Search

Various types of faults arise in industrial p rocesses owing to malfunctio n o f internal components of a process as well as to failures of measurement sensors and control actuators attached to the process. Over the last three or four decades, industrial automation has been increasingly fueled by various technological developments including the availability of highly complex electronic equipment and the overwhelming progress in computer technology. This has led not only to the development of complex control systems but also to higher demand of reliable and secure control systems. Thus it has become imperative that any faults that occur be detected and identified automatically without severely disturbing the yield the process generates. This has stimulated over the last two decades an extensive study of fault detection and identification methods. [ABSTRACT FROM AUTHOR]

The fault estimation problems formulated and studied in the previous chapter seek a residual signal that satisfies two important requirements: exact decoupling of the residual signal from the disturbance or noise, and the residual signal is an exact estimate of the fault signal. The first objective makes the residual signal completely insensitive to the disturbance or noise, and the second objective guarantees that the residual signal is equal to the fault signal. The solvability conditions for such a constrained fault signal estimation are strong. In Chapter 14, we also considered an almost version where the residual signal is arbitrarily close to the fault signal and is almost completely independent of the disturbance. This weakens the solvability conditions, but still the solvability conditions are very strong. [ABSTRACT FROM AUTHOR]

The generalized H2 OID, generalized H2 SOID, generalized EID, and the generalized H2 AID filtering problems are considered in depth in Chapter 12. We consider in this chapter the generalized y-level H∞ SOID as well as the generalized H∞ AID filtering problems. Let us recall that the generalization is due to the presence of additional unknown input signals containing linear combinations of sinusoidal signals, each of which has an unknown amplitude and phase but known frequency. [ABSTRACT FROM AUTHOR]

In the previous chapters, we have studied EID, H2 AID, H∞ AID, H2 OID, H2 SOID, as well as y-level H∞ SOID filtering problems. These filtering problems are reconsidered in this chapter and the next with additional unknown input signals containing linear combination of sinusoidal signals, each of which has an unknown amplitude and phase but known frequency. We will use the qualifier "generalized" to refer to each of the above problems when such additional inputs are present. For instance, the H2 OID, H2 SOID, and y-level H∞ SOID filtering problems described above when additional sinusoidal inputs (of unknown amplitude and phase but known frequency) are present are, respectively, referred to as generalized H2 OID, generalized H2 SOID, and generalized y -level H∞ SOID filtering problems. [ABSTRACT FROM AUTHOR]

We have been relaxing the performance requirements progressively and successively in previous chapters. Chapter 7 considers exact-input-decoupled (EID) filtering problems. When this is not possible, Chapters 8 and 9 consider almostinput-decoupled (AID) filtering problems, respectively, for the two cases, when the input is white noise and when no statistical information about the input is known. In Chapter 10, we look at optimally-input-decoupled (OID) filtering problems for the case when the input is white noise. As a natural continuation, this chapter looks at the optimally-input-decoupled (OID) filtering problems for the case when no information about the input is available except that it has a finite RMS value. [ABSTRACT FROM AUTHOR]

Chapter 8 considers almost input-decoupled (AID) filtering problems under white noise input with a known power spectral density (PSD). The objective of Chapter 8 is to check whether it is possible to make the impact of the unknown input on the asymptotic error arbitrarily small. Under white noise input with a known PSD, whenever the performance measure is the RMS norm of the error signal, such an objective translates to an objective of reducing the H2 norm of the transfer function from the unknown input to the error signal. [ABSTRACT FROM AUTHOR]

