## Publications

285 results found

Rezaee H, Parisini T, Polycarpou M, 2021, Resiliency in dynamic leader-follower multiagent systems, *Automatica*, Vol: 125, Pages: 1-10, ISSN: 0005-1098

Resilient control of multiagent systems (MASs) in the presence of dynamic leaders is studied in this paper. We consider a network of agents consisting of a leader, a set of healthy agents, and a set of attacked malicious agents. The objective is developing a control strategy for the healthy agents to follow the trajectory of the leader, while they are in interaction with the unknown malicious agents. The main contribution of this paper is resilient leader-follower control of MASs when a dynamic leader determines a continuous time-varying trajectory for the MAS. By defining the concept of r-robust leader-follower graphs, we propose and analyze sufficient conditions on interaction among the agents such that the mentioned objective is achieved. Numerical examples verify the accuracy of the proposed control scheme.

Bin M, Cheung PYK, Crisostomi E,
et al., 2021, Post-lockdown abatement of COVID-19 by fast periodic switching, *PLOS COMPUTATIONAL BIOLOGY*, Vol: 17, ISSN: 1553-734X

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Bin M, Parisini T, 2020, A distributed methodology for approximate uniform global minimum sharing

The paper deals with the distributed minimum sharing problem, in which anetwork of decision-makers - exchanging information through a communicationnetwork - computes the minimum of some local quantities of interest in adistributed and decentralized way. The problem is equivalently cast into acost-coupled distributed optimization problem, and an adjustable approximate(or sub-optimal) solution is presented which enjoys several properties ofcrucial importance in applications. In particular, the proposed solution isscalable in that the dimension of the state space does not grow with the sizeor topology of the communication network. Moreover, a global and uniform (bothin the initial time and in the initial condition) asymptotic stability resultis provided, as well as an attractiveness property towards a steady state whichcan be made arbitrarily close to the sought minimum. Exact asymptoticconvergence is also recovered at the price, however, of loosing uniformity ofthe convergence with respect to the initial time.

Barboni A, Parisini T, 2020, Towards Distributed Accommodation of Covert Attacks in Interconnected Systems, *Proceedings of the IEEE Conference on Decision and Control*, Vol: 2020-December, Pages: 5731-5736, ISSN: 0743-1546

The problem of mitigating maliciously injected signals in interconnected systems is dealt with in this paper. We consider the class of covert attacks, as they are stealthy and cannot be detected by conventional means in centralized settings. Distributed architectures can be leveraged for revealing these stealthy attacks by exploiting communication and local model knowledge. We show how such detection schemes can be improved to estimate the action of an attacker and we propose an accommodation scheme in order to mitigate or neutralize abnormal behavior of a system under attack.

Rezaee H, Parisini T, Polycarpou M, 2020, Almost Sure Resilient Consensus Under Stochastic Interaction: Links Failure and Noisy Channels, *IEEE Transactions on Automatic Control*, ISSN: 0018-9286

The resilient consensus problem over a classof discrete-time linear multiagent systems is addressed.Because of external cyber-attacks, some agents are assumed to be malicious and not following a desired cooperative behavior. Thus, the objective consists in designing acontrol strategy for the healthy agents to reach consensusupon their state vectors, while due to interaction among theagents, the malicious agents try to prevent them to achieveconsensus. Although this problem has been investigatedby some researchers, under the existing approaches in theliterature, achieving consensus is only guaranteed whenthe information exchange among the agents is deterministic. Based on this motivation, the main contribution ofthe paper is on almost sure resilient consensus control ofa network of healthy agents in the presence of stochastic links failure and communication noises. We design adiscrete-time protocol for the set of the healthy agents, andwe show that under some probabilistic conditions on interaction among the agents, achieving almost sure consensusamong the healthy agents can be guaranteed. The resultsalso are verified by numerical examples

