Stefano Miani

• PhD
• University of Udine

The frequency response of an evaporator for commercial refrigeration is investigated to develop a control-oriented model which balances simplicity with accuracy. The dynamics of such devices is highly nonlinear; the response curve was experimentally identified around an operating point by recording the output of the system for several sinusoidal in...

Accurate modelling of robotic links may lead to fractional–order descriptions that complicate controller synthesis. This paper explores whether an LQG controller derived for an integer–order approximation can be applied to the original fractional–order model without appreciably degrading the system performance. Simulations show that this is the cas...

This paper investigates the principal properties of time varying operation modes for tuneable vibration absorbers mounted on distributed structures to reduce vibrations produced by stationary broad frequency band disturbances. The study considers a practical application where an electro-mechanical tuneable vibration absorber, comprising a seismic c...

This paper presents the mathematical conditions and the associated design methodology of an active fault diagnosis technique for continuous-time linear systems. Given a set of faults known a priori, the system is modeled by a finite family of linear time-invariant systems, accounting for one healthy and several faulty configurations. By assuming bo...

This paper addresses set invariance properties for linear time-delay systems. More precisely, the first goal of the article is to review known necessary and/or sufficient conditions for the existence of invariant sets with respect to dynamical systems described by linear discrete time-delay difference equations (dDDEs). Secondly, we address the con...

In this chapter, a control design approach based on linear parameter-varying (LPV) systems, which can be exploited to solve several problems typically encountered in control engineering, is presented. By means of recent techniques based on Youla–Kucera parametrization , it is shown how it is possible not only to design and optimize stabilizing cont...

This paper presents a continuous time solution to the problem of designing a relatively optimal control, precisely, a dynamic control which is optimal with respect to a given initial condition and is stabilizing for any other initial state. This technique provides a drastic reduction of the complexity of the controller and successfully applies to s...

This paper deals with set invariance for time delay systems. The first goal of the paper is to review the known necessary or sufficient conditions for the existence of invariant sets with respect to dynamical systems described by discrete-time delay difference equations (dDDEs). Secondly, we address the construction of invariant sets in the origina...

This paper deals with set invariance for time delay systems. The first goal of the paper is to review the known necessary or su?cient conditions for the existence of invariant sets with respect to dynamical systems described by discrete-time delay difference equations (dDDEs). Secondly, we address the construction of invariant sets in the original...

We face the problem of stabilizing Linear Parameter Varying systems by means of Gain Scheduling Control. This technique consists on designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and we show a design procedure based on the construct...

The paper is concerned with the control of a linear plant with an output delay. As is known, when the plant parameters do not vary in time, the transfer function approach can be used to find a high-performing controller with the Smith-predictor structure. Such an approach in the domain of the Laplace transform is not directly applicable in the time...

In this section a jump back in the history of control is made and we consider problems which had been theoretically faced in the early 70s, and thereafter almost abandoned. The main reason is that the computational effort necessary to practically implement these techniques was not suitable for the computer technology of the time. Today, the situati...

In this chapter some basic results which concern the problem of switching and switched systems are reported. This chapter has been written in a period of intensive research so that, quite differently from the previous sections, many other new results are expected. We will briefly introduce the concept of hybrid systems, which are dynamical systems...

In this chapter, some problems and examples, which are in some way related to the set invariance and Lyapunov functions theory, are presented.

The second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint. This approach is linked to fundamental control problems, such as Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbanc...

This chapter contains the basic definitions and results concerning invariant sets in control and it is the core of the book. Indeed, the invariance concept is at the basis of many control schemes that will be considered later. Such a concept naturally arises when dealing with Lyapunov functions, as we have seen, since any Lyapunov function has posi...

In this chapter the problem of feedback control of uncertain systems is considered, with a special attention to the control of polytopic systems. To properly introduce the results, let us reconsider the stability analysis problem for an uncertain system of the form (Formula presented) where w(t) ∈ W, with W compact, and A(⋅) is continuous. In the c...

Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapunov functions and invariant sets. In this chapter, basic notions of Lyapunov and Lyapunov-like functions will be presented. Before introducing the main concept, a brief presentation of the class of dynamic models will be considered and some preliminary m...