Chapter 7 considers the exact input-decoupled (EID) filtering problem, whereas Chapters 8 and 9 consider almost input-decoupled (AID) filtering problems. EID filtering seeks perfect performance; i.e., it tries to make the impact of the input on the estimation error signal absolutely zero. AID filtering relaxes this requirement by trying to find conditions under which the impact of the input on the error signal can be made arbitrarily small. In particular, Chapter 8 pertains to AID filtering under white noise input, whereas Chapter 9 pertains to AID filtering without any statistical information on the input. AID filtering under white noise input seeks conditions such that one can render the RMS norm of the error signal as small as desired. On the other hand, AID filtering under no statistical information on the input seeks conditions such that one can render the ratio of RMS norm of the error signal to the RMS norm of the input as small as desired. In this chapter, we relax the requirement even further by seeking the impact of the input on the error signal be as small as possible rather than as small as desired. In particular, we follow here the direction set by AID filtering under white noise input. That is, we assume here that the input to the given system is a white noise of unit intensity and seek to make the RMS norm of the error signal as small as possible. The problems we deal with here are called optimally input-decoupling (OID) filtering problems under white noise input. The corresponding filters are of course termed as OID filters under white noise input. [ABSTRACT FROM AUTHOR]

Chapter 7 considers exact input-decoupled (EID) filtering problems. In that chapter, we seek perfect performance; that is, we try to make the impact of the unknown input on the asymptotic error absolutely zero irrespective of what is the input, whether it is persistent or not. Such a severe performance measure demands that the transfer function or transfer matrix from the input to the estimation error be identically zero. Of course, as discussed in Chapter 7, the EID filtering problem is not always solvable. It is natural then to think of methods of relaxing the performance requirements so that the solvability conditions can possibly be weakened and thus allowing us to deal with a larger class of systems. There are a number of ways by which the performance requirements can be weakened. As we said in the introduction to this book, we plan to relax the performance requirements progressively layer by layer to form a hierarchy of problems. In this chapter, we introduce the first layer of relaxing the performance requirements. We seek here to make the impact of the unknown input on the asymptotic error to be almost zero or equivalently arbitrarily small or as small as desired instead of being identically zero. To be more precise, we try to find a family of filters parameterized by some positive ε such that when applied to the system, the asymptotic error converges to zero as ε ↓ 0. Thus, in this chapter, we deal with what can be termed as almost-input-decoupled (AID) filtering problems, or for short AID filtering problems. The filters that solve the AID filtering problems are termed not surprisingly as AID filters. [ABSTRACT FROM AUTHOR]

Our goal in this chapter is to estimate a desired output of a linear time-invariant continuous- or discrete-time system by using a measured output of the system but not the inputs or the disturbances that affect the system. Obviously, various estimation or filtering problems emerge depending on the properties sought for the estimation error, i.e., the difference between the actual and the estimated values of the desired output. The problem we would like to study in this chapter is an exact estimation problem. By exact estimation, we mean that the error should tend to zero asymptotically as the time progresses to infinity irrespective of the nature of the unknown inputs into the system, including what can be called persistent inputs. Such a requirement of exact estimation dictates that the transfer function or transfer matrix from the unknown inputs to the estimation error be identically zero. In other words, in this chapter, we seek a filter that estimates the desired output in such a way that the error in the estimation of the desired output is completely decoupled from the unknown input(s). For this reason, we call the problem we study here as the exact input-decoupling filtering problem, or for short the EID filtering problem, and the filters that solve such a problem as the exact input-decoupling filters or EID filters. Clearly, the motivation to study the EID filtering problem and the ensuing EID filters arises from various fields of engineering including loop transfer recovery (see, for instance, [71]) and fault detection and isolation (see, for instance, [53]). [ABSTRACT FROM AUTHOR]

The objective of the exact disturbance decoupling (EDD) problem studied in Chapter 5 was to find a controller such that the controlled output was completely decoupled from an exogenous disturbance signal. In many cases, the EDD problem is not solvable and the next case to investigate is the almost disturbance decoupling (ADD) problem whose objective is to find a sequence of controllers such that the controlled output can be arbitrarily well decoupled from the disturbance by choosing an appropriate member of this sequence. To our knowledge, this problem was first introduced by J. L. Willems in [105]. A solution for this problem by state feedback was later obtained by J. C. Willems in [106, 107]. Many researchers have contributed to the understanding of ADD. In [72], the solvability conditions for different versions of the ADD problem can be found for the most general case. [ABSTRACT FROM AUTHOR]

