Minimum-fuel control of high-order systems

The minimum-fuel control problem is of special interest in various space systems. To date, solutions of minimum-fuel control problems have been carried out for relatively low-order systems. Space structures, however, are generally characterized by a large number of degrees of freedom, so that minimum-fuel control of such systems requires a new approach. In the independent modal-space control (IMSC) method, the control laws are designed in the modal space for each mode independently. The minimum-fuel problem reduces to that of a set of independent second-order systems, so that minimum-fuel control is possible. This paper shows how the IMSC method can be used to control a space structure with a minimum amount of fuel. A numerical example is presented.This research was supported by NASA Research Grant No. NAG-1-225, sponsored by the Spacecraft Control Branch, Langley Research Center.     

异结构离散型混沌系统的延迟同步

以异结构离散型混沌系统为研究对象,设计了一种延迟同步控制器实现了离散型Henon混沌系统和Ikeda混沌系统之间的同步控制．根据稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程．设计的延迟同步控制器对于不同的离散型混沌系统具有统一的形式,可以实现任意异结构离散型混沌系统之间的延迟同步．数值仿真模拟进一步验证了该控制器的有效性．     

不确定环境下多自主体系统的分布式估计与控制

多自主体系统是当前系统控制界研究的热点问题. 在实际中, 自主体系统通常并不是在理想的环境下执行任务, 而是面临多源头、多层次和多变化的各类不确定性因素的影响. 它们通过在微观层面上影响各自主体决策的正确性, 从而在宏观上对自主体系统的整体行为产生显著影响. 不确定性因素和多自主体系统分布式信息架构交互耦合, 给系统的设计与分析带来本质性困难. 本文围绕分布式估计与分布式控制问题, 研究在随机通信噪声、数据丢失、量化和系统未知结构参数等不确定因素影响下, 如何为各自主体设计更加鲁棒、更加有效的分布式估计算法及分布式控制律, 以实现全局估计与控制目标, 并对闭环系统性能进行系统分析.     

Control parameters in Boolean networks and cellular automata revisited from a logical and a sociological point of view

The use of “control parameters” as applied to describe the dynamics of complex mathematical systems within models of real social systems is discussed. Whereas single control parameters cannot sufficiently characterize the dynamics of such systems it is suggested that domains of values of certain sets of parameters are appropriately denoting necessary conditions for highly disordered dynamics of social systems. Various of those control parameters permit a straightforward interpretation in terms of properties of social rules and structures. © 1999 John Wiley & Sons, Inc.     

Localization phenomena in structural dynamics

A survey of vibration localization phenomena in the context of structural dynamics and vibrations is presented. The review covers the more common and relevant cases where mode localization and vibration confinement are likely to occur in engineering structures. Examples considered include periodic or nearly periodic multi-span beams and multi-bay trusses, large space structures, space antennas, and almost periodic (a.p.) structures with circular symmetry, e.g., bladed disks in turbomachines. Both analytical and numerical methods for analyzing and predicting localization in finite and infinite systems are discussed. In this paper, we show how the problem of mode localization and vibration confinement can be formulated as a problem in the theory of stability of differential equations with a.p. coefficients. Using stability theory, new definitions of mode localization can be established for both linear and nonlinear structures. The possibility of stabilizing certain nonconservative fluid-structure systems using structural disorder is demonstrated, and stability theorems are given for aeroelastic systems governed by normal operators. We also illustrate how the results from localization theory and the associated stability theory can be applied to the vibration control problem, by triggering vibration confinement by active or passive means.     