In this section, several applications of set-theoretic methods to the performance analysis of dynamic systems will be presented. Although, in principle, the proposed techniques are valid for general systems, their application is computationally viable in the case of (uncertain) linear systems and thus we restrict the attention to this case.

The purpose of this section is to remind the reader essential notions about convex sets and functions which will be useful in the sequel. For a more detailed exposition on convexity, the reader is referred to specialized literature (Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970; Rockafellar and Wets, Variational analysis...

There are several optimal control problems that can be naturally cast in a set-theoretic framework and for which set-theoretic techniques provide efficient tools. Although by far non-exhaustive, this chapter considers several cases and discusses several solutions.

This chapter is mainly devoted to evidencing difficulties of the set-theoretic approach in dealing with output feedback problems. Therefore the chapter (apparently the shortest of the book) will be essentially conceptual rather than technical. We will be interested in set-theoretic state estimation, and we will not consider, if not in passing, the...

Constraints are encountered practically in every real control problem. It is a tradition (although questionable) that in many textbooks constraints are mentioned but, with several exceptions, the design of control systems which take into account constraints is frequently disregarded. In this chapter is is shown how set-theoretic methods are appropr...

Gain switching is proven to be an effective technique for semiactive damping of vibrating structures. Typically, switching control is based on convex, in particular quadratic, Lyapunov functions, which impose conservative solutions. In this brief we propose a switching technique based on ad hoc nonconvex Lyapunov functions, recently introduced in t...

The paper deals with the motion control of an induction motor. Because the nonlinear state equations describing the dynamics of such a machine can be embedded into a linear model with the rotor speed ω as a varying parameter, advantage is taken of some recent results on the control of linear parameter-varying systems, thus ensuring stability indepe...

The paper is concerned with the design of a linear parameter varying (LPV) regulator for controlling the shaft angle and speed of an induction motor. The design is based on recent results concerning LPV systems and ensures stability independently of how the shaft angular velocity, chosen as the varying parameter, changes in time within a suitable c...

We consider the problem of optimal control of vibrating structures and we analyse the solution provided by collocated semiactive decentralised damping devices. We mainly consider the ℋ∞ criterion and we first study the case of constant dampers, showing that in the case of a single damper the performance is a quasi-convex function of friction so the...

Motivated by applications such as drainage canal control, where the disturbance acting on a system can be predicted on the basis of weather forecast, we propose a model predictive control technique consisting in the online tuning of a Youla–Kučera parameter. Essentially, the optimal control sequence is supplied to the system by properly setting the...

This paper is focused on the vibration effects produced by an array of decentralised velocity feedback loops that are evenly distributed over a rectangular thin plate to minimise its flexural response. The velocity feedback loops are formed by collocated ideal velocity sensor and point force actuator pairs, which are unconditionally stable and prod...

It has been recently shown that, given a plant described by a parametric transfer function, any compensator that internally stabilizes the plant for each constant value of the parameter can be realized in such a way that the closed-loop stability is guaranteed under arbitrary variations of the parameter (LPV stability), provided that certain necess...

The problem of controlling the liquid level in the mold of a continuous casting process is considered. Essentially, the system operates in two different modes: (a) one in which the system is affected only by small-amplitude high-frequency disturbances, and (b) one in which the system is affected by a comparatively large disturbance related to an ab...

In the stabilization problem for systems with control and state constraints a domain of attraction is a set of initial states that can be driven to the origin by a feedback control with-out incurring in constraints violations. If the problem is that of tracking a reference signal, that converges to a constant constraint–admissible value, a tracking...

Plasma current control was experimented in the RFX machine in early nineties with unsatisfactory results due to the frequent onset of unstable regimes leading to increasing voltage demand and saturation of the flat-top power supply. More recently, taking advantage of the new operating conditions disclosed by the active control system of MHD modes a...

The paper deals with the problem of optimal damping of vibrating structures by means of collocated decentralized devices. We consider both H 2 and H ∞ criteria. We prove that in the H 2 case the problem can be conduced to the minimization of a function which is the sum of a convex and a concave component. This structure is of help in the solution o...

