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Design and control of Power Supplies (PSs) feeding the magnets of a Synchrotron Light Source have to match severe specifications; high accuracy in the range of ppm in output current tracking is required for the correct operation of the magnets, while a Power Factor (PF) close to the unit is demanded at the input section due to the high power involved. In this paper an advanced control strategy is presented for a particular kind of Quadrupole Magnet Power Supply, where variable output current has to be imposed. The case of the "switch-mode" multilevel power converter for booster quadrupole magnets of the DIAMOND synchrotron radiation facility under construction at the Harwell Chilton Science Campus, Didcot, has been considered. High accuracy in the tracking of the desired output current reference is reached by means of a digital internal model-based controller. A multivariable controller is adopted in order to ensure current balancing between the stages of the multilevel converter. Front-end topology selection, proper dimensioning and control design are exploited to guarantee high power factor and low harmonic distortion of the input currents, and to avoid low-frequency components related to the quadrupole magnets' oscillating currents. For this purpose, confined oscillatory behavior imposed to the voltage of the DC-link capacitors plays a key role. Simulations and experimental validations are reported that confirm the expected results. [ABSTRACT FROM AUTHOR]

This paper gives an overview of a framework for analyzing hybrid dynamical systems. The emphasis is on modeling assumptions that guarantee robustness. These conditions lead to a general invariance principle and to results on the existence of smooth Lyapunov functions (converse theorems) for hybrid systems. In turn, the stability analysis tools motivate novel hybrid control algorithms for nonlinear systems. [ABSTRACT FROM AUTHOR]

This chapter presents a structural analysis approach for the design of fault tolerant estimation algorithms. The general fault tolerance problem setting is first given, and structural analysis is presented in the component based modeling frame. An original condition for structural observability is developed, which is constructive, since it allows to identify those Data Flow Diagrams by which unknown variables can be estimated, both in healthy and in faulty conditions. The link with two basic dependability concepts, namely critical faults and reliability is shown. [ABSTRACT FROM AUTHOR]

The Hamiltonian approach has turned out to be an effective tool for modeling, system analysis and controller design in the lumped parameter case. There exist also several extensions to the distributed parameter case. This contribution presents a class of extended distributed parameter Hamiltonian systems, which preserves some useful properties of the well known class of Port Controlled Hamiltonian systems with Dissipation. In addition, special ports are introduced to take the boundary conditions into account. Finally, an introductory example and the example of a piezoelectric structure, a problem with two physical domains, show, how one can use the presented approach for modeling and design. [ABSTRACT FROM AUTHOR]

In this chapter, we present the scenario approach, an innovative technology for solving convex optimization problems with an infinite number of constraints. This technology relies on random sampling of constraints, and provides a powerful means for solving a variety of design problems in systems and control. Specifically, the virtues of this approach are here illustrated by focusing on optimal control design in presence of input saturation constraints. [ABSTRACT FROM AUTHOR]

The goal of this paper is to propose a unique vision able to frame a number of results recently proposed in literature to tackle problems of output regulation for nonlinear systems. This is achieved by introducing the so-called asymptotic internal model property as the crucial property which, if fulfilled, leads to the design of the regulator for a fairly general class of nonlinear systems satisfying a proper minimum-phase condition. It is shown that recent frameworks based upon the use of nonlinear high-gain and adaptive observer techniques for the regulator design can be cast in this setting. A recently proposed technique for output regulation without immersion is also framed in these terms. [ABSTRACT FROM AUTHOR]

This paper surveys recent work of the author with several collaborators, principally Feng Lin, Weilin Wang, and Tae-Sic Yoo; they are kindly acknowledged. Decentralized control of discrete event systems, where local controllers cannot explicitly communicate in real-time, is considered in the first part of the paper. Then the problem of real-time communication among a set of local discrete-event controllers (or diagnosers) is discussed. The writing is descriptive and is meant to inform the reader about important conceptual issues and some recently-completed or on-going research efforts. [ABSTRACT FROM AUTHOR]

We offer an alternative way of evaluating the relative importance of the state coordinates of a nonlinear control system. Our approach is based on making changes of state coordinates to bring the controllability and observability functions into input normal form. These changes of coordinates are done degree by degree and the resulting normal form is unique through terms of degree seven. [ABSTRACT FROM AUTHOR]

We introduce two conceptual models for wireless sensing and control with power-limited sensors and controllers. The limited battery power of the wireless device is captured in the models by imposing hard constraints on either the number of available transmissions the device can make, or on the number of cycles it can stay awake. Such hard constraints can be viewed as a measurement budget, under which estimation or control policies will have to be developed over a given decision horizon. Among the two representative models studied here, the first one is one of optimal scheduling of a finite measurement budget for a Gauss-Markov process over an observation horizon. The second one is an optimal estimation problem where the number of transmissions the wireless sensor can make is limited to a number, M, which is less than the observation horizon, N. It is shown that both problems can be solved by employing dynamic-programming type arguments, and their solutions have a threshold characterization. [ABSTRACT FROM AUTHOR]