Different types of algebraic equations or inequalities are encountered in many filtering and control problems. In this chapter, we study in detail some such equations or inequalities. In particular, we study what are known as algebraic Riccati equations, linear matrix inequalities, and quadratic matrix inequalities, all of which ensue in connection with both continuous- as well as discrete-time systems. [ABSTRACT FROM AUTHOR]

The exact disturbance decoupling (EDD) problem is to find a controller such that the closed-loop transfer function from an exogenous disturbance signal to a controlled soutput is equal to zero. In classic as well as modern control theory, the problems of EDD as well as almost disturbance decoupling (ADD) occupy central positions. Several important problems can be recast as either EDD or ADD problems, for instance, H2 optimal control, robust control, decentralized control, noninteracting control, model reference, and tracking control. Several different versions of the EDD and ADD problems have been investigated extensively for the last two decades. In fact, it can be said that the development of the geometric approach to system theory started with the first version of a disturbance decoupling problem. Among others, the prominent works in disturbance decoupling include [1,3,32,50,87,95,104, 111]. The material of this chapter is based mainly on the work of Saberi et al. [75]. [ABSTRACT FROM AUTHOR]

In this chapter we bring together the notations and acronyms used in this book and various definitions and facts related to matrices, linear spaces, linear operators, norms of deterministic as well as stochastic signals, and norms of linear time- or shift-invariant systems. [ABSTRACT FROM AUTHOR]

Estimation theory and, in the same breath, filtering theory is vast and rich in the literature and is central to a wide variety of disciplines, including control, communications, and signal processing. Also, it is relevant to such diverse areas as statistics, economics, bioengineering, and operations research. The terms estimation and filtering evoke many and varied responses among engineers and scientists. In its primary level, "estimation" is the process of arriving at a value for a desired and unknown variable from certain observations or measurements of other variables related to the desired one but contaminated with noise. Although one could trace the origins of estimation back to ancient times, Karl Friederich Gauss is generally acknowledged to be the forefather of what is now referred to as estimation theory. In his quest to predict the motions of planets and comets from telescopic measurements, Gauss at the age of 18 formulated the now well-known method of least squares. In modern times and in particular in the second half of the twentieth century, filtering theory has become synonymous with estimation theory mainly in the engineering literature. It might look odd that the term "filter" would apply to an "estimator". In its common use, a "filter" is a physical device that can separate the wanted and unwanted fractions of a mixture. In electronics, a filter is seen as a circuit with a frequency-selective behavior, and thus can attenuate certain undesired components of the input signal and pass to the output certain desired components of the input signal. [ABSTRACT FROM AUTHOR]

We use here the notation of Chapter 3 in Part IV. We assume that $$ (\mathcal{H}\mathcal{P})\infty \left\{ \begin{gathered} ({\text{i}}){\text{ }}A{\text{ generates an analytic semigroup e}}^{tA} {\text{ in }}H \hfill \\ {\text{ of type }}\omega _{\text{0}} {\text{ and }}\lambda _0 {\text{ is a real number in }}\rho {\text{(}}A{\text{)such}} \hfill \\ {\text{ that }}\omega _{\text{0}} < \lambda _0 , \hfill \\ {\text{(ii) }}E \in \mathcal{L}(U;H), \hfill \\ {\text{(iii) }}\forall T {\text{ > 0, }}\exists K_T {\text{ > 0 such that}} \hfill \\ {\text{ }}\int_{\text{0}}^t {{\text{}}E{\text{*}}A{\text{*}}e^{sA{\text{*}}} x^2 ds \leqslant K_T^2 x^2 } ,{\text{ }}\forall x \in D(A*),t \geqslant 0, \hfill \\ {\text{(iv) }}C \in \mathcal{L}(H;Y). \hfill \\ \end{gathered} \right. $$ Clearly, if $$ (\mathcal{H}\mathcal{H})\infty $$ hold, then the hypotheses $$ (\mathcal{H}\mathcal{H}) $$ of Chapter 3 in Part IV are fulfilled with P0 = 0. We want to minimize the cost function: (1.1)$$ J_\infty (u) = \int_0^\infty {\{ Cx(s)^2 + u(s)^2 \} ds,} $$ over all controls u ∈ L2(0,∞;U) subject to the equation constraint (1.2)$$ \begin{array}{*{20}c} {x(t) = e^{tA} x_0 + G(u)(s),} \\ {G(u)(s) = (\lambda _0 - A)\int_0^t {e^{(t - s)A} Eu(s)ds.} } \\ \end{array} $$ Moreover, x0 ∈ H and u ∈ L2(0,∞;U). We recall that by Proposition 3.1 in Chapter 1 in Part II, x ∈ C([0, T];H) for all ∈ L2(0, T;U); more precisely $$ G \in \mathcal{L}(L^2 (0,T;U);C([0,T];H)),{\text{ }}\forall T > 0. $$ [ABSTRACT FROM AUTHOR]