We consider a class of nonlinear systems which are absorbable in a linear differential inclusion (LDI), namely whose trajectories are a subset of an LDI. We show than if such an LDI is stabilizable via a linear compensator then a parametrization of all non-linear stabilizing compensators can be derived. The proposed parametrization is simple and th...

The paper deals with the stabilizability of linear plants whose parameters vary with time in a compact set. First, necessary and sufficient conditions for the existence of a linear gain-scheduled stabilizing compensator are given. Next, it is shown that, if these conditions are satisfied, any compensator transfer function depending on the plant par...

We consider a plant the dynamics of which switch among a family of systems. Each of these systems has a single stable equilibrium point. We assume that a constraint region for the state is assigned and we consider the problem of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the a bsence of s...

We compare robust and gain scheduling control for continuous-time LPV systems. In the literature it has been shown that some duality properties as well as a separation principle hold for gain-scheduling control. This means that an LPV plant can be stabilized by a gain scheduling control law if and only if a proper gain scheduling LPV state observer...

The paper is concerned with the problem of regulating the molten metal level in the mold of a continuous casting plant despite the continual perturbations caused by mold shaking and the occasional perturbations due to the sudden uncloggings of the nozzle through which the liquid is poured into the mold. To deal with both kinds of perturbations, two...

The paper deals with the LPV stabilizability problem for linear plants whose parameters vary with time in a compact set. First, necessary and sufficient conditions for the existence of a linear gain-scheduled stabilizing compensator are given. Next, it is shown that, if these conditions are satisfied, any compensator transfer function depending on...

In this paper, discrete-time networked control systems (NCS) with packet dropouts and bounded-and-known delays in the sensor channel in a worst case setting are considered. Such systems are modeled as time-varying switching systems and analyzed by means of recent results in the area of switching control. By means of these results it is shown that:...

This paper is concerned with the control of network data transfer so as to avoid internet traffic congestion. Specifically, a new Active Queue Management (AQM) algorithm supporting the Transmission Control Protocol (TCP) is suggested. To this purpose, the TCP dynamics is described by means of a second-order model with delayed input obtained from th...

A Sliding Mode Control (SMC) strategy for Active Queue Management (AQM) routers supporting Transmission Control Protocol (TCP) data transfer is suggested. It is based on the input-delayed model of TCP behaviour developed in Misra et al. [2000], which is reduced to a delay-free model by means of Artstein's transformation Artstein [1982]. The suggest...

In this paper, we investigate the problem of designing a switching compensator for a plant switching amongst a (finite) family of given configurations ( A _i, B _i, C _i). We assume that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the curre...

The paper deals with the problem of positioning a manipulator in a cluttered environment while avoiding collision with obstacles. Recently a control strategy based on invariant sets has been introduced by some of the authors: it consists of covering the configuration space by means of a connected family of polyhedral regions which can be rendered c...

In this paper, we investigate the problem of designing a switching compensator for a plant switching amongst a (finite) family of given configurations (Ai, Bi, Ci). We assume that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the current configuration i.As a first result,...

Computing polytopic controlled invariant sets which are maximal inside a prescribed region often yields sets which have a really complex representation. Since the associated control has a complexity which drastically increases with that of the region, this turns out to be a major problem in the implementation of the theory of controlled invariant r...

There are several optimal control problems that can be naturally cast in a set-theoretic framework and for which set-theoretic techniques provide efficient tools. Although by far non-exhaustive, this chapter considers several cases and discusses several solutions.

This chapter contains the basic definitions and results concerning invariant sets in control and it is the core of the book. Indeed, the invariance concept is at the basis of many control schemes that will be considered later. Such a concept naturally arises when dealing with Lyapunov functions, as we have seen, since any Lyapunov function has posi...

This chapter is mainly devoted to evidencing difficulties of the set-theoretic approach in dealing with output feedback problems. Therefore the chapter (apparently the shortest of the book) will be essentially conceptual rather than technical. We will be interested in set-theoretic state estimation, and we will not consider, if not in passing, the...

Constraints are encountered practically in every real control problem. It is a tradition (although questionable) that in many textbooks constraints are mentioned but, with several exceptions, the design of control systems which take into account constraints is frequently disregarded. In this chapter is is shown how set-theoretic methods are appropr...