Petri nets are a family of powerful discrete event models whose interest has grown, within the automatic control community, in parallel with the development of the theory of discrete event systems. In this tutorial paper our goal is that of giving a flavor, by means of simple examples, of the features that make Petri nets a good model for systems theory and of pointing out at a few open areas for research. We focus on Place/Transitions nets, the simplest Petri net model. In particular we compare Petri nets with automata, and show that the former model has several advantages over the latter, not only because it is more general but also because it offers a better structure that has been used for developing computationally efficient algorithms for analysis and synthesis. [ABSTRACT FROM AUTHOR]

In this paper an internal model based approach to periodic input disturbance suppression for port-Hamiltonian systems is presented; more specifically, an adaptive solution able to deal with unknown periodic signal belonging to a given class is introduced. After an introductive section, the adaptive internal model design procedure is presented in order to solve the input disturbance problem. This theoretical machinery is specialized for the energy-based port-Hamiltonian framework in order to prove the global asymptotical stability of the solution. Finally, in order to clearly point out the effectiveness of the presented design procedure a tracking problem is solved for a robotic manipulator affected by torque ripples. [ABSTRACT FROM AUTHOR]

The minimum phase property is an important notion in systems and control theory. In this paper, a characterization of the minimum phase property of nonlinear control systems in terms of a dissipation inequality is derived. It is shown that this dissipation inequality is equivalent to the classical definition of the minimum phase property in the sense of Byrnes and Isidori, if the control system is affine in the input and the so-called input-output normal form exists. [ABSTRACT FROM AUTHOR]

The extension of application domains of robotics from factories to human environments leads to implementing proper strategies for close interaction between people and robots. In order to avoid dangerous collision, force and vision based control can be used, while tracking human motion during such interaction. [ABSTRACT FROM AUTHOR]

In the average consensus a set of linear systems has to be driven to the same final state which corresponds to the average of their initial states. This mathematical problem can be seen as the simplest example of coordination task and in fact it can be used to model both the control of multiple autonomous vehicles which all have to be driven to the centroid of the initial positions, and to model the decentralized estimation of a quantity from multiple measure coming from distributed sensors. In general we can expect that the performance of a consensus strategy will be strongly related to the amount of information the agents exchange each other. This contribution presents a consensus strategy in which the exchanged data are symbols and not real numbers. This is based on a logarithmic quantizer based state estimator. The stability of this technique is then analyzed. [ABSTRACT FROM AUTHOR]

This chapter presents an overview on the modeling and model-based control of autonomous helicopters. Firstly it introduces some of the platforms and control architectures that has been developed in the last 15 years. Later, the Chapter considers the modeling of the helicopter and the identification techniques. Then, it overviews different linear and non-linear model-based control approaches. This section also includes experiments on the control of the helicopter vertical motion that illustrate the presented techniques and point out the interest of nonlinear analysis methods to study the dynamic behavior of the helicopter. Finally, the Chapter presents open research lines coming from two challenging applications: the autonomous landing in oscillating platforms and the lifting and transporting of a single load with several helicopters. [ABSTRACT FROM AUTHOR]

The antiwindup and override design techniques have been developed in industrial design practice for controlling plants with input and output constraints. At present, various analysis and synthesis techniques are well established. These techniques have shown to be both effective and efficient for plants of dominant low order, which are either asymptotically stable or at least marginally stable. [ABSTRACT FROM AUTHOR]

Often one desires to control a nonlinear dynamical system in an optimal way taking constraints on the states and inputs directly into account. Classically this problem falls into the field of optimal control. Often, however, it is difficult, if not impossible, to find a closed solution of the corresponding Hamilton-Jacobi-Bellman equation. One possible control strategy that overcomes this problem is model predictive control. In model predictive control the solution of the Hamilton-Jacobi-Bellman equation is avoided by repeatedly solving an open-loop optimal control problem for the current state, which is a considerably simpler task, and applying the resulting control open-loop for a short time. [ABSTRACT FROM AUTHOR]

The aim of this chapter is the presentation of a technique for the design of stabilizing dynamic output feedback controllers for discrete-time linear systems with rate and amplitude saturating actuators. Two synthesis objectives are considered: the maximization of the domain of attraction of the closed-loop system under some time-domain performance constraints; and the guarantee that the trajectories of the system are bounded in the presence of L2-bounded disturbances, while ensuring an overbound for the L2 gain from the disturbance to the regulated output. [ABSTRACT FROM AUTHOR]

