Large-scale systems: Complexity, stability, reliability

After showing that a complex dynamic system with a competitive structure has highly reliable stability, a class of noncompetitive dynamic systems for which competitive models can be constructed is defined. It is shown that such a construction is possible in the context of the hierarchic stability analysis. The scheme is based on the comparison principle and vector Liapunov functions

Absolute Stability and Parameter Sensitivity

Absolute stability notion extended to include parameter variations of linear part of syste

Parameter plane analysis of forced nonlinear oscillations

Parameter plane analysis of forced oscillations and jump resonance phenomena in nonlinear system

Algebraic methods for control system analysis and design Final report, Apr. 1967 - Apr. 1969

Algebraic methods for analysis and design of control system

Absolute stability analysis of attitude control systems for large boosters

Absolute stability analysis of attitude control systems for large launch vehicle

Decomposition-aggregation stability analysis

This report presents the development and description of the decomposition aggregation approach to stability investigations of high dimension mathematical models of dynamic systems. The high dimension vector differential equation describing a large dynamic system is decomposed into a number of lower dimension vector differential equations which represent interconnected subsystems. Then a method is described by which the stability properties of each subsystem are aggregated into a single vector Liapunov function, representing the aggregate system model, consisting of subsystem Liapunov functions as components. A linear vector differential inequality is then formed in terms of the vector Liapunov function. The matrix of the model, which reflects the stability properties of the subsystems and the nature of their interconnections, is analyzed to conclude over-all system stability characteristics. The technique is applied in detail to investigate the stability characteristics of a dynamic model of a hypothetical spinning Skylab

A multilevel control system for the large space telescope

A multilevel scheme was proposed for control of Large Space Telescope (LST) modeled by a three-axis-six-order nonlinear equation. Local controllers were used on the subsystem level to stabilize motions corresponding to the three axes. Global controllers were applied to reduce (and sometimes nullify) the interactions among the subsystems. A multilevel optimization method was developed whereby local quadratic optimizations were performed on the subsystem level, and global control was again used to reduce (nullify) the effect of interactions. The multilevel stabilization and optimization methods are presented as general tools for design and then used in the design of the LST Control System. The methods are entirely computerized, so that they can accommodate higher order LST models with both conceptual and numerical advantages over standard straightforward design techniques

Algebraic methods for dynamic systems

Algebraic methods for application to dynamic control system

Primula vulgaris (primrose) genome assembly, annotation and gene expression, with comparative genomics on the heterostyly supergene

Primula vulgaris (primrose) exhibits heterostyly: plants produce self-incompatible pin- or thrum-form flowers, with anthers and stigma at reciprocal heights. Darwin concluded that this arrangement promotes insect-mediated cross-pollination; later studies revealed control by a cluster of genes, or supergene, known as the S (Style length) locus. The P. vulgaris S locus is absent from pin plants and hemizygous in thrum plants (thrum-specific); mutation of S locus genes produces self-fertile homostyle flowers with anthers and stigma at equal heights. Here, we present a 411 Mb P. vulgaris genome assembly of a homozygous inbred long homostyle, representing ~87% of the genome. We annotate over 24,000 P. vulgaris genes, and reveal more genes up-regulated in thrum than pin flowers. We show reduced genomic read coverage across the S locus in other Primula species, including P. veris, where we define the conserved structure and expression of the S locus genes in thrum. Further analysis reveals the S locus has elevated repeat content (64%) compared to the wider genome (37%). Our studies suggest conservation of S locus genetic architecture in Primula, and provide a platform for identification and evolutionary analysis of the S locus and downstream targets that regulate heterostyly in diverse heterostylous species