Ding H, Gao RX, Isaksson AJ,
et al., 2020, State of AI-Based Monitoring in Smart Manufacturing and Introduction to Focused Section, *IEEE/ASME Transactions on Mechatronics*, Vol: 25, Pages: 2143-2154, ISSN: 1083-4435

Higgins M, Teng F, Parisini T, 2020, Stealthy MTD against unsupervised learning-based blind FDI Attacks in power systems, *IEEE Transactions on Information Forensics and Security*, Vol: 16, Pages: 1275-1287, ISSN: 1556-6013

This paper examines how moving target defenses (MTD) implemented in power systems can be countered by unsupervised learning-based false data injection (FDI) attack and how MTD can be combined with physical watermarking to enhance the system resilience. A novel intelligent attack, which incorporates dimensionality reduction and density-based spatial clustering, is developed and shown to be effective in maintaining stealth in the presence of traditional MTD strategies. In resisting this new type of attack, a novel implementation of MTD combining with physical watermarking is proposed by adding Gaussian watermark into physical plant parameters to drive detection of traditional and intelligent FDI attacks, while remaining hidden to the attackers and limiting the impact on system operation and stability.

Pin G, Fenu G, Casagrande V,
et al., 2020, Robust stabilization of a class of nonlinear systems controlled over communication networks, *IEEE Transactions on Automatic Control*, Vol: 66, Pages: 3036-3051, ISSN: 0018-9286

The paper deals with the stabilization of nonlin-ear systems in which the loop is closed over a lossy non-acknowledged communication network. Given a Regional Input-to-State (ISS) stabilizing state-feedback control law, designedwithout accounting for the network-induced delays, we proposea non-acknowledged communication policy that allows to deploythe above controller over the network without any modification,while preserving the Regional ISS property. The time-varyingdelays and packet dropouts occurring on both the up-link andthe down-link are compensated through a model-based predictionscheme and a packet-management policy based on time-stamping.The consistency of the prediction, which is a major issue inthe context of nonlinear systems with an embedded networkedcontroller, is guaranteed through the exploitation of a novel move-blocking strategy for computing the command sequence to beforwarded to the actuators.

Gallo A, Turan M, Boem F,
et al., 2020, A distributed cyber-attack detection scheme with application to DC microgrids, *IEEE Transactions on Automatic Control*, Vol: 65, Pages: 3800-3815, ISSN: 0018-9286

DC microgrids often present a hierarchical control architecture, requiring integration of communication layers. This leads to the possibility of malicious attackers disrupting the overall system. Motivated by this application, in this paper we present a distributed monitoring scheme to provide attack-detection capabilities for linear Large-Scale Systems. The proposed architecture relies on a Luenberger observer together with a bank of Unknown-Intput Observers (UIOs) at each subsystem, providing attack detection capabilities. We describe the architecture and analyze conditions under which attacks are guaranteed to be detected, and, conversely, when they are stealthy . Our analysis shows that some classes of attacks cannot be detected using either module independently; rather, by exploiting both modules simultaneously, we are able to improve the detection properties of the diagnostic tool as a whole. Theoretical results are backed up by simulations, where our method is applied to a realistic model of a low-voltage DC microgrid under attack.

Barboni A, Rezaee H, Boem F,
et al., 2020, Detection of covert cyber-attacks in interconnected systems: a distributed model-based approach, *IEEE Transactions on Automatic Control*, Vol: 65, Pages: 3728-3741, ISSN: 0018-9286

Distributed detection of covert attacks for linear large-scale interconnected systems is addressed in this article. Existing results consider the problem in centralized settings. This article focuses on large-scale systems subject to bounded process and measurement disturbances, where a single subsystem is under a covert attack. A detection methodology is proposed, where each subsystem can detect the presence of covert attacks in neighboring subsystems in a distributed manner. The detection strategy is based on the design of two model-based observers for each subsystem using only local information. An extensive detectability analysis is provided and simulation results on a power network benchmark are given, showing the effectiveness of the proposed methodology for the detection of covert cyber-attacks.