As in Chapter 2 of Part IV we consider a dynamical system governed by the following equation: $$ \left\{ \begin{gathered} x'(t) = Ax(t) + (\lambda _0 - A)Du(t),{\text{ }}t \geqslant 0, \hfill \\ x(0) = x_0 , \hfill \\ \end{gathered} \right. $$ or equivalently (1.1)$$ x(t) = e^{tA} x_0 + (\lambda _0 - A)\int_0^t {Du(s)ds,} $$ where x0 ∈ H and u ∈ L2(0,∞;U). We assume that $$ (\mathcal{H}\mathcal{P})\infty \left\{ \begin{gathered} ({\text{i}}){\text{ }}A{\text{ generates an analytic semigroup e}}^{tA} {\text{of type }}\omega _{\text{0}} \hfill \\ {\text{ and }}\lambda _0 {\text{ is a real number in }}\rho {\text{(}}A{\text{)such that }}\omega _{\text{0}} < \lambda _0 , \hfill \\ {\text{(ii) }}\exists \alpha \in {\text{]0,1[ such that }}D \in \mathcal{L}(U;D([\lambda _0 - A]^\alpha )), \hfill \\ {\text{(iii) }}C \in \mathcal{L}(H;Y), \hfill \\ \end{gathered} \right. $$ Clearly, if hypotheses $$ (\mathcal{H}\mathcal{P})_\infty $$ hold, then the hypotheses $$ (\mathcal{H}\mathcal{P}) $$ of Chapter 2 of Part IV are fulfilled with P0 = 0. If α ≤ 1/2, we will choose once and for all a number β belonging to ]1 − α/2, 1 − α/2[. We want to minimize the cost function: (1.2)$$ J_\infty (u) = \int_0^\infty {\{ Cx(s)^2 + u(s)^2 \} ds} $$ over all controls u ∈ L2(0,∞;U) subject to the differential equation constraint (1.1). We say that the control u ∈ L2(0,∞;U) is admissible if J∞(u) < ∞. The definitions of optimal control, optimal state, and optimal pair are the same as in Chapter 1. When, for any x0 ∈ H, an admissible control exists, we say that (A,AD) is C-stabilizable. [ABSTRACT FROM AUTHOR]

As in Chapter 1 (Part IV) we consider a dynamical system governed by the following state equation: 1.1$$ \left\{ \begin{gathered} x'(t) = Ax(t) + Bu(t),{\text{ }}t \geqslant 0, \hfill \\ x(0) = x_0 \in H, \hfill \\ \end{gathered} \right. $$ and we use the notation introduced in §1 of that chapter. We assume that $$ (\mathcal{H})\infty \left\{ \begin{gathered} (i){\text{ }}A{\text{ generates a }}C_0 {\text{ semigroup }}e^{tA} {\text{ in }}H{\text{,}} \hfill \\ (ii){\text{ }}B \in \mathcal{L}(U;H), \hfill \\ (iii){\text{ }}C \in \mathcal{L}(U;H). \hfill \\ \end{gathered} \right. $$ Clearly, if the assumptions $$ (\mathcal{H})_\infty $$ hold, then the assumptions $$ (\mathcal{H}) $$ of §1 in Chapter 1 (Part IV) are verified with P0 = 0. [ABSTRACT FROM AUTHOR]

