A general linear-time evaluator for attribute grammars

The theory of the elastic fields round ellipsoidal inclusions and inhomogeneities together with the well-known analogy between linear elasticity and slow incompressible viscous flow are used to develop the governing equations for the finite deformation of a viscous ellipsoidal inhomogeneity in a viscous matrix undergoing a general linear time-dependent flow at infinity. The governing equations are then solved for an inhomogeneity in the form of an elliptic cylinder in a linear two-dimensional flow whose stream lines at infinity are steady. The behaviour of the inhomogeneity under pure shear and simple shear is considered in detail and it is shown that the boundaries of certain deforming inhomogeneities remain unchanged during simple shear. These steady inhomogeneities can appear also in general linear two-dimensional applied flows. In such flows the behaviour is influenced both by the initial shape and orientation of the inhomogeneity and by its viscosity. Inhomogeneities which are rather viscous or subject to an applied flow with high vorticity deform periodically, while most others elongate indefinitely. The patterns of behaviour may be described in terms of a number of regimes which can be classified by considering the singularities of the differential equations governing the variations of shape and orientation of the inhomogeneity, or, equivalently, by studying the invariants of the corresponding one-parameter Lie groups. Finally, some obvious extensions of the treatment are indicated. These make it possible to consider inhomogeneities (such as holes) whose volume does not remain constant, and which have constitutive relations more general than those of a linear viscous material.

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Modelling Systems over General Linear Time

2016 23rd International Symposium on Temporal Representation and Reasoning (TIME) ◽

10.1109/time.2016.21 ◽

2016 ◽

Author(s):

John McCabe-Dansted ◽

Mark Reynolds ◽

Tim French

Keyword(s):

Linear Time ◽

General Linear

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The complexity of the temporal logic with “until” over general linear time

Journal of Computer and System Sciences ◽

10.1016/s0022-0000(03)00005-9 ◽

2003 ◽

Vol 66 (2) ◽

pp. 393-426 ◽

Cited By ~ 28

Author(s):

M. Reynolds

Keyword(s):

Temporal Logic ◽

Linear Time ◽

General Linear

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Exact Model Matching and Disturbance Rejection for General Linear Time Delay Systems Via Measurement Output Feedback

2005 IEEE Conference on Emerging Technologies and Factory Automation ◽

10.1109/etfa.2005.1612571 ◽

2006 ◽

Cited By ~ 8

Author(s):

F.N. Koumboulis ◽

G.E. Panagiotakis

Keyword(s):

Time Delay ◽

Output Feedback ◽

Disturbance Rejection ◽

Linear Time ◽

Delay Systems ◽

General Linear ◽

Time Delay Systems ◽

Model Matching ◽

Exact Model ◽

Measurement Output

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An Optimal Control Approach for Consensus of General Linear Time-Invariant Multi-Agent Systems

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4050505 ◽

2021 ◽

Vol 143 (9) ◽

Author(s):

Poorya Shobeiry ◽

Ming Xin

Keyword(s):

Optimal Control ◽

Cooperative Control ◽

Linear Time ◽

General Linear ◽

Control Law ◽

Multi Agent Systems ◽

Agent Systems ◽

Linear Time Invariant ◽

Multi Agent ◽

Time Invariant

Abstract In this paper, the consensus problem for general linear time-invariant (LTI) multi-agent systems (MASs) with a single input is studied in a new optimal control framework. The optimal cooperative control law is designed from a modified linear quadratic regulator (LQR) method and an inverse optimal control formulation. Three cost function terms are constructed to address the consensus, control effort, and cooperative tracking, respectively. Three distinct features of this approach can be achieved. First, the optimal feedback control law is derived analytically without involving any numerical solution. Second, this formulation guarantees both asymptotic stability and optimality. Third, the cooperative control law is distributed and only requires local information based on the communication topology to enable the agents to achieve consensus and track a desired trajectory. The performance of this optimal cooperative control method is demonstrated through an example of attitude synchronization of multiple satellites.

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