In this chapter the problem of feedback control of uncertain systems is considered, with a special attention to the control of polytopic systems. To properly introduce the results, let us reconsider the stability analysis problem for an uncertain system of the form $$\displaystyle{\dot{x}(t) = A(w(t))x(t)}$$ where \(w(t) \in \mathcal{W}\), with \(\...

In this section, several applications of set-theoretic methods to the performance analysis of dynamic systems will be presented. Although, in principle, the proposed techniques are valid for general systems, their application is computationally viable in the case of (uncertain) linear systems and thus we restrict the attention to this case.

Lyapunov functions are crucial in the present book aims, given the strict relation between Lyapunov functions and invariant sets. In this chapter, basic notions of Lyapunov and Lyapunov-like functions will be presented. Before introducing the main concept, a brief presentation of the class of dynamic models will be considered and some preliminary m...

The purpose of this section is to remind the reader essential notions about convex sets and functions which will be useful in the sequel. For a more detailed exposition on convexity, the reader is referred to specialized literature (Rockafellar, Convex analysis, Princeton University Press, Princeton, 1970; Rockafellar and Wets, Variational analysis...

This paper presents a brief summary of some old ideas concerning the control of uncertain systems based on dynamic programming. We show some recent developments and mention some open problems in the area.

A class of production-distribution problems with unknown-but-bounded uncertain demand is considered. At each time, the demand is unknown but each of its components is assumed to belong to an assigned interval. Furthermore, the system has production and transportation capacity constraints. We face the problem of finding a control strategy that keeps...

In this paper, stabilizability problems for discrete and continuous time linear systems with switching or polytopic uncertainties are dealt with. Both state feedback and full-information controllers are considered, possibly with an integral action. Several cases will be analyzed, depending on the control, the uncertainty and the presence of uncerta...

In the present contribution, the control synthesis for state and input constrained systems for linear systems via set-valued techniques will be presented. The results will be developed for both uncertain and gain scheduled constrained control problems, where the difference between the two is the knowledge of the uncertain parameter entering the sys...

A minimum-time torque control strategy for permanent-magnet AC motor drives is presented. The proposed technique neither requires the solution of a HJB-type equation, which would be practically unfeasible, nor uses Pontryagin's maximum principle. Instead, the solution is obtained by an ad hoc procedure based on the computation of reachability and c...

In this paper, the class of real Lyapunov functions induced by complex polytopes is investigated. Such polytopes are in some sense the extension of real polytopes to the complex space, but have some peculiar aspects which might be relevant for the solution of constrained and/or robust control problems. In detail, analysis and synthesis results (whi...

This self-contained monograph describes basic set-theoretic methods for control and provides a discussion of their links to fundamental problems in Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. New computer technology has cat...

Without Abstract

The paper considers the problem of designing PI controllers for industrial processes approximated by a first-order time-delayed model. The suggested frequency-domain approach is based on a normalized open-loop transfer function and makes use of the loci of constant stability margins and other performance indices in the parameter space. In this way,...

With reference to a class of nonlinear systems exhibiting more unstable equilibrium points, possibly in conjunction with stable ones, the paper presents a state-feedback control strategy capable of simultaneously stabilizing them all. The proposed control law, which does not require explicit knowledge of the equilibria, entails evaluating the Jacob...

The paper considers a novel technique for manipulator motion in a constrained environment due to the presence of obstacles. The basic problem is that of avoiding collisions of the manipulator with the obstacles. The main idea is to cover the free space (i.e. the points of the configurations space in which no collisions are possible) by a connected...

The paper presents an efficient procedure for synthesizing PID controllers so as to maximize Smith’s vector stability margin, i.e., to minimize the H∞ norm of the sensitivity function, while ensuring specified values of the phase margin and gain crossover frequency. In this way, a trade-off between dynamic performance and robustness is achieved. Th...

In this paper, the problem of efficiently computing polyhedral Lyapunov functions for poly topic time-varying linear discrete-time systems, is considered. Two strictly related problems are considered: the robust case, when the designer is unaware of the value of the uncertain parameter entering the system, and the gain scheduled case, when such val...