Yilmaz S, Dudkina E, Bin M, et al., 2020, Kemeny-based testing for COVID-19

Testing, tracking and tracing abilities have been identified as pivotal inhelping countries to safely reopen activities after the first wave of theCOVID-19 virus. Contact tracing apps give the unprecedented possibility toreconstruct graphs of daily contacts, so the question is who should be tested?As human contact networks are known to exhibit community structure, in thispaper we show that the Kemeny constant of a graph can be used to identify andanalyze bridges between communities in a graph. Our "Kemeny indicator" is thechange in Kemeny constant when a node or edge is removed from the graph. Weshow that testing individuals who are associated with large values of theKemeny indicator can help in efficiently intercepting new virus outbreaks, whenthey are still in their early stage. Extensive simulations provide promisingresults in early identification and in blocking possible "super-spreaders"links that transmit disease between different communities.

Li P, Boem F, Pin G,
et al., 2020, Kernel-based simultaneous parameter-state estimation for continuous-time systems, *IEEE Transactions on Automatic Control*, Vol: 65, Pages: 3053-3059, ISSN: 0018-9286

In this note, the problem of jointly estimating thestate and the parameters of continuous-time systems is addressed.Making use of suitably designed Volterra integral operators,the proposed estimator does not need the availability of time-derivatives of the measurable signals and the dependence ontheunknown initial conditions is removed. As a result, the estimatesconverge to the true values in arbitrarily short time in noise-freescenario. In the presence of bounded measurement and processdisturbances, the estimation error is shown to be bounded. Thenumerical implementation aspects are dealt with and extensivesimulation results are provides showing the effectivenessof theestimator.

Cervellera C, Maccio D, Parisini T, 2020, Learning robustly stabilizing explicit model predictive controllers: A non-regular sampling approach, *IEEE Control Systems Letters*, Vol: 4, Pages: 737-742, ISSN: 2475-1456

Off-line supervised learning from data of robustly-stabilizing nonlinear explicit model predictive controllers (EMPC) is dealt with in this letter. The learning procedure relies on the construction of a suitably large set of specifically chosen sampling points of the state space in which the values of the optimal EMPC control function have to be computed. When bounding the magnitude of approximation errors is important for stability or performance specifications, regular gridding techniques are not feasible due to the curse of dimensionality arising from the structural exponential growth of the number of points with the state dimension. In this note, we consider non-regular sampling techniques – namely, i.i.d. sampling with uniform distribution, low-discrepancy sequences and lattice point sets – that offer a good covering of the state space without suffering from an unfeasible growth of the number of points, while preserving at the same time the method guarantees in terms of robustness and stability. Some theoretical properties of the proposed sampling schemes are briefly discussed, and their successful application is showcased in a practically-relevant optimal heating problem involving a 21-dimensional state space that rules out the use of regular gridding techniques.

Barrere M, Hankin C, Nicolau N,
et al., 2020, Measuring cyber-physical security in industrial control systems via minimum-effort attack strategies, *Journal of Information Security and Applications*, Vol: 52, Pages: 1-17, ISSN: 2214-2126

In recent years, Industrial Control Systems (ICS) have become increasingly exposed to a wide range of cyber-physical attacks, having massive destructive consequences. Security metrics are therefore essential to assess and improve their security posture. In this paper, we present a novel ICS security metric based on AND/OR graphs and hypergraphs which is able to efficiently identify the set of critical ICS components and security measures that should be compromised, with minimum cost (effort) for an attacker, in order to disrupt the operation of vital ICS assets. Our tool, META4ICS (pronounced as metaphorics), leverages state-of-the-art methods from the field of logical satisfiability optimisation and MAX-SAT techniques in order to achieve efficient computation times. In addition, we present a case study where we have used our system to analyse the security posture of a realistic Water Transport Network (WTN).

