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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]

Autonomous navigation of mobile robots requires the continuous estimation of the vehicle position and orientation in a given reference frame (localization problem). When moving in unknown environments, the more challenging problem of building a map, while at the same time localizing within it, must be faced (simultaneous localization and map building, SLAM). By adopting a landmark-based description of the environment, both tasks can be cast as a state estimation problem for an uncertain dynamic system, based on noisy measurements. Under the assumption that both process disturbances and measurement errors are unknown but bounded, the estimation process can be carried out in terms of feasible sets. This chapter reviews efficient set membership localization and mapping techniques for different kinds of available measurements and different classes of approximating regions. An extension of the SLAM algorithm to the case of a team of cooperating robots is also presented. The proposed techniques are validated through extensive numerical simulations and experimental tests performed in a laboratory setup. [ABSTRACT FROM AUTHOR]

In this paper an implicit fault tolerant control scheme is specialized for an n-degrees-of-freedom fully actuated mechanical manipulator subject to sinusoidal torque disturbances acting on joints. We show in detail how a standard tracking controller can be "augmented" with an internal model unit designed to compensate the unknown spurious torque harmonics. In this way the controller is proved to be global implicitly fault tolerant to all the faults belonging to the model embedded in the regulator. Moreover, by simply testing the state of the internal model we will show how to perform fault detection and isolation. [ABSTRACT FROM AUTHOR]

The problem of controlling the interaction of a flexible link arm with a compliant environment is considered. The arm's tip is required to keep contact with a surface by applying a constant force and maintaining a prescribed position or following a desired path on the surface. Using singular perturbation theory, the system is decomposed into a slow subsystem associated with rigid motion and a fast subsystem associated with link flexible dynamics. A parallel force and position control developed for rigid robots is adopted for the slow subsystem, while a fast control action is employed to stabilize the link deflections. Simulation results are presented for a two-link planar arm under gravity in contact with an elastically compliant surface. [ABSTRACT FROM AUTHOR]

Several tasks of the most recent robotics applications require high control performances, which cannot be achieved by the classical joint independent control schemes widely used in the industrial field. The necessity to directly take into account parasitic phenomena affecting motion control, such as friction, often leads to the development of model-based control schemes. The actual effectiveness of such schemes is strongly dependent on the accuracy with which the robot dynamics and the friction effects are compensated by the identified models, and it must be assessed by suitable experimental tests. In this chapter, different solutions are investigated for the development of a model-based control scheme, including joint friction compensation, for a two-links, planar, direct-drive manipulator. In particular, the use of available nominal robot inertial parameters for the identification of a nonlinear friction function, based on the well-known LuGre model, is compared with a complete dynamic calibration of the manipulator, including the estimation of both the robot dynamics and the parameters of a polynomial friction function. The identification results are discussed in the two cases, and inverse dynamics control schemes, based on the identified models, are experimentally applied to the manipulator for the execution of different trajectories, which allow the evaluation of the control performances in different conditions. [ABSTRACT FROM AUTHOR]

The plant model appropriate for designing the control strongly depends on the requirements. Simple models are enough to compute nondemanding controls. The parameters of well-defined structural models of flexible robot manipulators are difficult to determine because their effect is only visible if the manipulator is under strong actions or with high-frequency excitation. Thus, in this chapter, an iterative approach is suggested. This approach is applied to a one-degree-of-freedom flexible robot manipulator, first using some well-known models and then controlling a lab prototype. This approach can be used with a variety of control design and/or identification techniques. [ABSTRACT FROM AUTHOR]

Finite-time stability (FTS) is a concept that was first introduced in the 1950s. The FTS concept differs from classical stability in two important ways. First, it deals with systems whose operation is limited to a fixed finite interval of time. Second, FTS requires prescribed bounds on system variables. For systems that are known to operate only over a finite interval of time and whenever, from practical considerations, the systems' variables must lie within specific bounds, FTS is the only meaningful definition of stability. This overview will first present a short history of the development of the concept of FTS. Then it will present some important analysis and design results for linear, nonlinear, and stochastic systems. Finally some applications of the theory will be presented. [ABSTRACT FROM AUTHOR]

