Output regulation for linear distributed parameter systems

This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in Francis (1997) and Isidori and Byrnes (1990). We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system     

Nonlinear regulation for a class of discrete-time systems

This paper deals with nonlinear discrete-time regulation for multi-input, multi-output plants. Conditions involving solvability of nonlinear transcendental equations are set. Following the approach recently developed by Isidori and Byrnes (1990) for continuous time systems, the existence of solutions to the posed problem is proved by investigating the properties of the zero dynamics. Finally a condition is given for the existence of an arbitrary approximation of the nonlinear solution.     

Stability and robustness for nonlinear systems decoupled and linearized by feedback

We give some stability and robustness results for nonlinear systems which are transformed by feedback and immersion into decoupled linear systems. In particular we give a necessary condition involving the Euler-Poincaré characteristic of asymptotic unobservable submanifolds. This condition is successfully applied to a non-minimum-phase example (see Byrnes and Isidori [2]) borrowed from robotics which displays K-stability.     

非线性系统的输出调节与受控中心流形

本文用中心流形理论＾［７］及动力系统方法＾［８］，考虑了一般非线性系统的输出调节问题，在弱于Ｉｓｉｄｏｒｉ和Ｂｙｒｎｅｓ＾［６］的条件下，得到了这问题可解的充分必要条件。     

Fast solution of volume–surface integral equation for scattering from composite conducting‐dielectric targets using multilevel fast dipole method

This article presents a fast solution to the volume–surface integral equation for electromagnetic scattering from three‐dimensional (3D) targets comprising both conductors and dielectric materials by using the multilevel fast dipole method (MLFDM). This scheme is based on the concept of equivalent dipole‐moment method (EDM) that views the Rao–Wilton–Glisson and the Schaubert–Wilton–Glisson basis functions as dipole models with equivalent dipole moments. In the MLFDM, a simple Taylor's series expansion of the terms R^α (α = 1, ?1, ?2, ?3) and R? R? in the formulation of the EDM transforms the interaction between two equivalent dipoles into an aggregation–translation–disaggregation form naturally. Furthermore, benefiting from the multilevel grouping scheme, the matrix‐vector product can be accelerated and the memory cost is reduced remarkably. Simulation results are presented to demonstrate the efficiency and accuracy of this method. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

多变量非线性动态系统的全局稳定化控制器

对可化为Bymes-Isidori正规型的多变量非线性系统,仅利用线性组成部分的状态设计了全局稳定化控制器。引入了有限时间滑动模态的概念,其优点是线性部分的状态在有限时间内趋近于零。当非线性系统是最小相位时,所设计的控制器保证了系统的全局稳定性。     

Mixed ℋ︁2/ℋ︁∞ nonlinear filtering

In this paper, we consider the mixed ??₂/??_∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled Hamilton–Jacobi–Isaacs equations (HJIEs). For linear systems, it is shown that these conditions reduce to a pair of coupled Riccati equations similar to the ones for the control case. Both the finite‐horizon and the infinite‐horizon problems are discussed. Simulation results are presented to show the usefulness of the scheme, and the results are generalized to include other classes of nonlinear systems. Copyright © 2008 John Wiley & Sons, Ltd.     

A Dissipation Inequality for the Minimum Phase Property

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.     

Control‐oriented modeling and deployment of tensegrity–membrane systems

This study addresses control‐oriented modeling and control design of tensegrity–membrane systems. Lagrange's method is used to develop a control‐oriented model for a generic system. The equations of motion are expressed as a set of differential‐algebraic equations (DAEs). For control design, the DAEs are converted into second‐order ordinary differential equations (ODEs) based on coordinate partitioning and coordinate mapping. Because the number of inputs is less than the number of state variables, the system belongs to the class of underactuated nonlinear systems. A nonlinear adaptive controller based on the collocated partial feedback linearization (PFL) technique is designed for system deployment. The stability of the closed‐loop system for the actuated coordinates is studied using the Lyapunov stability theory. Because of system complexity, numerical tests are used to conduct stability analysis for the dynamics of the underactuated coordinates, which represents the system's zero dynamics. For the tensegrity–membrane systems studied in this work, analytical proof of zero dynamics stability remains an open theoretical problem. An H_∞ controller is implemented for rapid stabilization of the system at the final deployed configuration. Simulations are conducted to test the performance of the two controllers. The simulation results are presented and discussed in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

