset-free tracking when constant disturbances are present, 2) the use of a tube-based approach to cope with non-constant but bounded disturbances, 3) the use of reference outputs as arguments of the optimization problem to cope with infeasible references. Convergence results are derived by suitably defining the auxiliary control law and the terminal set used in the problem formulation.

Results Towards Identifiability Properties of Biochemical Reaction Networks

In this paper we consider the question of parameter identifiability for biochemical reaction networks, as typically encountered in systems biology. Specifically, we are interested in deriving conditions on the biochemical reaction network and on the measured outputs that guarantee identifiability of the parameters. Taking the specific system structure of biochemical reaction networks into account, we derive sufficient conditions for local parameter identifiability based on a suitable system expansion which does not any more directly depend on the parameters. Rather, as shown, the problem of identifiability can be recast as the question of observability of the (parameter free) expanded system. The conditions derived are exemplified considering a simple example

A probabilistic approach to Model Predictive Control

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.