This chapter illustrates various finite-time analysis and design problems for linear systems. Most of this work deals with continuous-time systems. First, some conditions for finite-time stability and boundedness are presented; then we turn to the design problem. In this context, we consider both the state feedback and the output feedback synthesis. For both cases, we end up with some sufficient conditions involving linear matrix inequalities (both algebraic and differential). The last section of the chapter extends the previous results to discrete-time systems. [ABSTRACT FROM AUTHOR]

This chapter gives an overview of simple controllers for SISO systems based on the generalization of the linear pole assignment method for constrained systems with dynamics ranging from relay minimum time systems to linear pole assignment systems. The design is based on splitting the nth-order system dynamics into n first-order ones, which can be constrained without any problems with stability and overshooting. It requires a successive decrease of the distance of the representative point from the next invariant set with lower dimension. Since the distance of the representative point to such invariant set can be defined in many ways, the construction of the constrained controllers is not unique. The controllers derived from the second-order integrator are simple, appropriate also for extremely fast application, and easy to tune by a procedure that generalizes the well-known methods by Ziegler and Nichols, or ?Aström and Hägglund, respectively. [ABSTRACT FROM AUTHOR]

In this chapter we discuss a constructive method for anti-windup design for general linear saturated plants with exponentially unstable modes. The constructive solution is independent of the controller dynamics, so the size of the (necessarily bounded) operating region in the exponentially unstable directions of the plant state space is large. We discuss the features of the anti-windup algorithm and illustrate its potential on several examples. [ABSTRACT FROM AUTHOR]

The chapter presents an expository survey of ongoing research by the author on a system theory for oscillators. Oscillators are regarded as open systems that can be interconnected to robustly stabilize ensemble phenomena characterized by a certain level of synchrony. The first part of the chapter provides examples of design (stabilization) problems in which synchrony plays an important role. The second part of the chapter shows that dissipativity theory provides an interconnection theory for oscillators. [ABSTRACT FROM AUTHOR]

This chapter provides numerical examples to illustrate the recent results by the authors relating asymptotic stability and dissipativity of a linear differential or difference inclusion to these properties for the corresponding dual linear differential or difference inclusion. It is shown how this duality theory broadens the applicability of numerical algorithms for stability and performance analysis that have appeared previously in the literature. [ABSTRACT FROM AUTHOR]

The problem of piecewise affine identification is addressed by studying four recently proposed techniques for the identification of PWARX/HHARX models, namely a Bayesian procedure, a bounded-error procedure, a clustering-based procedure and a mixed-integer programming procedure. The four techniques are compared on suitably defined one-dimensional examples, which help to highlight the features of the different approaches with respect to classification, noise and tuning parameters. The procedures are also tested on the experimental identification of the electronic component placement process in pick-and-place machines. [ABSTRACT FROM AUTHOR]

Algebraic methods are presented for solving nonlinear least-squares type problems that arise in the parameter identification of nonlinear systems. The tracking of the induction motor rotor time constant is solved in detail. Also, an approach to estimating state variables using algebraic relationships (in contrast to dynamic observers) is discussed in the context of speed estimation for induction motors. [ABSTRACT FROM AUTHOR]

Robustness had become a central issue in system and control theory, focusing the researchers' attention from the study of a single model to the investigation of a set of models, described by a set of perturbations of a "nominal" model. This set, often indicated as the uncertainty model set, has to be suitably constructed to describe the inherent uncertainty about the system under consideration and to be used for analysis and design purposes. H∞ identification methods deliver uncertainty model sets in a form suitable to be used by well-established robust design techniques, based on H∞ or μ optimization methods. The literature on H∞ identification is now very extensive. Some of the most relevant contributions related to assumption validation, evaluation of bounds on unmodeled dynamics, convergence analysis, and optimality properties of different algorithms are here surveyed from a deterministic point of view. [ABSTRACT FROM AUTHOR]

This chapter gives an overview of the "circle-criterion" design of nonlinear observers, initiated and further developed by the author in a series of papers. It summarizes these results in a concise and unified manner and illustrates them with physically motivated design examples from fuel cell power systems, ship control, and active magnetic bearing systems. [ABSTRACT FROM AUTHOR]