Wang Y, Pin G, Serrani A, et al., 2020, Removing SPR-Like Conditions in Adaptive Feedforward Control of Uncertain Systems, 55th IEEE Conference on Decision and Control (CDC), Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, Pages: 2309-2324, ISSN: 0018-9286

Wang Y, Pin G, Serrani A,
et al., 2020, Removing SPR-like conditions in adaptive feedforward control of uncertain systems, *IEEE Transactions on Automatic Control*, Vol: 65, Pages: 2309-2324, ISSN: 0018-9286

The paper considers the problem of designing Adaptive Feedforward Control (AFC) systems for uncertain SISO linear systems perturbed by multi-sinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation be known for AFC to be applicable, which is referred to in this paper as an SPR-like condition. Notable features of the solution are that persistence of excitation is not required and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented.

Boem F, Gallo A, Raimondo DM,
et al., 2020, Distributed fault-tolerant control of large-scale systems: An active fault diagnosis approach, *IEEE Transactions on Control of Network Systems*, Vol: 7, Pages: 288-301, ISSN: 2325-5870

The paper proposes a methodology to effectively address the increasingly important problem of distributed faulttolerant control for large-scale interconnected systems. The approach dealt with combines, in a holistic way, a distributed fault detection and isolation algorithm with a specific tube-based model predictive control scheme. A distributed fault-tolerant control strategy is illustrated to guarantee overall stability and constraint satisfaction even after the occurrence of a fault. In particular, each subsystem is controlled and monitored by a local unit. The fault diagnosis component consists of a passive set-based fault detection algorithm and an active fault isolation one, yielding fault-isolability subject to local input and state constraints. The distributed active fault isolation module - thanks to a modification of the local inputs - allows to isolate the fault that has occurred avoiding the usual drawback of controllers that possibly hide the effect of the faults. The Active Fault Isolation method is used as a decision support tool for the fault tolerant control strategy after fault detection. The distributed design of the tube-based model predictive control allows the possible disconnection of faulty subsystems or the reconfiguration of local controllers after fault isolation. Simulation results on a well-known power network benchmark show the effectiveness of the proposed methodology.

Khalili M, Zhang X, Cao Y,
et al., 2020, Distributed fault-tolerant control of multi-agent systems: An adaptive learning approach, *IEEE Transactions on Neural Networks and Learning Systems*, Vol: 31, Pages: 420-432, ISSN: 2162-2388

This paper focuses on developing a distributed leader-following fault tolerant tracking control scheme for a class of high-order nonlinear uncertain multi-agent systems. Neural network based adaptive learning algorithms are developed to learn unknown fault functions, guaranteeing the system stability and cooperative tracking even in the presence of multiple simultaneous process and actuator faults in the distributed agents. The time-varying leader’s command is only communicated to a small portion of follower agents through directed links, and each follower agent exchanges local measurement information only with its neighbors through a bidirectional but asymmetric topology. Adaptive fault-tolerant algorithms are developed for two cases, i.e., with full-state measurement and with only limited output measurement, respectively. Under certain assumptions, the closed-loop stability and asymptotic leader-follower tracking properties are rigorously established.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, The basic infinite-dimensional or functional optimization problem, Communications and Control Engineering, Pages: 1-38

In infinite-dimensional or functional optimization problems, one has to minimize (or maximize) a functional with respect to admissible solutions belonging to infinite-dimensional spaces of functions, often dependent on a large number of variables. As we consider optimization problems characterized by very general conditions, optimal solutions might not be found analytically and classical numerical methods might fail. In these cases, one must use suitable approximation methods. This chapter describes an approximation method that uses families of nonlinear approximators – including commonly used shallow and deep neural networks as special cases – to reduce infinite-dimensional problems to finite-dimensional nonlinear programming ones. It is named “Extended Ritz Method” (ERIM). This term originates from the classical Ritz method, which uses linear combinations of functions as an approximation tool. It does not seem that the Ritz method has met with important successes as regards problems whose admissible solutions depend on large number of variables. This might be ascribed to the fact that this method can be subject to one of the forms of the so-called “curse of dimensionality.” However, theoretical and numerical results show that the ERIM might mitigate this drawback. Examples of infinite-dimensional optimization problems are presented that can be approximated by nonlinear programming ones.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Optimal control problems over an infinite Horizon, Communications and Control Engineering, Pages: 471-511

