Håvard Fjær Grip

Washington State University, Pullman, Washington, United States

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Publications (44)27.95 Total impact

  • Tao Yang, Ali Saberi, Anton A. Stoorvogel, Håvard Fjær Grip
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    ABSTRACT: In this paper, we consider the output synchronization problem for heterogeneous networks of right-invertible linear agents. We assume that all the agents are introspective, meaning that they have access to their own local measurements. Under this assumption, we then propose a decentralized control scheme for solving the output synchronization problem for a set of network topologies. The proposed scheme can also be applied to solve the output formation problem with arbitrary formation vectors. We also consider the regulation of output synchronization problem, where the output of each agent has to track an a priori specified reference trajectory, generated by an exosystem. In this case, we assume that the root agent has access to its own output relative to the reference trajectory.Copyright © 2013 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 09/2014; 24(13). · 1.90 Impact Factor
  • Håvard Fjær Grip, Ali Saberi
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    ABSTRACT: In this paper, we consider the observer design problem for a class of observable linear systems perturbed by nonlinear, time-varying terms. Our design methodology is based on a canonical form, similar to canonical forms used elsewhere in the literature, that allows the nonlinearities to be dominated using high gain. We show that linear state and output transformations to this canonical form exist if, and only if, the data of the system satisfies a certain admissibility property. Moreover, the appropriate transformations can easily be constructed using available tools. We furthermore show that, if a system does not satisfy the admissibility property, it may be possible to extend it with an invertible output filter that makes the data of the extended system admissible. We refer to the problem of constructing such a filter as the output shaping problem and introduce an algorithm that solves the problem whenever it is solvable. Copyright © 2012 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 04/2014; 24(6). · 1.90 Impact Factor
  • Tao Yang, Anton A. Stoorvogel, Håvard Fjær Grip, Ali Saberi
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    ABSTRACT: In this paper, we consider the semi-global regulation of output synchronization problem for heterogeneous networks of invertible linear agents subject to actuator saturation. That is, we regulate the output of each agent according to an a priori specified reference model. The network communication infrastructure provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates while some agents have access to their own outputs relative to the reference trajectory.Copyright © 2012 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 02/2014; 24(3). · 1.90 Impact Factor
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    ABSTRACT: This paper brings forward the notion of “H∞H∞ almost output synchronization” for heterogeneous multi-agent systems under directed interconnection structures. Agents are assumed to be linear, right-invertible and introspective (i.e. agents have partial knowledge of their own states). The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the H∞H∞ norm of the corresponding closed-loop transfer function. In addition, the problem of regulating the consensus trajectories to a reference signal is addressed. The application of the proposed method to the problem of formation is furthermore elucidated. Simulation results are provided to illustrate the method.
    Automatica. 01/2014;
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    ABSTRACT: This paper studies the synchronization problem for a network of identical discrete-time agents with unknown uniform constant communication delay. When the agents are non-introspective, the problem is solvable via a decentralized low-gain-based synchronization controller if the delay satisfies the proposed upper bound. When the agents are introspective, the synchronization problem can be solved with arbitrary bounded communication delay. Copyright © 2013 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 07/2013; · 1.90 Impact Factor
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    ABSTRACT: We introduce the notions of “ℌ∞ almost regulated synchronization” and “ℌ∞ almost formation” for multi-agent systems subject to external disturbances and under directed interconnection structures. We assume that agents are linear, right-invertible and introspective with non-identical dynamics. The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the ℌ∞ norm of the corresponding closed-loop transfer function. Inspired by the time-scale structure assignment techniques based on the singular perturbation theory, a family of observer-based protocols is introduced to achieve synchronization with any desired accuracy.
    Control Conference (ECC), 2013 European; 01/2013
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    ABSTRACT: In this paper we study the problem of achieving regulated output synchronization in a network of minimum-phase SISO agents. Our problem formulation is characterized by the combination of three different challenges: the network is heterogeneous (meaning that the agents are governed by non-identical models); the agents are non-introspective (meaning that they do not have access to information about their own state or output); and the agents are not allowed to exchange internal controller states via the network. To handle these challenges, we present an observer-based control methodology that combines elements of low-gain and high-gain design techniques.