Correction to ‘Mixed ℋ︁2/ℋ︁∞ Nonlinear Filtering’

In Section 5 of Aliyu and Boukas (Int. J. Robust Nonlinear Control 2009; 19 :394–417), the authors have presented certainty‐equivalent filters for the mixed ??₂/??_∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of the problem with a finite‐dimensional filter are given in terms of a pair of coupled Hamilton–Jacobi–Isaacs equations (HJIEs). In this note, we supply a correction to these HJIEs. Moreover, for linear systems this correction is not necessary. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete‐time mixed ℋ︁2/ℋ︁∞ nonlinear filtering

In this paper, we consider the discrete‐time mixed ??₂/??_∞ filtering problem for affine nonlinear systems. Necessary and sufficient conditions for the solvability of this problem with a finite‐dimensional filter are given in terms of a pair of coupled discrete‐time Hamilton–Jacobi‐Isaac's equations (DHJIE) with some side‐conditions. For linear systems, it is shown that these conditions reduce to a pair of coupled discrete‐time algebraic‐Riccati‐equations (DAREs) or a system of linear matrix inequalities (LMIs) similar to the ones for the control case. Both the finite‐horizon and infinite‐horizon problems are discussed. Moreover, sufficient conditions for approximate solvability of the problem are also derived. These solutions are especially useful for computational purposes, considering the difficulty of solving the coupled DHJIEs. An example is also presented to demonstrate the approach. Copyright © 2010 John Wiley & Sons, Ltd.     

The Bang‐bang principle of time optimal controls for the Kuramoto–Sivashinsky–KdV equation with internal control

This paper is concerned with the time optimal control problem governed by the internal controlled Kuramoto–Sivashinsky–Korteweg‐de Vries equation, which describes many physical processes in motion of turbulence and other unstable process systems. We prove the existence of optimal controls with the help of the Carleman inequality, which has been widely used to obtain the local controllability or null controllability of parabolic differential systems. More precisely, with the help of the Carleman inequality, we obtain a relationship between the null controllability and time optimal control problem. Moreover, we give the bang‐bang principle for an optimal control of our original problem by using the one of approximate problems. This method is new for time optimal control problems. The bang‐bang principle established here seems also to be new for fourth‐order parabolic differential equations. Copyright © 2015 John Wiley & Sons, Ltd.     

On the design of output regulators for nonlinear systems

This paper considers the output regulation problem for nonlinear systems. By adding the assumption that the decoupling matrix of the system under consideration has maximum rank, the general results presented in Isidori and Byrnes (IEEE Trans. Automat. Control 35(2) (1990) 131–140) have been improved in three ways. Firstly, the precise form of the regulators is presented for multi-input multi-output affine nonlinear systems. Secondly, the number of unknown functions in the controller parameterization has been reduced. Finally, by introducing a hyperbolic realization and constructing auxiliary systems, a sufficient and generically necessary condition for the existence of the unknown functions is obtained. This condition is easily verifiable using only algebraic computation. These results provide a complete solution to the output regulation problem, for a class of nonlinear systems. It is also shown that for this class of systems, the output regulation problem is always generically solvable.     

Adaptive neural network control for a nonlinear Euler‐Bernoulli beam in three‐dimensional space with unknown control direction

In this paper, an adaptive neural network control system is developed for a nonlinear three‐dimensional Euler‐Bernoulli beam with unknown control direction. The Euler‐Bernoulli beam is modeled as a combination of partial differential equations (PDEs) and ordinary differential equations (ODEs). Adaptive radial basis function–based neural network control laws are designed to determine approximation of disturbances. A projection mapping operator is adopted to realize bounded approximation of disturbances. A Nussbaum function is introduced to compensate for the unknown control direction. The goal of this study is to suppress the vibrations of the Euler‐Bernoulli beam in three‐dimensional space. In addition, unknown control direction problem and bounded disturbances are considered to guarantee that the signals of the system are uniformly bounded. Numerical simulations demonstrate the effectiveness of the proposed method.     