Stochastic stability analysis for joint process driven and networked hybrid systems

The stochastic stability and impulsive noise disturbance attenuation in a class of joint process driven and networked hybrid systems with coupling delays (JPDNHSwD) has been investigated. In particular, there are two separable processes monitoring the networked hybrid systems. One drives inherent network structures and properties, the other induces random variations in the control law. Continuous dynamics and control laws in networked subsystems and couplings among subsystems change as events occur stochastically in a spatio-temporal fashion. When an event occurs, the continuous state variables may jump from one value to another. Using the stochastic Lyapunov functional approach, sufficient conditions on the existence of a remote time-delay feedback controller which ensures stochastic stability for this class of JPDNHSwD are obtained. The derived conditions are expressed in terms of solutions of LMIs. An illustrative example of a dynamical network driven by two Markovian processes is used to demonstrate the satisfactory control performance.     

Optimal actuator locations and precision micro-control actions on free paraboloidal membrane shells

Flexible paraboloidal shells, as key components, are increasingly utilized in antennas, reflectors, optical systems, aerospace structures, etc. To explore precise shape and vibration control of the paraboloidal membrane shells, this study focuses on analysis of microscopic control actions of segmented actuator patches laminated on the surface of a free paraboloidal membrane shell. Governing equations of the membrane shell system and modal control forces of distributed actuator patches are presented first, and followed by the analysis of dominating micro-control actions based on various natural modes, actuator locations and geometrical parameters. Finally, according to the parametric analysis, simulation data reveal main factors significantly influencing active control behavior on smart free-floating paraboloidal membrane shell systems, thus providing design guidelines to achieve optimal control of paraboloidal shell systems.     

A Hybrid Systems Framework for Motion Planning with Motion Primitives of Mechanical Systems

Motion planning with motion primitives is a solution concept for the optimal control of mechanical systems based on a quantization of the search space. In this contribution, we write the resulting system as a hybrid automaton and discuss the arising structures. In this context, we focus on the exploitation of symmetries. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration reduction in a 2DOF twin-tail system to parametric excitations

The use of active feedback control strategy is a common way to stabilize and control dangerous vibrations in vibrating systems and structures, such as bridges, highways, buildings, space and aircrafts. These structures are distributed-parameter systems. Unfortunately, the existing vibrations control techniques, even for these simplified models, are fraught with numerical difficulties and engineering limitations. In this paper, a negative velocity feedback is added to the dynamical system of twin-tail aircraft, which is represented by two coupled second-order nonlinear differential equations having both quadratic and cubic nonlinearities. The system describes the vibration of an aircraft tail subjected to multi-parametric excitation forces. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations and obtain approximate solutions up to the third order approximations. The stability of the system is investigated applying frequency response equations. The effects of the different parameters are studied numerically. Some different resonance cases are investigated. A comparison is made with the available published work.     

Design of an optimal tuned mass damper for a system with parametric uncertainty

Structural control is becoming an attractive alternative for enhanced performance of civil engineering structures subject to seismic and wind loads. However, in order to guarantee stability and performance of structures when implemented with a passive or active control technique, there is a need to include information of uncertainty in the structural models due to the fact that civil engineering structures are time variant and nonlinear. These variations in the structure are often due to parameters such as variable live loads and inelastic behavior and, in cases, may be modeled as parametric uncertainty. The design of an optimal tuned mass damper (TMD) for a one degree-of-freedom (SDOF) system with parametric uncertainty is presented in this paper. The optimization of the connection between the absorber and the primary structure is cast as a constant feedback problem which is solved using structured singular value, μ, synthesis with D-K iteration and decentralized H _∞ design. Results are presented of the TMD that minimize the harmonic response of the primary structure represented by a set of systems within an uncertainty set.     

Chaos control for Willamowski–Rössler model of chemical reactions

Real systems evolving towards complex state encounter chaotic behavior. This behavior is very important in chemical processes or in biological structures because it defines the direction of the evolution of the system. From this point of view, the capability of deliberate control of these phenomena has a great practical impact despite the fact that it is very difficult; this is the reason why theoretical models are useful in these situations. In order to obtain chaos control in chemical reactions, the analysis of the dynamics of Willamowski–Rössler system involving the synchronization of two Minimal Willamowski–Rössler (MWR) systems based on the adaptive feedback method of control is presented in this work. As opposed to previous studies where in order to obtain synchronization 3 controllers were used, implying from a practical point of view the control of the concentrations of three chemical species, in this study we showed that the use of just one is sufficient which in practice is important as controlling the concentration of a single chemical species would be much easier. We also showed that the transient time until synchronization depends on initial conditions of two systems, the strength and number of the controllers and we attempted to identify the best conditions for a practical synchronization.     