The problems of constructing observers in the presence of unknown inputs and of detecting and recognizing inputs of a special kind are considered for linear time delay systems with commensurable delays. Both problems are studied from an algebraic and geometric point of view, making use of models with coefficients in a ring, of invariant subspaces of the space module and of suitable canonical decomposition into subsystems. Feasible and constructive procedures for the analysis and solution of the problems are presented. [ABSTRACT FROM AUTHOR]

Recurrent and non-recurrent congestions on freeways may be substantially reduced if today's "spontaneous" infrastructure utilisation is replaced by an orderly, controllable operation via comprehensive application of ramp metering and freeway-to-freeway control, combined with powerful optimal control techniques. This chapter first explains why ramp metering can lead to a dramatic amelioration of traffic conditions on freeways. Subsequently, a large-scale example demonstrates the high potential of advanced ramp metering approaches. It is demonstrated that the proposed control scheme is efficient, fair and real-time feasible. [ABSTRACT FROM AUTHOR]

This chapter provides a review of the research on design of control systems for automated highway applications that has been conducted at the California PATH Program of the University of California, Berkeley. The primary focus is on the research areas that Pravin Varaiya led directly, particularly while serving as PATH Director from 1994 to 1997. He and the researchers working directly with him made significant contributions to the definition of control strategies for coordinating maneuvers of neighboring vehicles and for managing the flows of vehicles along network links, while also developing the hybrid system modeling and simulation tools needed to evaluate the effectiveness of these strategies. [ABSTRACT FROM AUTHOR]

We discuss how decentralized network resource allocation problems fit within the context of mechanism design (realization theory and implementation theory), and how mechanism design can provide useful insight into the nature of decentralized network resource allocation problems. The discussion is guided by the unicast problem with routing and Quality of Service (QoS) requirements, and the multi-rate multicast service provisioning problem in networks. For these problems we present decentralized resource allocation mechanisms that achieve the solution of the corresponding centralized resource allocation problem and are informationally efficient. We show how the aforementioned mechanisms can be embedded into the general framework of realization theory, and indicate how realization theory can be used to establish the mechanisms' informational efficiency in certain instances. We also present a conjecture related to implementation in Nash equilibria of the optimal centralized solution of the unicast service provisioning problem. [ABSTRACT FROM AUTHOR]

Motivated by resource allocation problems in communication networks as well as power systems, we consider the design of market mechanisms for such settings which are robust to gaming behavior by market participants. Recent results in this work are reviewed, including: (1) efficiency loss guarantees for a data rate allocation mechanism first proposed by Kelly, both when link capacities are fixed and when they are elastic; (2) characterization of mechanisms that minimize the efficiency loss, within a certain class of "simple" mechanisms; (3) extensions to general networks; and (4) mechanism design for supply function bidding in electric power systems. [ABSTRACT FROM AUTHOR]

Many distributed multiple access (MAC) protocols use an exponential backoff mechanism. In that mechanism, a node picks a random backoff time uniformly in an intervals that doubles in size after a collision. When used in an Ad-Hoc network, this backoff mechanism is unfair towards nodes in the middle of the network. Indeed, such nodes tend to experience more collisions than nodes with fewer neighbors; consequently, they often choose larger delays than those other nodes. We propose a different backoff mechanism that achieves a fairer allocation of the available bandwidth by decreasing the backoff delay upon collision or failure to send a packet. That is, a node becomes more aggressive after each failure. Accordingly, we call the mechanism the Impatient Backoff Algorithm (IBA). The nodes maintain the stability of the algorithm by resetting, in a distributed way, the average backoff delays when they become too small. We perform a Markov analysis of the system to prove stability and fairness in simple topologies. We also use simulations to study the performance of IBA in random Ad-Hoc networks and compare with an exponential backoff scheme. Results show that IBA achieves comparable mean throughput, while delivering significantly better fairness. [ABSTRACT FROM AUTHOR]