This chapter deals with two problems on stabilization of linear discrete systems by static feedbacks which are bounded and time-delayed, namely global asymptotic stabilization and finite gain lp-stabilizability, p ∈ [1,∞]. Furthermore, an explicit construction of the corresponding feedback laws is given. The feedback laws constructed also result in a closedloop system that is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

We are concerned here with the stabilization of a linear time invariant system subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers. When there exists no actuator saturation, i.e. when we consider just linear time invariant systems, it is known that global stabilization can be done via decentralized control while using linear time invariant dynamic controllers only if the so-called decentralized fixed modes of it are all in the open left half complex plane. [ABSTRACT FROM AUTHOR]

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 system at each time instant in the gain scheduled case. It will be shown how slew-rate constrained control problems can be recast into standard constrained control problems by means of an extended system. To present such technique, an overview of some of the existing results with some numerical algorithms to derive the stability conditions and the control will be given. [ABSTRACT FROM AUTHOR]

In this chapter we address several case studies using LMI optimization methods for designing output feedback control laws to achieve regional performance and stability of linear control systems with input saturation. Algorithms are developed for minimizing the upper bound on the regional L2 gain for exogenous inputs with L2 norm bounded by a given value, and for minimizing this upper bound with a guaranteed reachable set or domain of attraction. Based on the structure of the optimization problems, using the projection lemma, the output feedback controller synthesis is cast as a convex optimization over linear matrix inequalities. The problems are studied in a general setting where the only requirement on the linear plant is detectability and stabilizability. [ABSTRACT FROM AUTHOR]

In the past few years, control of Linear Parameter Varying Systems (LPV) has been the object of considerable attention, as a way of formalizing the intuitively appealing idea of gain scheduling control for nonlinear systems. However, currently available LPV techniques are both computationally demanding and (potentially) very conservative. In this chapter we propose to address these difficulties by combining Receding Horizon and Control Lyapunov Functions techniques in a risk-adjusted framework. The resulting controllers are guaranteed to stabilize the plant and have computational complexity that increases polynomially, rather than exponentially, with the prediction horizon. [ABSTRACT FROM AUTHOR]

The most common way of dealing with constraints in control systems is to ignore them, pretend that the system is linear, and fix things up in a more-or-less ad-hoc fashion after performing a linear design. There are some rather systematic ways of ‘fixing things up', including certain anti-windup techniques, but logically they are an afterthought, a way of dealing with the nuisance of constraints after the central work has been done. Until recently, things could not be done differently, because almost all the control design techniques available to us were linear techniques.3 [ABSTRACT FROM AUTHOR]

In this contribution, explicit model predictive control is applied to the benchmark problems. Emphasis is put on the reduction of complexity both for the off-line and on-line computation. For the pendulum, a control-invariant set is computed first. By using this set in the subsequent optimal control problem, a simple solution can be attained which guarantees invariance of the resulting closed-loop system by construction. The computation of such invariant sets for systems with a partially constrained state-space is discussed. [ABSTRACT FROM AUTHOR]

This chapter addresses the problems of design of anti-windup schemes for linear systems subject to amplitude limitations in actuator and sensor. The design of anti-windup loops, using both measured and estimated variables, is considered in order to enlarge the region of stability of the closed-loop system, whereas some performance in terms of bounded controlled output is guaranteed. Based on the modelling of the closed-loop saturated system including the observer loop as a linear system with dead-zone nested nonlinearities, constructive stability conditions are formulated in terms of linear matrix inequalities by using Finsler's Lemma. [ABSTRACT FROM AUTHOR]

This chapter describes the theory and application of a ‘decoupled' approach to anti-windup compensation. One of the salient features of this approach is that the anti-windup problem can be posed in a manner which decouples the nominal linear closed-loop from the nonlinear stability problem associated with actuator saturation and the anti-windup compensator. This process also reveals a logical and intuitive performance criterion which one can optimise by means of linear matrix inequalities. Details of how the anti-windup problem can be solved using various forms of compensator are given, together with some robustness considerations. Initially, the problem is posed for globally asymptotically stable plants, although this condition is later relaxed to allow the consideration of plants with exponentially unstable modes. Finally, the results are demonstrated on a multivariable aircraft model and the benchmark inverted pendulum. [ABSTRACT FROM AUTHOR]

This chapter proposes an anti-windup design for linear systems in the absence of precise knowledge of the actuator nonlinearity. The actuator input output characteristic is assumed to reside in a nonlinear sector bounded by two convex/concave piecewise linear curves. For the closed-loop system with a given anti-windup compensation gain matrix, stability properties, both in the absence and in the presence of external disturbances are characterized in terms of matrix inequalities. The estimation of the domain of attraction with a contractive invariant ellipsoid as well as the assessment of the disturbance tolerance and disturbance rejection properties of the closed-loop system are then formulated and solved as LMI optimization problems. The design of the anti-windup compensation gain matrix for a large domain of attraction and/or a large disturbance tolerance/rejection capability is then carried out by viewing the anti-windup compensation gain as an additional free parameter in these optimization problems. Numerical examples as well as an experimental setup are used to illustrate the proposed analysis and design approach and its effectiveness. [ABSTRACT FROM AUTHOR]