Optimal control problems over an infinite number of decision stages are considered with emphasis on the deterministic scenario. Both the open-loop and the closed-loop formulations are given and conditions for the existence of a stationary optimal control law are provided. Unless strong assumptions are made on the dynamic system and on the random variables (if present), the design of the optimal infinite-horizon controllers is an almost impossible task. Then, the well-known “receding-horizon” (RH) approximation is considered and the optimal control problem is restated accordingly. In the second part of the chapter, we consider the fundamental issue of closed-loop stability that arises owing to the infinite number of decision stages. More specifically, we address the stability properties of the closed-loop deterministic system under the action of approximate RH control laws obtained by the “extended Ritz method” and implemented through fixed-structure parametrized functions containing vectors of “free” parameters. Conditions are established on the maximum allowable approximation errors so as to ensure the boundedness of the state trajectories.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Stochastic optimal control with imperfect state information over a finite Horizon, Communications and Control Engineering, Pages: 383-426

Discrete-time stochastic optimal control problems are considered. These problems are stated over a finite number of decision stages. The state vector is assumed to be observed through a noisy measurement channel. Because of the very general assumptions under which the problems are stated, obtaining analytically optimal solutions is practically impossible. Note that the controller has to retain the vector of all the measures and of all the controls in memory, up to the most recent decision stage. Such measures and controls constitute the “information vector” that the control function depends on. The increasing dimension of the information vector makes it practically impossible to use dynamic programming. Then, we resort to the “extended Ritz method” (ERIM). The ERIM consists in substituting the admissible functions with fixed-structure parametrized functions containing vectors of “free” parameters. Of course, if the number of decision stages is large, the application of the ERIM is also impossible. Therefore, an approximate approach is followed by truncating the information vector and retaining in the memory only a suitable “limited-memory information vector.”

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Deterministic optimal control over a finite Horizon, Communications and Control Engineering, Pages: 255-298

This chapter addresses discrete-time deterministic problems, where optimal controls have to be generated at a finite number of decision stages. No random variables influence either the dynamic system or the cost function. Then, there is no necessity of estimating the state vector. Such optimization problems are stated for their intrinsic practical importance and to describe the basic concepts of dynamic programming. As the problems are formulated under very general assumptions, their optimal solutions cannot be found in an analytical form. Therefore, we resort to an approximation consisting of the discretization of the state space into suitable grids at each decision stage. The discretization by regular grids is the simplest approach (and the one most widely used until some time ago). However, unless a small dimension of the state space is considered, this approach leads to an exponential growth of the number of samples, and thus to the curse of dimensionality. Therefore, the discretization by deterministic sequences of samples is addressed, which spread the samples in the most uniform way. Specifically, low-discrepancy sequences are considered, like quasi-Monte Carlo sequences. We also point out that the optimization problem can even be viewed as a nonlinear programming problem solvable by gradient-based descent techniques.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, From functional optimization to nonlinear programming by the extended ritz method, Communications and Control Engineering, Pages: 39-88

This chapter describes the approximate solution of infinite-dimensional optimization problems by the “Extended Ritz Method” (ERIM). The ERIM consists in substituting the admissible functions with fixed-structure parametrized (FSP) functions containing vectors of “free” parameters. The larger the dimensions, the more accurate the approximations of the optimal solutions of the original functional optimization problems. This requires solving easier nonlinear programming problems. In the area of function approximation, we review the definition of approximating sequences of sets, which enjoy the property of density in the sets of functions one wants to approximate. Then, we provide the definition of polynomially complex approximating sequences of sets, which are able to approximate functions provided with suitable regularity properties by using, for a desired arbitrary accuracy, a number of “free” parameters increasing at most polynomially when the number of function arguments grows. In the less studied area of approximate solution of infinite-dimensional optimization problems, the optimizing sequences and the polynomially complex optimizing sequences of FSP functions are defined. Results are presented that allow to conclude that, if appropriate hypotheses occur, polynomially complex approximating sequences of sets give rise to polynomially complex optimizing sequences of FSP functions, possibly mitigating the curse of dimensionality.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Team optimal control problems, Communications and Control Engineering, Pages: 427-469