Semi-global stabilization of partially linear composite systems via feedback of the state of the linear part

We consider the problem of semi-global stabilization of a class of partially linear composite systems. We show, by explicit construction of the control laws, that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi-globally stabilizable by a dynamic feedback of the state of the linear subsystem if (a) the linear subsystem is right invertible and has all its invariant zeros in the closed left half s-plane, and (b) the only linear variables entering the nonlinear subsystem are the output of the linear subsystem. Our work generalizes previous results by C.I. Byrnes and A. Isidori (1991), H.J. Sussmann and P.V. Kokotovic (1991), and A.R. Teel (1992).     

Solving the block–Toeplitz least‐squares problem in parallel

In this paper we present two versions of a parallel algorithm to solve the block–Toeplitz least‐squares problem on distributed‐memory architectures. We derive a parallel algorithm based on the seminormal equations arising from the triangular decomposition of the product T^TT. Our parallel algorithm exploits the displacement structure of the Toeplitz‐like matrices using the Generalized Schur Algorithm to obtain the solution in O(mn) flops instead of O(mn²) flops of the algorithms for non‐structured matrices. The strong regularity of the previous product of matrices and an appropriate computation of the hyperbolic rotations improve the stability of the algorithms. We have reduced the communication cost of previous versions, and have also reduced the memory access cost by appropriately arranging the elements of the matrices. Furthermore, the second version of the algorithm has a very low spatial cost, because it does not store the triangular factor of the decomposition. The experimental results show a good scalability of the parallel algorithm on two different clusters of personal computers. Copyright © 2005 John Wiley & Sons, Ltd.     

A cache‐efficient implementation of the lattice Boltzmann method for the two‐dimensional diffusion equation

The lattice Boltzmann method is an important technique for the numerical solution of partial differential equations because it has nearly ideal scalability on parallel computers for many applications. However, to achieve the scalability and speed potential of the lattice Boltzmann technique, the issues of data reusability in cache‐based computer architectures must be addressed. Utilizing the two‐dimensional diffusion equation, , this paper examines cache optimization for the lattice Boltzmann method in both serial and parallel implementations. In this study, speedups due to cache optimization were found to be 1.9–2.5 for the serial implementation and 3.6–3.8 for the parallel case in which the domain decomposition was optimized for stride‐one access. In the parallel non‐cached implementation, the method of domain decomposition (horizontal or vertical) used for parallelization did not significantly affect the compute time. In contrast, the cache‐based implementation of the lattice Boltzmann method was significantly faster when the domain decomposition was optimized for stride‐one access. Additionally, the cache‐optimized lattice Boltzmann method in which the domain decomposition was optimized for stride‐one access displayed superlinear scalability on all problem sizes as the number of processors was increased. Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation of the Helmholtz–Kohlrausch effect for natural images

The Helmholtz–Kohlrausch (H‐K) effect is the phenomenon in which two color stimuli have the same luminance but different chroma in a certain hue, so the perceived brightness induced by the two stimuli are different. In expanding gamut, it is necessary to consider the H‐K effect. A quantification of the H‐K effect is required in order to evaluate and develop display devices for which the change of perceived brightness of gamut expansion must be considered. For quantification of the H‐K effect, prediction equations that can derive the equivalent luminance in a single color image have been proposed in previous studies. However, these equations have not been applied to natural images that are important. Therefore, the purpose of this study is to quantify the H‐K effect by deriving calculated values for natural images. For this purpose, first, we conducted the quantification of the H‐K effect in natural images by deriving the equivalent luminance as calculated values expanding the three prediction equations proposed in previous studies. Next, we carried out a subjective evaluation experiment by varying image's chroma and luminance. We then verified the effectiveness of the calculated values by comparing them with the result from the experiment.     

Linear‐Quadratic Optimal Control Problems for Mean‐Field Stochastic Differential Equations with Jumps

In this paper, we study a linear‐quadratic optimal control problem for mean‐field stochastic differential equations driven by a Poisson random martingale measure and a one‐dimensional Brownian motion. Firstly, the existence and uniqueness of the optimal control is obtained by the classic convex variation principle. Secondly, by the duality method, the optimality system, also called the stochastic Hamilton system which turns out to be a linear fully coupled mean‐field forward‐backward stochastic differential equation with jumps, is derived to characterize the optimal control. Thirdly, applying a decoupling technique, we establish the connection between two Riccati equations and the stochastic Hamilton system and then prove the optimal control has a state feedback representation.