In the Advanced Tokamak (AT) operating mode of the DIII-D tokamak, an integrated multivariable controller takes into account highly coupled influences of plasma equilibrium shape, profile, and stability control. Time-scale separation in the system allows a multiloop design: the inner loop closed by the nominal vertical controller designed to control a linear exponentially unstable plant and the outer loop closed by the nominal shape controller designed to control a nonlinear stabilized plant. Due to actuator constraints, the nominal vertical controller fails to stabilize the vertical position of the plasma inside the tokamak when large or fast disturbances are present or when the references coming from the shape controller change suddenly. Anti-windup synthesis is proposed to find a nonlinear modification of the nominal vertical controller that prevents vertical instability and undesirable oscillations but leaves the inner loop unmodified when there is no input saturation. [ABSTRACT FROM AUTHOR]

In nearly all control applications, the output signal of the compensator cannot be transferred to the system with unlimited amplitudes and arbitrarily fast. Such limitations in magnitude and rate can lead to performance degradations and they may even cause an unstable behaviour of the closed loop. These undesired effects of actuator saturation are called windup. The problem most intensively investigated is that of amplitude saturation. The prevention of windup effects due to input magnitude restrictions is the subject of a great variety of papers. The references in [3], [8] and [26] give a good overview of the existing literature. [ABSTRACT FROM AUTHOR]

Hamiltonian control systems [11, 6] are the systems described by Hamilton's canonical equations which represent general physical systems. Recently portcontrolled Hamiltonian systems are introduced as a generalization of Hamiltonian systems [3] They can represent not only ordinary mechanical, electrical and electro-mechanical systems, but also nonholonomic systems [4]. The special structure of physical systems allows us to utilize the passivity which they innately possess and a lot of fruitful results were obtained so far. These methods are so called passivity based control [8]. [ABSTRACT FROM AUTHOR]

In this paper we analyze the equations of motion of a submerged rigid body. Our motivation is based on recent developments done in trajectory design for this problem. Our goal is to relate some properties of singular extremals to the existence of decoupling vector fields. The ideas displayed in this paper can be viewed as a starting point to a geometric formulation of the trajectory design problem for mechanical systems with potential and external forces. [ABSTRACT FROM AUTHOR]

A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here. [ABSTRACT FROM AUTHOR]

Recently, the investigation of design approaches to nonlinear control, which can thoroughly exploit the structure and the properties of the physical systems, has been given much attention due to the designed controllers with relatively simple form and effective operation. And it has been shown that for the mechanical and electromechnical systems, by incorporating the Hamiltonian structure into passivity-based control design techniques, the controllers based on physical considerations can be obtained [1],[2],[3]. This design idea has been successfully realized alized in the control of power systems and a lot of achievements have been gotten (see e.g. [1]-[9). In [4], the fact that the power system with excitation control is a Hamiltonian structure is exploited by selecting a storage function constructed by system potential and kinetic energy and an appropriate passivating output on the basis of physical arguments. Along this research line, the excitation control problem for multi-machine power systems has been investigated in [5],[6]. Moreover, an adaptive L2 disturbance attenuation controller based on Hamiltonian structure has been provided for power systems in [7]. [ABSTRACT FROM AUTHOR]

In this paper we present some additional results regarding the pumping-damping strategy for swinging up a pendulum introduced in [3]. Here, the family of energy functions is enlarged and the corresponding pumping-damping functions are proposed giving rise to new smooth controllers that swing up and stabilize the pendulum. Furthermore, a generalization of the stability criterion is introduced for this larger class of controllers. [ABSTRACT FROM AUTHOR]

We present a new coordinated control law for a group of vehicles in the plane that stabilizes an arbitrary desired group shape. The control law is derived for an arbitrary shape using models of tensegrity structures which are spatial networks of interconnected struts and cables. The symmetries in the coupled system and the energy-momentum method are used to investigate stability of relative equilibria corresponding to steady translations of the prescribed rigid shape. [ABSTRACT FROM AUTHOR]

A geodesic-based formulation of geometric PD tracking control for fully actuated mechanical systems is derived from the Riemannian metric. The region of stability is determined directly from the magnitude of the system's injectivity radius and, for a restricted set of control problems, the locus of cut points about a desired reference point in the manifold. Exponential stability is proven for controlled motion along a geodesic, yielding a particularly simple, yet elegant, methodology for control design. [ABSTRACT FROM AUTHOR]