    Control Conference (ECC), 2013 European; 01/2013
  • Xu Wang, Ali Saberi, Håvard Fjær Grip, Anton A. Stoorvogel
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    ABSTRACT: In this paper, we study the disturbance response of open‐loop neutrally stable linear systems with saturating linear feedback controller. It is shown that the closed‐loop states remain bounded if the disturbances consists of those signals that do not have large sustained frequency components corresponding to the system's eigenvalues on the imaginary axis (continuous‐time) or on the unit circle (discrete‐time). Copyright © 2011 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 01/2013; 23(2). · 1.90 Impact Factor
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    ABSTRACT: For applications with limited computational capacity, observers designed based on nonlinear stability theory offer an alternative to computationally demanding extended Kalman filters. In this paper, we present a semiglobally stable nonlinear observer for estimating position, velocity, attitude, and gyro bias by combining a GNSS receiver with an inertial measurement unit including a magnetometer. Previous work by the authors on this topic was based on local navigation equations that ignored the Earth's rotation and curvature. Moreover, the attitude was represented by an over-parameterized 9-degrees-of-freedom matrix. The current paper improves on these aspects by using navigation equations that take the Earth's rotation and curvature into account, and by representing the attitude estimate as a unit quaternion. Furthermore, the observer is tested experimentally on data from a light fixed-wing aircraft.
    American Control Conference (ACC), 2013; 01/2013
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    ABSTRACT: In this paper, synchronization for multi-agent systems subject to external disturbances is studied, and the notion of H∞ almost synchronization” is introduced. The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the H∞ norm of the corresponding closed-loop transfer function to any arbitrarily value. We focus on networks of non-identical linear, right-invertible agents under directional communication links. The key assumption is that agents are introspective; that is, they have a partial knowledge about their own states.
    American Control Conference (ACC), 2013; 01/2013
  • Håvard Fjær Grip, Tao Yang, Ali Saberi, Anton A. Stoorvogel
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    ABSTRACT: In this paper we consider the output synchronization problem for heterogeneous networks of linear agents. The network’s communication infrastructure provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates. We design decentralized controllers based on setting the control input of a single root agent to zero and letting the remaining agents synchronize to the root agent. A distinguishing feature of our work is that the agents are assumed to be non-introspective, meaning that they possess no knowledge about their own state or output separate from what is received via the network. We also consider the problem of regulating the agreement trajectory according to an a priori specified reference model. In this case we assume that some of the agents have access to their own output relative to the reference trajectory.
    Proceedings of the American Control Conference 10/2012; 48(10):2444–2453.
  • Håvard Fjær Grip, Ali Saberi, Tor A. Johansen
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    ABSTRACT: In this paper we begin by assuming that an observer with a corresponding quadratic-type Lyapunov function has been designed for a given nonlinear system. We then consider the problem that arises when the output of that nonlinear system is not directly available; instead, it acts as an input to a second, linear system from which a partial-state measurement is in turn available. We develop an observer design methodology for the resulting cascade interconnection, based on estimating the unavailable output together with the states of the linear system. We also extend this methodology to a more general class of feedback-interconnected systems. Under a set of technical assumptions, the overall error dynamics is proven to be globally exponentially stable if the gains are chosen to satisfy an H∞H∞ condition. We illustrate application of the methodology by considering a navigation example based on integration of inertial and satellite measurements.
    Automatica. 07/2012; 48(7):1339–1346.