From one-dimensional to infinite-dimensional dynamical systems: Ideal turbulence

There is a very short chain that joins dynamical systems with the simplest phase space (real line) and dynamical systems with the “most complicated” phase space containing random functions, as well. This statement is justified in this paper. By using “simple” examples of dynamical systems (one-dimensional and two-dimensional boundary-value problems), we consider notions that generally characterize the phenomenon of turbulence—first of all, the emergence of structures (including the cascade process of emergence of coherent structures of decreasing scales) and self-stochasticity.     

RECOGNIZING ESSENTIALLY DISCONNECTED BENZENOIDS WITH FIXED DOUBLE BONDS

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Logarithmic Frobenius structures and Coxeter discriminants

We consider a class of solutions of the WDVV equation related to the special systems of covectors (called ∨-systems) and show that the corresponding logarithmic Frobenius structures can be naturally restricted to any intersection of the corresponding hyperplanes. For the Coxeter arrangements the corresponding structures are shown to be almost dual in Dubrovin's sense to the Frobenius structures on the strata in the discriminants discussed by Strachan. For the classical Coxeter root systems this leads to the families of ∨-systems from the earlier work by Chalykh and Veselov. For the exceptional Coxeter root systems we give the complete list of the corresponding ∨-systems. We present also some new families of ∨-systems, which cannot be obtained in such a way from the Coxeter root systems.     

Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.

ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.

Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.

In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.

In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.     

Robust inverse optimal control for flexible structures

An inverse optimal control problem is formulated to develop robust control laws for purely oscillatory systems. The optimal control solution requires output feedback with specified constraints, leading to robustness with respect to unmodeled modes and a large class of parameter variations. The robustness properties are proved directly from known properties of control laws resulting from quadratic performance indices. The control laws are useful for poorly damped flexible structures.This research was supported by the Office of Naval Research, Contract No. N00014-77-C-0247.     

A computational method for solving optimal control of a system of parallel beams using Legendre wavelets

The optimal control of transverse vibration of two Euler–Bernoulli beams coupled in parallel by discrete springs is considered. An index of performance is formulated which consists of a modified energy functional of two coupled structures at a specified time and penalty functions involving the point control forces. The minimization of the performance index over these forces is subject to the equation of motion governing the structural vibrations, the imposed initial condition as well as the boundary conditions. By use of the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of a linear time-invariant lumped-parameter systems. A computationally attractive method based on Legendre wavelets in time domain for solving the optimal control of the lumped parameter systems for any finite interval is proposed. Legendre wavelet integral operational matrix and the properties of a Kronecker product are used to find the approximated optimal trajectory and optimal law of the linear systems with respect to a quadratic cost function by only solving a linear system of algebraic equations. This method provides a straightforward and convenient approach for digital computation. A numerical example is provided to demonstrate the applicability and effectiveness of the proposed method.     

Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas

The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Positivity embedding for noncolocated and nonsquare flexible systems

Positivity based control design for flexible structures provides closed-loop stability regardless of parameter variations and unmodeled dynamics. The present framework requires the plant to be square and the actuators colocated with rate sensors. These constraints severely limit achievable performance in control systems using the positivity approach. In this paper, a dynamic embedding is derived to render a nonsquare plant with noncolocated actuators and sensors positive real. The dynamic embedding is parametrized for general flexible structures. A numerical algorithm is developed to compute the embedding parameters. The Draper tetrahedral truss structure is used to demonstrate the design of dynamic embeddings. Relaxing the colocation constraint in a positivity based design significantly improves the closed-loop performance.