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    Output-feedback controlled-invariant sets for systems with linear parameter-varying state transition matrix
    (IEEE, 2011)
    Hempel, Andreas B.
    ;
    Kominek, Andreas B.
    ;
    Werner, Herbert
    The notion of output-feedback controlled-invariant sets is extended from LTI systems to systems with linear parameter-varying state transition matrix. A theorem is presented that can be used to verify whether a given polytope can be made invariant under output-feedback. The theorem also provides the constraints a control input has to fulfill to make the candidate set invariant. Predictive output-feedback controllers based on such a set can satisfy hard constraints on both the plant state and the control inputs in the presence of process disturbances and measurement noise. Simulation results demonstrate the strength of such a controller that can guarantee constraints for a subset of the state space without requiring state information or estimation.
    Publicationtype: Conference Paper
      35
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    A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions
    (IEEE, 2011)
    Faulwasser, Timm
    ;
    Findeisen, Rolf
    We discuss a model predictive control approach to trajectory tracking problems of constrained nonlinear continuous time systems, where the reference trajectory is a priori known and asymptotically constant. The proposed NMPC scheme is able to explicitly consider input and state constraints while guaranteeing recursive feasibility. To handle the time-varying nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov functions as terminal regions. We prove a necessary and sufficient condition for positive invariance of these sets and show how these sets can be efficiently computed, if a quadratic Lyapunov function is available. As an example we consider a nonlinear CSTR reactor.
    Publicationtype: Conference Paper
      9
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    Observer-based LPV control of a nonlinear PDE
    (IEEE, 2011)
    Hashemi, Seyed Mahdi
    ;
    Werner, Herbert
    In this paper, observer-based linear parameter-varying (LPV) control of the one-dimensional nonlinear Burgers' equation is presented. The partial differential equation is discretized using a finite difference scheme and the boundary conditions are taken as control inputs. A nonlinear high-order state space model is generated and proper orthogonal decomposition based Galerkin projection is used for model order reduction. A discrete-time quasi-LPV model that is affine in scheduling parameters is derived based on the reduced model and a polytopic dynamic output feedback LPV controller is synthesized. Since the scheduling parameters are linear combinations of system states, the synthesized output-feedback controller is converted to an observer-based state feedback controller which provides an estimate of the scheduling parameters. Simulation results demonstrate that the designed observer-based LPV controller has almost the same level of disturbance and measurement noise rejection capability compared to an output feedback LPV controller combined with a nonlinear observer. Moreover, both of the LPV controllers outperform an LQG controller based on a linearized model.
    Publicationtype: Conference Paper
      38
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    Two-degree-of-freedom LPV control for a through-the-road hybrid electric vehicle via torque vectoring
    (IEEE, 2011)
    Liu, Qin
    ;
    Kaiser, Gerd
    ;
    Boonto, Sudchai
    ;
    Werner, Herbert
    ;
    Holzmann, Frédéric
    This paper presents an application of linear-Parameter-Varying (LPV) control to solve the torque vectoring problem of a through-the-road hybrid electric vehicle (TtR-HEV). To achieve high performance both in reference tracking and disturbance rejection, a two-degree-of-freedom LPV self-scheduled controller is synthesized by using mixed sensitivity loop shaping. The controller is based on a single Lyapunov function and guarantees stability and a level of control performance for all admissible trajectories of varying parameters. Moreover, an anti-windup control scheme is derived by employing a two-step design procedure. Finally the designed controller is tested in various driving maneuvers and compared with a flatness-based controller.
    Publicationtype: Conference Paper
      37