434 research outputs found
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Distributed LQR Methods for Networks of Non-Identical Plants
Two well-established complementary distributed linear quadratic regulator (LQR) methods applied to networks of identical agents are extended to the non-identical dynamics case. The first uses a top-down approach where the centralized optimal LQR controller is approximated by a distributed control scheme whose stability is guaranteed by the stability margins of LQR control. The second consists of a bottom-up approach in which optimal interactions between self-stabilizing agents are defined so as to minimize an upper bound of the global LQR criterion. In this paper, local state-feedback controllers are designed by solving model-matching type problems and mapping all the agents in the network to a target system specified a priori. Existence conditions for such schemes are established for various families of systems. The single-input and then the multi-input case relying on the controllability indices of the plants are first considered followed by an LMI approach combined with LMI regions for pole clustering. Then, the two original top-down and bottom-up methods are adapted to our framework and the stability problem for networks of non-identical dynamical agents is solved. The applicability of our approach for distributed network control is illustrated via a simple example
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Distributed LQR design for identical dynamically coupled systems: Application to load frequency control of multi-area power grid
The paper proposes a distributed LQR method for the solution to regulator problems of networks composed of dynamically dependent agents. It is assumed that these dynamical couplings among agents can be expressed in a state-space form of a certain structure. Following a top-down approach we approximate a centralized LQR optimal controller by a distributed scheme the stability of which is guaranteed via a stability test applied to convex combination of Hurwitz matrices. The method is applied to N-identical-area power grid where a distributed state-feedback Load Frequency Controller (LFC) is proposed to achieve frequency regulation under power demand variations. An illustrative numerical example demonstrates the applicability of the method
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Distributed Model Predictive Load Frequency Control of multi-area Power Grid: A Decoupling Approach
A model-predictive scheme for load frequency control of a multi-area power system is proposed. The method depends on a decoupling technique which allows for a control design with a distributed architecture. Treating the total power inflows of each area as input variables, a decoupled linearized model for each area is derived. This allows for the formulation and solution of a model predictive control problem with a quadratic performance index and input saturating constraints on the individual tie-line power flows, along with an overall equality constraint to address the energy balance of the network. It is assumed that the interconnection topology (tie-lines) coincides with the communication topology of the network. The only information which needs to be shared between interconnected areas is the local frequency variables. The effectiveness of the method is illustrated via a simulation study of a three-area network. Future work will attempt to establish formally the stability of the control scheme and to enhance the versatility of the method by including constraints on the state variables
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Cooperative distributed LQR control for longitudinal flight of a formation of non-identical low-speed experimental UAV's
In this paper, an established distributed LQR control methodology applied to identical linear systems is extended to control arbitrary formations of non-identical UAV's. The nonlinear model of a low-speed experimental UAV known as X-RAE1 is utilized for simulation purposes. The formation is composed of four dynamically decoupled X-RAE1 which differ in their masses and their products of inertia about the xz plane. In order to design linear controllers the nonlinear models are linearized for horizontal flight conditions at constant velocity. State-feedback, input and similarity transformations are applied to solve model-matching type problems and compensate for the mismatch in the linearized models due to mass and symmetry discrepancies among the X-RAE1 models. It is shown that the method is based on the controllability indices of the linearized models. Distributed LQR control employed in networks of identical linear systems is appropriately adjusted and applied to the formation of the nonidentical UAV's. The applicability of the approach is illustrated via numerous simulation results
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Distributed optimal and predictive control methods for networks of dynamic systems
Several recent approaches to distributed control design over networks of interconnected dynamic systems rely on certain assumptions, such as identical subsystem dynamics, absence of dynamical couplings, linear dynamics and undirected interaction schemes. In this thesis, we investigate systematic methods for relaxing a number of simplifying factors leading to a unifying approach for solving general distributed-control stabilization problems of networks of dynamic agents.
We show that the gain-margin property of LQR control holds for complex multiplicative input perturbations and a generic symmetric positive definite input weighting matrix. Proving also that the potentially non-simple structure of the Laplacian matrix can be neglected for stability analysis and control design, we extend two well-known distributed LQR-based control methods originally established for undirected networks of identical linear systems, to the directed case.
We then propose a distributed feedback method for tackling large-scale regulation problems of a general class of interconnected non-identical dynamic agents with undirected and directed topology. In particular, we assume that local agents share a minimal set of structural properties, such as input dimension, state dimension and controllability indices. Our approach relies on the solution of certain model matching type problems using local linear state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting well-established distributed LQR control design methodologies to our framework, the stabilization problem of a network of non-identical dynamical agents is solved. We thereafter consider a networked scheme synthesized by multiple agents with nonlinear dynamics. Assuming that agents are feedback linearizable in a neighborhood near their equilibrium points, we propose a nonlinear model matching control design for stabilizing networks of multiple heterogeneous nonlinear agents.