As before, we shall denote by H, U, and Y the Hilbert spaces of states, controls, and observations, respectively, and consider a dynamical system, whose state x(·) is the solution of the following equation: $$ \left\{ {\begin{array}{*{20}c} {x'(t) = Ax(t) + Bu(t),t \in [0,T],} \\ {x(0) = x_0 \in H,} \\ \end{array} } \right. $$ where u ∈ L2(0, T;U) and A: D(A) ⊂ H → H generates a strongly continuous group on H. We identify the elements of H′ with those of H so that the linear operator (A*)*: H → D(A*)′ is a linear extension of the linear operator A: D(A) → H. As in the previous chapter, the linear operator B is not supposed to be bounded from U into H, but it belongs to $$ \mathcal{L}(U;D(A*)') $$, or equivalently, B is of the form B = (λ0−A)E, where E ∈ $$ E \in \mathcal{L}(U;H) $$ and λ0 is an element in ρ(A). More precisely, following I. LASIECKA and R. TRIGGIANI [1, 2, 11], we shall assume that $$ (\mathcal{H}\mathcal{H})_1 \left\{ \begin{gathered} ({\text{i}}){\text{ }}A{\text{ generates a strongly continuous group e}}^{tA} {\text{of type }}\omega _{\text{0}} \hfill \\ {\text{ and }}\lambda _0 {\text{ is a real number in }}\rho {\text{(}}A{\text{)such that }}\omega _{\text{0}} < \lambda _0 , \hfill \\ {\text{(ii) }}E \in \mathcal{L}(U;H), \hfill \\ {\text{(iii) }}\exists K {\text{ > 0 such that}}\int_0^T E*A*e^{sA*} x^2 ds \leqslant K^2 x^2 ,\forall x \in D(A*). \hfill \\ \end{gathered} \right. $$ If assumptions $$ (\mathcal{H}\mathcal{H})_1 $$ hold, then we can give a precise meaning to the state equation. We have in fact the following result due to I. LASIECKA and R. TRIGGIANI [1, 2, 11] [ABSTRACT FROM AUTHOR]

As in the previous chapter, we shall denote by H, U, and Y the Hilbert spaces of states, controls, and observations, respectively. We consider a dynamical system, whose state x(t) is subject to the following equation: $$ x'(t) = Ax(t) + Bu(t),{\text{ }}x(0) = x_0 \in H, $$ where u ∈ L2(0, T;U) and A: D(A) ⊂ H → H generates an analytic semigroup in H. However, in the current case, the linear operator B is not supposed to be bounded from U into H. This situation has been discussed at length in Chapters 1 and 2 (Part II). However some key constructions will be repeated here as needed. In that case many possibilities could be considered. However, in practice, it will be natural to consider situations where B maps U into the dual space (D(A*)′ of D(A*). This will be apparent in the following Examples 1.1 and 1.2. Equivalently, B is supposed to be of the form B = (λ0−A)D, where $$ D \in \mathcal{L}{\text{(}}U;H{\text{)}} $$ and λ0 is an element in ρ(A). Under these assumptions we write the state equation as $$ x'(t) = Ax(t) + (\lambda _0 - A)Du(t),{\text{ }}x(0) = x_0 , $$ or in the mild form as 1.1$$ x(t) = e^{tA} x_0 + (\lambda _0 - A)\int_0^t {e^{(t - s)A} } Du(s)ds. $$ Remark that formula (1.1) is meaningful and x ∈ L2(0, T;H); see Chapters 1 to 3 of Part II. This formula will represent the state of our system. [ABSTRACT FROM AUTHOR]