We consider discrete-time stochastic optimal control problems over a finite number of decision stages in which several controllers share different information and aim at minimizing a common cost functional. This organization can be described within the framework of “team theory.” Unlike the classical optimal control problems, linear-quadratic-Gaussian hypotheses are sufficient neither to obtain an optimal solution in closed-loop form nor to understand whether an optimal solution exists. In order to obtain an optimal solution in closed-loop form, additional suitable assumptions must be introduced on the “information structure” of the team. The “information structure” describes the way in which each controller’s information vector is influenced by the stochastic environment and by the decisions of the other controllers. Dynamic programming cannot be applied unless the information structure takes particular forms. On the contrary, the “extended Ritz method” (ERIM) can be always applied. The ERIM consists in substituting the admissible functions with fixed-structure parametrized functions containing vectors of “free” parameters. The ERIM is tested in two case studies. The former is the well-known Witsenhausen counterexample. The latter is an optimal routing problem in a store-and-forward packet-switching network.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Some families of FSP functions and their properties, Communications and Control Engineering, Pages: 89-150

We report properties of fixed-structure parametrized (FSP) functions that give insights into the effectiveness of the “Extended Ritz Method” (ERIM) as a methodology for the approximate solution of infinite-dimensional optimization problems. First, we present the structure of some widespread FSP functions, including linear combinations of fixed-basis functions, one-hidden-layer (OHL) and multiple-hidden-layer (MHL) networks, and kernel smoothing models. Second, focusing on the case of OHL neural networks based on ridge and radial constructions, we report their density properties under different metrics. Third, we present rates of function approximation via ridge OHL neural networks, by reporting a fundamental theorem by Maurey, Jones, and Barron, together with its extensions, based on a norm tailored to approximation by computational units from a given set of functions. We also discuss approximation properties valid for MHL networks. Fourth, we compare the classical Ritz method and the ERIM from the point of view of the curse of dimensionality, proving advantages of the latter for a specific class of problems, where the functional to be optimized is quadratic. Finally, we provide rates of approximate optimization by the ERIM, based on the concepts of modulus of continuity and modulus of convexity of the functional to be optimized.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Design of mathematical models by learning from data and FSP functions, Communications and Control Engineering, Pages: 151-206

First, well-known concepts from Statistical Learning Theory are reviewed. In reference to the problem of modelling an unknown input/output (I/O) relationship by fixed-structure parametrized functions, the concepts of expected risk, empirical risk, and generalization error are described. The last error is then split into approximation and estimation errors. Four quantities of interest are emphasized: the accuracy, the number of arguments of the I/O relationship, the model complexity, and the number of samples generated for the estimation. The possibility of generating such samples by deterministic algorithms like quasi-Monte Carlo methods, orthogonal arrays, Latin hypercubes, etc. gives rise to the so-called Deterministic Learning Theory. This possibility is an intriguing alternative to the random generation of input data, typically obtained by using Monte Carlo techniques, since it enables one to reduce the number of samples (under the same accuracy) and to obtain upper bounds on the errors in deterministic terms rather than in probabilistic ones. Deterministic learning relies on some basic quantities such as variation and discrepancy. Special families of deterministic sequences called “low-discrepancy sequences” are useful in the computation of integrals and in dynamic programming, to mitigate the danger of incurring the curse of dimensionality deriving from the use of regular grids.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Numerical methods for integration and search for minima, Communications and Control Engineering, Pages: 207-253

