Daisuke Tsubakino

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

Abstract This paper proposes an eigenvector-based method for analysis and design of hierarchical networks for multi-agent systems. We first define the concept of eigen-connection by characterizing low rank information flow between layers based on the eigenvector of lower level interconnection structures. It is shown that the resulting intergroup interconnections affect only a few eigenvalues of interconnection structures in the lower layer, and we derive explicit expressions for shifted eigenvalues. Then a procedure for designing hierarchical networks that result in desirable eigenvalue distributions is proposed, where the eigen-connection is used for a key to move undesirable eigenvalues selectively. The effectiveness of the procedure is demonstrated by a numerical example.

Computation of nonlinear balanced realization and model reduction based on Taylor series expansion

In this paper a computational algorithm for nonlinear balanced realization and model reduction based on Taylor series expansion is proposed. This algorithm requires recursive computations with respect to the order of the Taylor series in which we need to solve linear equations with unknown parameters in each step. Furthermore, the proposed method is applied to a double pendulum system. Some numerical simulations demonstrate the effectiveness of the proposed algorithm.

Effective Layout of Plasma Actuators for a Flow Separation Control on a Wing

Eect of locations of dielectric barrier discharge (DBD) plasma actuators is computationally investigated in order to control the o w separations around NACA 0012 airfoil. For o w conditions, low speed o w of M1 = 0:1 with the relatively low Reynolds number based on wing chord Rec = 1:0 10 5 is considered. The plasma actuators located on the 5%, 10% and 20% chord from the leading edge. The dierence in the layout is not observed when the induced velocity is low with a low input voltage. Whereas, the dierence appears when the induced velocity is enough high. Totally, to induce higher velocity at the leading edge is the most eectiv e way to control the o w separation in this condition. Besides, the use of multiple actuator is discussed. The multiple actuator can reduced the input voltage.

On computation of nonlinear balanced realization and model reduction

In this paper a computational algorithm for nonlinear balanced realization and model reduction based on Taylor series expansion is proposed. This algorithm requires recursive computations with respect to the order of the Taylor series in which we need to solve linear equations with unknown parameters in each step. Furthermore, the proposed method is applied to a double pendulum system. Some numerical simulations demonstrate the effectiveness of the proposed algorithm

Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L 2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations.

Hierarchical network synthesis for output consensus by eigenvector-based interlayer connections

In this paper, we study consensus problem for hierarchical multi-agent dynamical systems with low rank interconnection by eigenvector-based connection. The system considered is more general than the existing one in a sense that the number of agents in each subsystem and the connection structure of each subsystem are allowed to be different from each other. We provide analytical expressions of the eigenvalue sets of the hierarchical interconnection matrices and systematic synthesis procedures for achieving the output consensus with Lyapunov stability. The results are applicable to more general class of hierarchical interconnection structures than previous work, and numerical examples with simulations confirm the effectiveness of the proposed design method.

An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems

This paper considers a linear quadratic optimal hierarchical control problem for large-scale dynamical systems modeled by an interconnected system under multi-scale information exchange networks. We first propose an algebraic characterization of hierarchies by using semigroups the Kronecker product. The multiplication rule of the Kronecker product quite fits to the property of semigroups. As a result, a condition under which the stabilizing solution of the Riccati equation inherits the hierarchy is obtained with the aid of the previous result. Furthermore, the proposed framework makes it possible to understand several previous results on decentralized optimal control from a unified viewpoint.

Extremum Seeking for Static Maps With Delays

In this paper, we address the design and analysis of multi-variable extremum seeking for static maps subject to arbitrarily long time delays. Both Gradient and Newton-based methods are considered. Multi-input systems with different time delays in each individual input channel as well as output delays are dealt with. The phase compensation of the dither signals and the inclusion of predictor feedback with a perturbation-based (averaging-based) estimate of the Hessian allow to obtain local exponential convergence results to a small neighborhood of the optimal point, even in the presence of delays. The stability analysis is carried out using backstepping transformation and averaging in infinite dimensions, capturing the infinite-dimensional state due the time delay. In particular, a new backstepping-like transformation is introduced to design the predictor for the Gradient-based extremum seeking scheme with multiple and distinct input delays. The proposed Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the nonlinear map to be optimized, being user-assignable as in the literature free of delays. A source seeking example illustrates the performance of the proposed delay-compensated extremum seeking schemes.

Predictor-feedback for multi-input LTI systems with distinct delays

In this paper, we propose a predictor-based state feedback controller for multi-input linear time-invariant systems with different time delays in each individual input channel. The controller is designed based on the backstepping method. Since the conventional backstepping transformation is not applicable to the systems due to the differences among delays, a modified transformation is introduced. This transformation enables us to design an exponentially stabilizing controller under which the plant behaves as if the delay were absent after a finite time interval. In addition, an explicit Lyapunov functional is constructed. The performance of the controller is demonstrated by a numerical simulation.

Exact predictor feedbacks for multi-input LTI systems with distinct input delays

This paper proposes a predictor-based state feedback controller for multi-input linear time-invariant (LTI) systems with different time delays in each individual input channel. The controller is derived based on the backstepping method. Since the conventional backstepping transformation is not applicable to the systems due to the differences among delays, a modified transformation is introduced. This transformation enables us to design an exponentially stabilizing controller under which the plant behaves as if the delays were absent after a finite time interval. As a dual of the controller design, we also present the observer design for multi-output LTI systems with distinct sensor delays. A numerical simulation confirms the performance of the proposed controller.