Motivated by the structure of a large-scale LQR optimal problem, we propose a stabilizing distributed state-feedback controller for networks of identical dynamically coupled linear agents. First, a fully centralized controller is designed which is subsequently substituted by a distributed state-feedback gain with sparse structure. The control scheme is obtained byoptimizing an LQR performance index with a tuning parameter utilized to emphasize/deemphasize relative state difference between coupled systems. Sufficient conditions for stability of the proposed scheme are derived based on the inertia of a convex combination of two Hurwitz matrices. An extended simulation study involving distributed load frequency control design of a multi-area power network, illustrates the applicability of the proposed method. Finally, we propose a fully distributed consensus-based model matching scheme adapted to a model predictive control setting for tackling a structured receding horizon regulation problem
A disk-wind model with correct crossing of all MHD critical surfaces
The classical Blandford & Payne (1982) model for the magnetocentrifugal
acceleration and collimation of a disk-wind is revisited and refined. In the
original model, the gas is cold and the solution is everywhere subfast
magnetosonic. In the present model the plasma has a finite temperature and the
self-consistent solution of the MHD equations starts with a subslow
magnetosonic speed which subsequently crosses all critical points, at the slow
magnetosonic, Alfven and fast magnetosonic separatrix surfaces. The superfast
magnetosonic solution thus satisfies MHD causality. Downstream of the fast
magnetosonic critical point the poloidal streamlines overfocus towards the axis
and the solution is terminated. The validity of the model to disk winds
associated with young stellar objects is briefly discussed. ~Comment: 13 pages, MNRAS accepted for publicatio
Two-component jet simulations: II. Combining analytical disk and stellar MHD outflow solutions
Theoretical arguments along with observational data of YSO jets suggest the
presence of two steady components: a disk wind type outflow needed to explain
the observed high mass loss rates and a stellar wind type outflow probably
accounting for the observed stellar spin down.
Each component's contribution depends on the intrinsic physical properties of
the YSO-disk system and its evolutionary stage. The main goal of this paper is
to understand some of the basic features of the evolution, interaction and
co-existence of the two jet components over a parameter space and when time
variability is enforced. Having studied separately the numerical evolution of
each type of the complementary disk and stellar analytical wind solutions in
Paper I of this series, we proceed here to mix together the two models inside
the computational box. The evolution in time is performed with the PLUTO code,
investigating the dynamics of the two-component jets, the modifications each
solution undergoes and the potential steady state reached.Comment: accepted for publication in A&
Two-component jet simulations: I. Topological stability of analytical MHD outflow solutions
Observations of collimated outflows in young stellar objects indicate that
several features of the jets can be understood by adopting the picture of a
two-component outflow, wherein a central stellar component around the jet axis
is surrounded by an extended disk-wind. The precise contribution of each
component may depend on the intrinsic physical properties of the YSO-disk
system as well as its evolutionary stage. In this context, the present article
starts a systematic investigation of two-component jet models via
time-dependent simulations of two prototypical and complementary analytical
solutions, each closely related to the properties of stellar-outflows and
disk-winds. These models describe a meridionally and a radially self-similar
exact solution of the steady-state, ideal hydromagnetic equations,
respectively. By using the PLUTO code to carry out the simulations, the study
focuses on the topological stability of each of the two analytical solutions,
which are successfully extended to all space by removing their singularities.
In addition, their behavior and robustness over several physical and numerical
modifications is extensively examined. It is found that radially self-similar
solutions (disk-winds) always reach a final steady-state while maintaining all
their well-defined properties. The different ways to replace the singular part
of the solution around the symmetry axis, being a first approximation towards a
two-component outflow, lead to the appearance of a shock at the super-fast
domain corresponding to the fast magnetosonic separatrix surface. Conversely,
the asymptotic configuration and the stability of meridionally self-similar
models (stellar-winds) is related to the heating processes at the base of the
wind.Comment: Accepted for publication in A&
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Model-matching methods and distributed control of networks consisting of a class of heterogeneous dynamic agents
Many recent results on distributed control of multi-agent networks rely on a number of simplifying assumptions that facilitate the solution of regulation problems associated with large-scale networked systems. Identical subsystem models are a typical assumption made in networked control systems which often fail in practice. In this paper, we propose a systematic method for removing this assumption, leading to a general approach to distributed-control design for stabilising networks of multiple non-identical dynamic agents. Local subsystems represented as autonomous dynamic agents are assumed to share a set of structural properties, (controllability) indices. Our approach relies on the solution of certain model-matching type problems using local state-feedback and state/input-matrix transformations that map local dynamics to a target system, selected to minimise joint control effort. By adapting well-established distributed LQR control design methodologies to our framework, the stabilisation problem of networks of non-identical dynamic agents is solved. The applicability of our approach is illustrated via a synchronisation example of eleven harmonic oscillators with non-identical dynamics communicating over a connected graph
Velocity asymmetries in YSO jets: Intrinsic and extrinsic mechanisms
It is a well established fact that some YSO jets (e.g. RW Aur) display
different propagation speeds between their blue and red shifted parts, a
feature possibly associated with the central engine or the environment in which
the jet propagates. In order to understand the origin of asymmetric YSO jet
velocities, we investigate the efficiency of two candidate mechanisms, one
based on the intrinsic properties of the system and one based on the role of
the external medium. In particular, a parallel or anti-parallel configuration
between the protostellar magnetosphere and the disk magnetic field is
considered and the resulting dynamics are examined both in an ideal and a
resistive magneto-hydrodynamical (MHD) regime. Moreover, we explore the effects
of a potential difference in the pressure of the environment, as a consequence
of the non-uniform density distribution of molecular clouds. Ideal and
resistive axisymmetric numerical simulations are carried out for a variety of
models, all of which are based on a combination of two analytical solutions, a
disk wind and a stellar outflow. We find that jet velocity asymmetries can
indeed occur both when multipolar magnetic moments are present in the star-disk
system as well as when non-uniform environments are considered. The latter case
is an external mechanism that can easily explain the large time scale of the
phenomenon, whereas the former one naturally relates it to the YSO intrinsic
properties. [abridged]Comment: accepted for publication in A&
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