We consider a set of networked controllers where multiple control systems coexist with their control loops closed over a shared wireless network that induces random delays and packet losses. This system requires a joint design of the wireless network and the controllers, where the design objective is to optimize the control performance. This performance is a complex function of the controller design and the network parameters, such as throughput, packet delay and packet loss probability. Random delays and packet losses in the feedback loop impose new challenges on the optimal controller design. We first investigate controller design with randomly dropped packets. We prove the separation of estimation and control under certain assumptions of the network and show that the Kalman filter can be modified to generate the optimal state estimate when part or all of the observation is lost. The wireless network needs to provide a sufficient throughput for each of the sensor measurements in order to guarantee the stability of the Kalman filter. We then focus on the wireless network design for this controller. The goal of optimizing the control performance imposes implicit tradeoffs on the wireless network design as opposed to the explicit tradeoffs typical in wireless data and voice applications. Specifically, the tradeoffs between network throughput, time delay and packet loss probability are intricate and implicit in the control performance index, which complicates network optimization. We show that this optimization requires a cross-layer design framework, and propose such a framework for a broad class of networked control applications. We then illustrate this framework by a cross-layer optimization of the link layer, MAC layer, and sample period selection in a double inverted pendulum system. [ABSTRACT FROM AUTHOR]

Varaiya and Walrand found an elegant insight regarding the use of feedback in a causal coding context: While generally useful, feedback becomes useless when the channel is sufficiently symmetric. The goal of this note is to extend this insight to scenarios inspired by sensor networks. Specifically, two such scenarios are considered: a situation with a single sensor but where the source is observed through a noisy channel, and a genuine network scenario where all source and noise distributions are assumed to be Gaussian. For the latter, it is shown that feedback is useless if source and channel bandwidth are equal, but that, if the latter is larger, feedback is strictly useful. Varaiya and Walrand establish their results via dynamic programming arguments. It is unclear to date whether such arguments can be extended to the distributed scenario considered in the present chapter. Instead, our results are established via information-theoretic bounds. [ABSTRACT FROM AUTHOR]

I take this opportunity with great pleasure to thank Prof. Pravin Varaiya for his guidance over the past fifteen years not only in my academic research but also at Teja Technologies, Inc. In this chapter I have outlined some of the emerging themes in system design particularly for network equipment. Factors such as the proprietary nature of many of the developments, the rapid pace of change in the field, and also the desire to keep out material that may appear promotional of commercial interests have required this chapter to be kept at a fairly general level. My doctoral thesis work with Prof. Varaiya dealt with the modeling, analysis and control of hybrid systems—i.e., systems which combined continuous and discrete state dynamics tikya[1]. Subsequently, as a member of a research team at California PATH Laboratory of the UC-Berkeley, directed by Prof. Varaiya, I contributed to the development of a hybrid system specification and simulation system called SHIFT tikya[2]. After forming Teja Technologies, Inc., where Prof. Varaiya was on the Board of Directors for several years, I continued the core work on a commercial basis with emphasis on high-performance execution applied to fast path network applications. [ABSTRACT FROM AUTHOR]

This chapter gives a survey of the theory of square-integrable martingales and the construction of basic sets of orthogonal martingales in terms of which all other martingales may be expressed as stochastic integrals. Specific cases such as Brownian motion, Lévy processes and stochastic jump processes are discussed, as are some applications to mathematical finance. [ABSTRACT FROM AUTHOR]

This chapter deals with the problem of measurement feedback control under setmembership uncertainty for systems with original linear structure and hard bounds on the uncertain items. It indicates feedback control strategies which ensure guaranteed deviation from a given terminal set despite the uncertain disturbances and incomplete feedback. Routes for numerical treatment of the solutions are suggested on the basis of ellipsoidal techniques. [ABSTRACT FROM AUTHOR]

This chapter presents applications of polytopic approximation methods for reachable set computation using dynamic optimization. The problem of computing exact reachable sets can be formulated in terms of a Hamilton-Jacobi partial differential equation (PDE). Numerical solutions which provide convergent approximations of this PDE have computational complexity which is exponential in the continuous variable dimension. Using dynamic optimization and polytopic approximation, computationally efficient algorithms for overapproximative reachability analysis have been developed for linear dynamical systems tikya[1]. In this chapter, we extend these to feedback linearizable nonlinear systems, linear dynamic games, and norm-bounded nonlinear systems. Three illustrative examples are presented. [ABSTRACT FROM AUTHOR]