Two topics are addressed. The first refers to the numerical computation of integrals and expected values of functions that may depend on a large number of random variables. Of course, integration includes the computation of the expected values of functions dependent on random variables. However, the latter shows peculiar nontrivial aspects that the former does not have. In case of a large number of random variables, the use of regular grids implies the risk of incurring the curse of dimensionality. Then, suitable sampling methods are taken into account to reduce such risk. In particular, Monte Carlo and quasi-Monte Carlo sequences are addressed. The second topic refers to the solution of the nonlinear programming problems obtained from the approximation of infinite-dimensional optimization problems by the Extended Ritz Method. We mention a few well-known direct techniques and gradient-based descent algorithms. In the case of nonlinear programming problems stated in stochastic frameworks, the stochastic approximation approach deserves attention and thus it is considered in some detail. Within this context, we describe the stochastic gradient algorithm enabling one to avoid the computation of integrals, hence, the computation of expected values of functions dependent on random variables. Convergence properties of that algorithm are reported.

Zoppoli R, Sanguineti M, Gnecco G, et al., 2020, Stochastic optimal control with perfect state information over a finite Horizon, Communications and Control Engineering, Pages: 299-382

Discrete-time stochastic optimal control problems are stated over a finite number of decision stages. The state vector is assumed to be perfectly measurable. Such problems are infinite-dimensional as one has to find control functions of the state. Because of the general assumptions under which the problems are formulated, two approximation techniques are addressed. The first technique consists of an approximation of dynamic programming. The approximation derives from the fact that the state space is discretized. Instead of using regular grids, which lead to an exponential growth of the number of samples (and thus to the curse of dimensionality), low-discrepancy sequences (as quasi-Monte Carlo ones) are considered. The second approximation technique is given by the application of the “Extended Ritz Method” (ERIM). The ERIM consists in substituting the admissible functions with fixed-structure parametrized functions containing vectors of “free” parameters. This requires solving easier nonlinear programming problems. If suitable regularity assumptions are verified, such problems can be solved by stochastic gradient algorithms. The computation of the gradient can be performed by resorting to the classical adjoint equations, which solve deterministic optimal control problems with the addition of one term, dependent on the chosen family of fixed-structure parametrized functions.

Pin G, Chen B, Parisini T, 2019, Robust deadbeat continuous-time observer design based on modulation integrals, *Automatica*, Vol: 107, Pages: 95-102, ISSN: 0005-1098

In this paper, the state estimation problem of linear continuous-time systems is dealt with by a non-asymptotic state observer,which allows the state estimation error to decay within an arbitrarily-small finite time without resorting to high-gaininjection.By processing the measured input and output signals throughmodulation integrals, a number of auxiliary signals not affectedby the initial conditions are obtained, from which the system state can be computed by simple algebra. The problem of internalinstability of modulation integrals is addressed by resorting to a periodic rescaling mechanism that prevents error accumulationand singularities. We show that the combination of modulation integrals with periodic rescaling can be implemented as ajump-linear system. The robustness of the devised method with respect to additive measurement perturbations on the system’sinput/output is characterized by Input-to-State Stability arguments.

Chen B, Li P, Pin G,
et al., 2019, Finite-time estimation of multiple exponentially-damped sinusoidal signals: A kernel-based approach, *Automatica*, Vol: 106, Pages: 1-7, ISSN: 0005-1098

The problem of estimating the parameters of biased and exponentially-damped multi-sinusoidal signals is addressed in this paper by a finite-time identification scheme based on Volterra integral operators. These parameters are the amplitudes, frequencies, initial phase angles, damping factors and the offset. The proposed strategy entails the design of a new kind of kernel function that, compared to existing ones, allows for the identification of the initial conditions of the signal-generator system. The worst-case behavior of the proposed algorithm in the presence of bounded additive disturbances is fully characterized by Input-to-State Stability arguments. Numerical examples including the comparisons with some existing tools are reported to show the effectiveness of the proposed methodology.

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