This note deals with the problem of characterizing a class of second-order three-parameter controllers [including proportional-integral-derivative (PID) and lead/lag compensators] satisfying given H_∞ closed-loop specifications. Design characterizations of similar form as in the recent work on PID control, are derived for a larger class o...

In the steel industry, the steel bars coming out from the last stand of the rolling train must be conveyed to the cooling bed. For this purpose, various types of devices are used in the different steel factories. In this paper, the rotating channel used in a single steel company is described and investigated. The problem of deriving an adequate dyn...

In this paper we consider the problem of controlling a multi-inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer levels and we face the problem of minimizing the wo...

In this paper, the problem of the stabilization of linear parameter varying systems by means of gain scheduling control is considered. This technique consists on designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and we show a design pr...

Solving a continuous-time optimal control problem under state and control constraints is known to be a very hard task. In this note, we propose a suboptimal solution based on the Euler auxiliary system (EAS). We show that we can determine a continuous-time stabilizing control whose cost not only converges to the optimal as the EAS time parameter va...

This note studies min-max systems which are dynamic systems involving three operations (min,max,+). We present a feedback stabilization policy for a class of min-max systems such that the closed-loop systems have a global cycle time which is the same ...

In this paper, we consider different aspects of the problem of controlling a multi-inventory system in the presence of uncertain demand and setups. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be constant in its operating regime and to incur setup whenever a variation of this regime is required. Both...

We consider the problem of stabilizing linear parameter varying (LPV) systems by means of gain scheduling control. This technique amounts to designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and show a design procedure based on the con...

The paper deals with the problem of characterizing a class of second-order three-parameter controllers (including PID and lag/lead) satisfying given H∞ closed-loop specifications. Simple geometric considerations allow us to easily prove and extend to a larger class of compensators some recent results on PID control [A. Datta et al., 2000], [M.T. Ho...

PI controllers for first-order time-delayed processes can be designed on the basis of a normalized model according to open-loop frequency-domain specifications. To this purpose, it is convenient to refer to the charts representing the loci of constant stability margins and cross-over frequencies in the plane of normalized parameters. It is shown ho...

We consider multi-inventory systems in the presence of unknown but bounded demand and uncertain setups. The control input is assumed to be constant in its operating regime and incur setup whenever a variation of this regime is required. Both the setup times and setup configurations are unknown. We provide necessary and sufficient stabilizability co...

The modeling and control of a rotating channel, used in a steel company to convey steel bars coming out from the last stand of the rolling train to the cooling bed, is described. We deal with the problem of synthesizing a controller in order to satisfy the performance needed for the real application. To this aim a lumped parameters model is first d...

In the paper study the possibility of tracking constant reference signals for a linear time-invariant dynamic system in the presence of state constraints. Resort to the theory of invariant sets due to its good capability of handling this kind of problem. Attention is placed on the determination of suitable sets for the attainable steady state value...

We consider multi-inventory systems in the presence of unknown but bounded demand and uncertain setups. The control input is assumed to be constant in its operating regime and incur setup whenever a variation of this regime is required. Both the setup times and setup configurations are unknown. We provide necessary and sufficient stabilizability co...

We consider production-distribution systems with buffer and capacity constraints in the presence of unknown inputs. We face the problem of finding a control that drives the buffer levels to a prescribed value. We consider a continuous-time model and we show that some important properties hold which generally fail in the discrete-time case. In parti...

We face the problem of determining a tracking domain of attraction, say the set of initial states starting from which it is possible to track reference signals in a given class, for discrete-time systems with control and state constraints. We show that the tracking domain of attraction is exactly equal to the domain of attraction, say the set of st...

This papers addresses the problem of globally minimizing the worst-case response to persistent l∞ bounded disturbances in linear systems with bounded control action. The main result of the paper shows that in the state-feedback case the best performance among all stabilizing controllers (possibly discontinuous, nonlinear time varying) is achieved b...

This paper focuses on the derivation of polyhedral Lyapunov functions for robust synthesis fur linear discrete-time dynamic systems. First Ihe background basic theoretical results will be reported and subsequently an algorithm for the determination of such functions will be presented and described. An example will drive the reader through the prese...