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    ABSTRACT: This paper studies the consensus among identical agents that are at most critically unstable and coupled through networks with uniform constant communication delay. An achievable upper bound of delay tolerance is obtained which explicitly depends on agent dynamics and network topology. The dependence on network topology disappears in the case of undirected networks. For any delay satisfying this upper bound, a controller design methodology without exact knowledge of the network topology is proposed so that the multi-agent consensus in a set of unknown networks can be achieved. Moreover, when the network topology is known, a larger delay tolerance is possible via a topology-dependent consensus controller. The results are illustrated by simulations.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
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    ABSTRACT: We present an observer for estimating position, velocity, attitude, and gyro bias, by using inertial measurements of accelerations and angular velocities, magnetometer measurements, and satellite-based measurements of position and (optionally) velocity. The design proceeds in two stages: in Stage I, an attitude and gyro bias estimator is designed based on an unmeasured signal. In Stage II, that design is recovered using measured signals only, by combining it with a position and velocity estimator. We prove global exponential stability of the estimation error and test the design using realistic flight simulation.
    American Control Conference (ACC), 2012; 01/2012
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    ABSTRACT: In this paper, we develop a new low-and-high gain feedback design methodology using a ultra-short-horizon Model Predictive Controller (MPC) for global asymptotic stabilization of discrete-time linear system subject to input saturation. The proposed method yields improved performance over classical low-and-high gain design and has reduced computational complexity and guaranteed global asymptotic stability of closed-loop system compared to MPC with a long prediction horizon.
    American Control Conference (ACC), 2012; 01/2012
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    ABSTRACT: This paper studies the consensus among identical agents that are at most critically unstable and coupled through networks with uniform constant communication delay. An achievable upper bound of delay tolerance is obtained which explicitly depends on agent dynamics and network topology. The dependence on network topology disappears in the case of undirected networks. For any delay satisfying this upper bound, a controller design methodology without exact knowledge of the network topology is proposed so that the multi-agent consensus in a set of unknown networks can be achieved. Moreover, when the network topology is known, a larger delay tolerance is possible via a topology-dependent consensus controller. The results are illustrated by simulations.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
  • Source
    Xu Wang, Ali Saberi, Anton A. Stoorvogel, Håvard Fjær Grip
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    ABSTRACT: In this paper, we study the response to external disturbances of a double integrator with a saturating feedback. For a class of disturbances that have bounded integrals over all intervals, we show that a linear static feedback law can always be designed to ensure boundedness of the states. Moreover, boundedness can be preserved if the disturbance is biased by a small DC signal. In the special case that the disturbance is made up of a finite number of sinusoids and a small bias, any linear static feedback ensures boundedness of the states. These results are an extension of previous results by Wen, Roy, and Saberi (2008).
    Automatica. 01/2012; 48:430-435.
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    ABSTRACT: In this paper we consider the output synchronization problem for heterogeneous networks of linear agents. The network provides each agent with a linear combination of its own output relative to that of neighboring agents, and it allows the agents to exchange information about their own internal observer estimates. We design decentralized controllers based on setting the control input of a single root agent to zero and letting the remaining agents synchronize to the root agent. A distinguishing feature of our work is that the agents are assumed to be non-introspective, meaning that they possess no knowledge about their own state or output separate from what is received via the network.
    American Control Conference (ACC), 2012; 01/2012
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    ABSTRACT: A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched between linear systems. We focus first on single-layer sandwich systems, which consist of a single saturation sandwiched between two linear systems. For such systems, we present necessary and sufficient conditions for semi-global and global stabilization problems by state feedback, and develop design methodologies to achieve the prescribed stabilization. We extend the results to single-layer sandwich systems subject to additional actuator saturation. Finally, we discuss further extension to general multi-layer sandwich systems with an arbitrary number of saturations sandwiched between linear systems, both with and without actuator saturation. The design methodologies can be viewed as extensions of classical low-gain design methodologies developed during the 1990s in the context of stabilizing linear systems subject to actuator saturation. Copyright © 2010 John Wiley & Sons, Ltd.
    International Journal of Robust and Nonlinear Control 11/2011; 21(16):1841 - 1864. · 1.90 Impact Factor
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    Håvard Fjær Grip, Ali Saberi, Tor Arne Johansen
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    ABSTRACT: We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modular design technique for estimating the system states and the unknown parameters. The design consists of a high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator constructed by the designer to invert a nonlinear equation. We illustrate the technique on a simulated dc motor with friction.
    Systems & Control Letters. 01/2011; 60:771-777.