Constrained LQR Using Online Decomposition Techniques

This paper presents an algorithm to solve the infinite horizon constrained linear quadratic regulator (CLQR) problem using operator splitting methods. First, the CLQR problem is reformulated as a (finite-time) model predictive control (MPC) problem without terminal constraints. Second, the MPC problem is decomposed into smaller subproblems of fixed dimension independent of the horizon length. Third, using the fast alternating minimization algorithm to solve the subproblems, the horizon length is estimated online, by adding or removing subproblems based on a periodic check on the state of the last subproblem to determine whether it belongs to a given control invariant set. We show that the estimated horizon length is bounded and that the control sequence computed using the proposed algorithm is an optimal solution of the CLQR problem. Compared to state-of-the-art algorithms proposed to solve the CLQR problem, our design solves at each iteration only unconstrained least-squares problems and simple gradient calculations. Furthermore, our technique allows the horizon length to decrease online (a useful feature if the initial guess on the horizon is too conservative). Numerical results on a planar system show the potential of our algorithm.Comment: This technical report is an extended version of the paper titled "Constrained LQR Using Online Decomposition Techniques" submitted to the 2016 Conference on Decision and Contro

Guaranteeing Input Tracking For Constrained Systems: Theory and Application to Demand Response

A method for certifying exact input trackability for constrained discrete time linear systems is introduced in this paper. A signal is assumed to be drawn from a reference set and the system must track this signal with a linear combination of its inputs. Using methods inspired from robust model predictive control, the proposed approach certifies the ability of a system to track any reference drawn from a polytopic set on a finite time horizon by solving a linear program. Optimization over a parameterization of the set of reference signals is discussed, and particular instances of parameterization of this set that result in a convex program are identified, allowing one to find the largest set of trackable signals of some class. Infinite horizon feasibility of the methods proposed is obtained through use of invariant sets, and an implicit description of such an invariant set is proposed. These results are tailored for the application of power consumption tracking for loads, where the operator of the load needs to certify in advance his ability to fulfill some requirement set by the network operator. An example of a building heating system illustrates the results.Comment: Technical Not

Graded Dorsal and Differential Gene Regulation in the Drosophila Embryo

A gradient of Dorsal activity patterns the dorsoventral (DV) axis of the early Drosophila melanogaster embryo by controlling the expression of genes that delineate presumptive mesoderm, neuroectoderm, and dorsal ectoderm. The availability of the Drosophila melanogaster genome sequence has accelerated the study of embryonic DV patterning, enabling the use of systems-level approaches. As a result, our understanding of Dorsal-dependent gene regulation has expanded to encompass a collection of more than 50 genes and 30 cis-regulatory sequences. This information, which has been integrated into a spatiotemporal atlas of gene regulatory interactions, comprises one of the best-understood networks controlling any developmental process to date. In this article, we focus on how Dorsal controls differential gene expression and how recent studies have expanded our understanding of Drosophila embryonic development from the cis-regulatory level to that controlling morphogenesis of the embryo

Quantitative imaging of the Dorsal nuclear gradient reveals limitations to threshold-dependent patterning in Drosophila

The NF-κB-related transcription factor, Dorsal, forms a nuclear concentration gradient in the early Drosophila embryo, patterning the dorsal-ventral (DV) axis to specify mesoderm, neurogenic ectoderm, and dorsal ectoderm cell fates. The concentration of nuclear Dorsal is thought to determine these patterning events; however, the levels of nuclear Dorsal have not been quantified previously. Furthermore, existing models of Dorsal-dependent germ layer specification and patterning consider steady-state levels of Dorsal relative to target gene expression patterns, yet both Dorsal gradient formation and gene expression are dynamic. We devised a quantitative imaging method to measure the Dorsal nuclear gradient while simultaneously examining Dorsal target gene expression along the DV axis. Unlike observations from other insects such as Tribolium, we find the Dorsal gradient maintains a constant bell-shaped distribution during embryogenesis. We also find that some classical Dorsal target genes are located outside the region of graded Dorsal nuclear localization, raising the question of whether these genes are direct Dorsal targets. Additionally, we show that Dorsal levels change in time during embryogenesis such that a steady state is not reached. These results suggest that the multiple gene expression outputs observed along the DV axis do not simply reflect a steady-state Dorsal nuclear gradient. Instead, we propose that the Dorsal gradient supplies positional information throughout nuclear cycles 10-14, providing additional evidence for the idea that compensatory combinatorial interactions between Dorsal and other factors effect differential gene expression along the DV axis

Lipoplatin Formulation Review Article

Patented platform technologies have been used for the liposomal encapsulation of cisplatin (Lipoplatin) into tumor-targeted 110 nm (in diameter) nanoparticles. The molecular mechanisms, preclinical and clinical data concerning lipoplatin, are reviewed here. Lipoplatin has been successfully administered in three randomized Phase II and III clinical trials. The clinical data mainly include non-small-cell lung cancer but also pancreatic, breast, and head and neck cancers. It is anticipated that lipoplatin will replace cisplatin as well as increase its potential applications. For the first time, a platinum drug has shown superiority to cisplatin, at least in non-squamous non-small-cell lung cancer as reported in a Phase III study which documented a simultaneous lowering of all of the side effects of cisplatin

Image analysis and empirical modeling of gene and protein expression

Protein gradients and gene expression patterns are major determinants in the differentiation and fate map of the developing embryo. Here we discuss computational methods to quantitatively measure the positions of gene expression domains and the gradients of protein expression along the dorsal–ventral axis in the Drosophila embryo. Our methodology involves three layers of data. The first layer, or the primary data, consists of z-stack confocal images of embryos processed by in situ hybridization and/or antibody stainings. The secondary data are relationships between location, usually an x-axis coordinate, and fluorescent intensity of gene or protein detection. Tertiary data comprise the optimal parameters that arise from fits of the secondary data to empirical models. The tertiary data are useful to distill large datasets of imaged embryos down to a tractable number of conceptually useful parameters. This analysis allows us to detect subtle phenotypes and is adaptable to any set of genes or proteins with a canonical pattern. For example, we show how insights into the Dorsal transcription factor protein gradient and its target gene ventral-neuroblasts defective (vnd) were obtained using such quantitative approaches

Size-dependent regulation of dorsal–ventral patterning in the early Drosophila embryo

How natural variation in embryo size affects patterning of the Drosophila embryo dorsal–ventral (DV) axis is not known. Here we examined quantitatively the relationship between nuclear distribution of the Dorsal transcription factor, boundary positions for several target genes, and DV axis length. Data were obtained from embryos of a wild-type background as well as from mutant lines inbred to size select embryos of smaller or larger sizes. Our data show that the width of the nuclear Dorsal gradient correlates with DV axis length. In turn, for some genes expressed along the DV axis, the boundary positions correlate closely with nuclear Dorsal levels and with DV axis length; while the expression pattern of others is relatively constant and independent of the width of the Dorsal gradient. In particular, the patterns of snail (sna) and ventral nervous system defective (vnd) correlate with nuclear Dorsal levels and exhibit scaling to DV length; while the pattern of intermediate neuroblasts defective (ind) remains relatively constant with respect to changes in Dorsal and DV length. However, in mutants that exhibit an abnormal expansion of the Dorsal gradient which fails to scale to DV length, only sna follows the Dorsal distribution and exhibits overexpansion; in contrast, vnd and ind do not overexpand suggesting some additional mechanism acts to refine the dorsal boundaries of these two genes. Thus, our results argue against the idea that the Dorsal gradient works as a global system of relative coordinates along the DV axis and suggest that individual targets respond to changes in embryo size in a gene-specific manner