In §2.1 and §2.2 of Chapter 1 of Part I, we have discussed criteria for controllability, and observability for finite dimensional systems and have also shown that when the system is controllable we can transfer the state z0 ∈ H at time t0 to the state z1 ∈ H at time t1 using minimum energy controls. These results were obtained by considering the controllability operator $$ \begin{gathered} L_T :L^2 (0,T;U) \to H \hfill \\ {\text{ }}:u \mapsto \int_0^T {e^{(T - s)A} Bu(s)ds,} \hfill \\ \end{gathered} $$ and its adjoint $$ \begin{gathered} L_T^* :H \to L^2 (0,T;U) \hfill \\ {\text{ }}:y \mapsto B*e^{(T - \cdot )A*} y, \hfill \\ \end{gathered} $$ and studying the relation between the ranges and null spaces of these two operators and by showing that controllability is equivalent to invertibility of LTLT*. As we have remarked (see Remark 2.1, Chapter 1 of Part I) in some sense the same ideas can be used to obtain characterizations of controllability when the spaces U and X are infinite dimensional Hilbert spaces, but at the expense of using much elaborate technical machinery. In this chapter we discuss questions of controllability for parabolic and second-order hyperbolic equations, the plate equation, and Maxwell's equations. [ABSTRACT FROM AUTHOR]

In this chapter we consider the dynamical system governed by the equation $$ \left\{ \begin{gathered} x'(t) = Ax(t) + Bu(t),t \geqslant 0, \hfill \\ x(0) = x_0 \in H, \hfill \\ \end{gathered} \right. $$ where A: D(A) ⊂ H → H, B: U → H are linear operators defined on the Hilbert spaces H (state space) and U (control space), respectively. x is the state and u the control of the system. We shall also consider another Hilbert space Y, the space of observations. The inner product and norm in H, U, and Y will be denoted by (·, ·) and · . Whenever confusion is possible a subscript H, U or Y will be added. [ABSTRACT FROM AUTHOR]

In this chapter our objective is to present a modern approach that provides a unifying framework for a large family of differential and integro-differential systems with delays. This point of view is of paramount importance for the Control Theory, Filtering Theory, and Realization Theory of such systems. The material presented in this chapter is an outgrowth of the lecture notes in French presented at the INRIA School on Representation and Control of Delay Systems in June 1984 by M. C. DPELFOUR [14]. The original material has been restructured, the proofs have been streamlined, and new results have been introduced in §6. [ABSTRACT FROM AUTHOR]

Let S(t) be a strongly continuous semigroup on the Hilbert space H. Let · and (·, ·) be the norm and inner product in H. Denote by A the infinitesimal generator of S(t) and by D(A) its domain. When D(A) is endowed with the graph norm of A(1.1)$$ h_A^2 = h^2 + Ah^2 ,{\text{ }}h \in D(A), $$ it becomes a Hilbert space and (1.2)$$ A:D(A \to H $$ is a continuous linear operator. [ABSTRACT FROM AUTHOR]

A complete treatment of variational differential equations is beyond the scope of this book. We shall mainly quote some results from the books of J. L. LIONS and E. MAGENES [1]. In order to motivate the chosen constructions and models, we give a series of classical examples. We assume that the reader is familiar with Sobolev spaces and their properties. [ABSTRACT FROM AUTHOR]

We shall denote by X a complex Banach space of norm · , and by $$ \mathcal{L}{\text{(}}X{\text{)}} $$ the Banach algebra of all linear continuous mappings T: X → X. The linear space $$ \mathcal{L}{\text{(}}X{\text{)}} $$ is endowed with the usual norm: For any $$ T \in \mathcal{L}{\text{(}}X{\text{)}} $$(1.1)$$ T{\text{ = sup \{ }}Tx{\text{:}}x \in X,x \leqslant 1\} . $$ [ABSTRACT FROM AUTHOR]

In this chapter we broaden the general perspective of the book and consider two-player zero-sum games with linear dynamics and a quadratic utility function over a finite time horizon. They can be viewed as a natural extension of the single player linear quadratic optimal control problem. In particular they illustrate the occurrence of symmetrical solutions to the matrix Riccati differential equation that are not necessarily positive semi-definite. It also connects with the glimpse of H∞-theory given in the previous chapter. [ABSTRACT FROM AUTHOR]

This Part I serves the purpose of an introduction to Parts III to V of the book, which are mainly concerned with the quadratic cost optimal control problem for distributed parameter systems and systems with time delay, both over a finite and an infinite time interval. For problems over a finite time interval, the main tool used is Dynamic Programming, which leads to a Hamilton-Jacobi equation for the value function. For the class of control problems considered, the Hamilton-Jacobi equation can be explicitly solved via the study of an operator Riccati equation. The study of the operator Riccati equation when control is exercised through the boundary in the case of distributed parameter systems or when delays are present in the control in the case of systems with time delay poses additional technical difficulties. The results of Part II are needed to overcome these difficulties. For problems over an infinite time interval, the concepts of controllability and observability (and the weaker concepts of stabilizability and detectability) play an essential role in the development of the theory. [ABSTRACT FROM AUTHOR]

The primary concern of this book1 is the control of linear infinite dimensional systems, that is, systems whose state space is infinite dimensional and its evolution is typically described by a linear partial differential equation, linear functional differential equation or linear integral equation. [ABSTRACT FROM AUTHOR]

Finite-time stability of nonlinear networked control systems is studied in this chapter. Focusing on packet dropping, a deterministic model for networked control systems is realized by incorporating the network dynamics. This links the fields of control of networks and networked control systems. [ABSTRACT FROM AUTHOR]

The vast progress in network technology over the past decade has certainly influenced the area of control systems. Nowadays, it is becoming more common to use networks in systems, especially in those that are large scale and physically distributed or that require extensive cabling. A network-based decentralized control of multirate sampled-data systems approach is introduced and analyzed as an effectiveness solution to the control problem of large-scale continuous-time plant. The main idea is that of information exchange among the various input-output channels of a complex system throughout a local area network. The chapter analyzes the stabilization problem for decentralized control of a large-scale continuous-time plant with different sampling rates in the input-output plant channels. Existence conditions and synthesis procedures are introduced and discussed. The results on the analysis and control of periodic discrete-time systems are used for finding such solutions. The chapter ends with some remarks on the possible extensions to the robust stabilization for the decentralized control of multirate sampled-data systems. [ABSTRACT FROM AUTHOR]

This chapter addresses the control of spatially distributed processes via communication networks with a fixed delay. A distributed architecture is utilized in which multiple local controllers coordinate their efforts through a data network that allows information exchange. We focus our work on linear time-invariant processes disturbed by Gaussian white noise and propose several logics to determine when the local controllers should communicate. Necessary conditions are given under which these logics guarantee boundedness and the trade-off is investigated between the amount of information exchanged and the performance achieved. The theoretical results are validated through Monte Carlo simulations. The resulting closed loop systems evolve according to stochastic differential equations with resets triggered by stochastic counters. This type of stochastic hybrid system is interesting on its own. [ABSTRACT FROM AUTHOR]

In multi-retailer inventory control the possibility of sharing setup costs motivates communication and coordination among the retailers. We solve the problem of finding suboptimal distributed reordering policies that minimize setup, ordering, storage, and shortage costs incurred by the retailers over a finite horizon. Neuro-dynamic programming (NDP) reduces the computational complexity of the solution algorithm from exponential to polynomial on the number of retailers. [ABSTRACT FROM AUTHOR]

An optimal scheduling problem for a two-part type symmetric manufacturing system subject to nonnegligible setup times and characterized by finite buffer capacity is addressed. The solution method relies on i) restricting the possible control policies to those that respect some general necessary conditions of optimality, ii) exploiting such properties to introduce a two-dimensional sampled version of the original system, and iii) mapping such a planar model onto an equivalent scalar one. This modeling approach makes it possible to derive the analytical solution, which exhibits a simple feedback structure. [ABSTRACT FROM AUTHOR]

In maxplus algebra, linear projectors on an image of a morphism B parallel to the kernel of another morphism C can be built under transversality conditions of the two morphisms. The existence of a transverse to an image or a kernel of a morphism is obtained under some regularity conditions. We show that those regularity and transversality conditions can be expressed linearly as soon as the space to which Im(B) and Ker(C) belong is free and its order dual is free. The algebraic structure has these two properties. Projectors are constructed following a previous work. Application to aggregation of linear dynamical systems is discussed. [ABSTRACT FROM AUTHOR]

A neural network model reference adaptive controller for trajectory tracking of nonlinear systems is developed. The proposed control algorithm uses a single layer neural network that bypasses the need for information about the system's dynamic structure and characteristics and provides portability. Numerical simulations are performed using nonlinear dynamic models of marine vehicles. Results are presented for two separate vehicle models, an autonomous surface vehicle and an autonomous underwater vehicle, to demonstrate the controller performance in terms of tuning, robustness, and tracking. [ABSTRACT FROM AUTHOR]

In this chapter, we stabilize the planar vertical takeoff and landing (PVTOL) aircraft using a camera. The camera is used to measure the position and orientation of the PVTOL moving on an inclined plane. We have developed a simple control strategy to stabilize the system in order to facilitate the real experiments. The proposed control law ensures convergence of the state to the origin. [ABSTRACT FROM AUTHOR]

Decentralized control of large-scale systems with uncertain, unmatched interconnections is considered. A stable decentralized adaptive controller is proposed for both linear and nonlinear interconnections. Sufficient conditions under which the overall large-scale system is stable are developed; results from algebraic Riccati equations are used to develop these conditions. The choice of the class of large-scale systems considered is directly motivated by control of web processing machines used in processing of materials. A large experimental web platform is considered for experimental study of the proposed decentralized adaptive controller and its comparison to a decentralized PI controller, which is widely used in the web processing industry. Extensive experiments were conducted; a representative sample of the experiments is presented and discussed. [ABSTRACT FROM AUTHOR]

In this chapter we provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances. More specifically, we consider the full 3n-dimensional model of the n-generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements that, as is well known, hamper the assignment of simple "gradient" energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system, which is obtained via the introduction of state-modulated interconnections. [ABSTRACT FROM AUTHOR]

In this chapter, we present two main contributions: (1) a leader-follower formation controller based on dynamic feedback linearization, and (2) a framework for coordinating teams of mobile robots (i.e., swarms). We derive coordination algorithms that allow robot swarms having independent goals but sharing a common environment to reach their target destinations. Derived from simple potential fields and the hierarchical composition of potential fields, our framework leads to a decentralized approach to coordinate complex group interactions. Because the framework is decentralized, it can potentially scale to teams of tens and hundreds of robots. Simulation results verify the scalability and feasibility of the proposed coordination scheme. [ABSTRACT FROM AUTHOR]

The chapter focuses on concepts and methodologies of coordinating and motion control aimed at maintaining complex spatial behaviour of nonlinear dynamical systems. The main approach is discussed in connection with problems of control of mechanical systems (rigid bodies, robotic manipulators, and mobile robots) and is naturally extended to coordinating the motions of redundant robots, underactuated mechanisms, and walking machines. [ABSTRACT FROM AUTHOR]

In this chapter we present an epipolar-based visual servoing for holonomic mobile robots equipped with panoramic camera. The proposed visual servoing is based on epipolar geometry and exploits the auto-epipolar property, a special configuration for the epipoles that occurs when the desired and the current panoramic views undergo a pure translation. This occurrence is detectable directly in the image plane simply controlling when the so-called biosculating conics all co-intersect at only two points. Our visual servoing control law exploits the auto-epipolar property in order to retrieve the equal orientation between target and current camera. Translation is performed by exploiting the epipoles. Simulation results and Lyapunov-based stability analysis demonstrate the parametric robustness of the proposed method. We also provide a short introduction to the Epipolar Geometry Toolbox (EGT), a free MATLAB software package developed at the University of Siena, with which all simulation results have been obtained. EGT can be downloaded from the EGT web site together with a detailed manual and code examples. [ABSTRACT FROM AUTHOR]