Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns

In this paper, a backpropagating constraints-based trajectory tracking control (BCTTC) scheme is addressed for trajectory tracking of a quadrotor with complex unknowns and cascade constraints arising from constrained actuator dynamics, including saturations and dead zones. The entire quadrotor system including actuator dynamics is decomposed into five cascade subsystems connected by intermediate saturated nonlinearities. By virtue of the cascade structure, backpropagating constraints (BCs) on intermediate signals are derived from constrained actuator dynamics suffering from nonreversible rotations and nonnegative squares of rotors, and decouple subsystems with saturated connections. Combining with sliding-mode errors, BC-based virtual controls are individually designed by addressing underactuation and cascade constraints. In order to remove smoothness requirements on intermediate controls, first-order filters are employed, and thereby contributing to backstepping-like subcontrollers synthesizing in a recursive manner. Moreover, universal adaptive compensators are exclusively devised to dominate intermediate tracking residuals and complex unknowns. Eventually, the closed-loop BCTTC system stability can be ensured by the Lyapunov synthesis, and trajectory tracking errors can be made arbitrarily small. Simulation studies demonstrate the effectiveness and superiority of the proposed BCTTC scheme for a quadrotor with complex constrains and unknowns

The growth defect of <i>elo-5</i>(<i>lf</i>) is suppressed by mutations in <i>prx-5</i> and <i>prx-6</i>.

<p>(A) Structure of mmBCFA C17ISO (15-methyl hexadecanoic acid) and C15ISO (13-methyl tetradecanoic acid). ELO-5 and ELO-6 are responsible for synthesis of C15ISO and C17ISO. (B-E) Microscopic images of <i>C. elegans</i> of indicated genotypes and treatments. Unlike WT (B) <i>elo-5</i>(<i>lf</i>) mutants depleted for mmBCFA after hatching display a robust L1 growth arrest phenotype (indicated by arrows) (C) that can be overcome by dietary supplementation of C17ISO (D). The growth arrest phenotype of <i>elo-5</i>(<i>lf</i>) is suppressed by the <i>ku517</i> allele (E). (F) Schematic representation of the suppressor screen. The extrachromosomal array is composed of two transgenic markers: GFP and <i>rol-6</i>(<i>dn</i>), but only GFP is shown in the cartoon for simplicity. (G) Bar graph showing percentage of animals that reached adulthood for strains with indicated genotypes. Three loss-of-function (<i>lf</i>) mutations in the <i>prx-5</i> and <i>prx-6</i> genes significantly suppressed the L1 arrest phenotype of <i>elo-5</i>(<i>lf</i>).</p

<i>prx-5/6</i> mutations likely cause a decrease in mmBCFA degradation.

<p>(A) qRT-PCR data showing mRNA levels of the <i>elo-6</i> gene in worms of indicated genotypes. <i>elo-5</i>(<i>lf</i>)<i>; Ex</i>[<i>elo-6</i>] is a transgenic strain that significantly overexpressed the <i>elo-6</i> gene and was not sufficient to suppress the L1 arrest phenotype of <i>elo-5</i>(<i>lf</i>). The data suggest that a higher level of <i>elo-6</i> expression is not likely the cause of the suppression. (B) qRT-PCR data showing mRNA levels corresponding to several other FA elongation enzymes in worms of indicated genotypes. Since the <i>elo-5</i> mRNA being measured is from the <i>elo-5</i>(<i>gk208, deletion</i>) allele, the significant decrease in <i>elo-5</i> mRNA level is likely due to mutation-induced mRNA degradation. (C) Comparison of mmBCFA composition in the indicated strains. Percentage of C15ISO and C17ISO has a statistically significant increase in the <i>maoc-1</i>(<i>lf</i>) mutant.</p

<i>prx-5</i>(<i>lf</i>) increases mmBCFA C17ISO level in <i>elo-5</i>(<i>lf</i>) mutant and its suppression depends on the <i>elo-6</i>.

<p>(A) C17ISO levels in worms of indicated genotypes cultured without mmBCFA supplementation. C17ISO concentration is dramatically decreased in <i>elo-5</i>(<i>lf</i>) animals compared to wild-type worms, and partially recovered in two suppressor mutants <i>prx-5</i>(<i>ku517</i>)<i>; elo-5</i>(<i>lf</i>) and <i>prx-5</i>(<i>tm4948</i>)<i>; elo-5</i>(<i>lf</i>). Three replicates were done for each sample. Data are presented as average concentration with corresponding standard deviation (s.d.). (B-C) Microscopic images of <i>C. elegans</i> of indicated genotypes and treatments. <i>prx-5</i>(<i>ku517</i>) overcame the L1 arrest of <i>elo-5</i>(<i>lf</i>) (B), but this suppression was reversed when <i>elo-6</i> was knocked down by RNAi (C). (D) Bar graph showing percentage of animals that reached adulthood for <i>prx-5</i>(<i>ku517</i>)<i>; elo-5</i>(<i>lf</i>) with or without <i>elo-6</i> RNAi.</p

Somatic Trangene Silencing by <i>tam-1(lf)</i> Is Desilenced by RNAi of the SynMuv Suppressor Genes and Dicer

<div><p>(A–B) <i>myo-3</i> promoter driving-GFP reporters <i>(myo-3::Ngfp-lacZ</i>, <i>myo-3::Mtgfp)</i> displayed significant transgene silencing in the somatic tissues (mainly the muscles) in the <i>tam-1(cc567)</i> mutant (B), but not in the WT animals (A) [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-b011" target="_blank">11</a>].</p><p>(C–F) RNAi of the SynMuv suppressors, <i>mes-4</i> (C), <i>mrg-1</i> (D), and <i>isw-1</i> (E) as well as a non-SynMuv suppressor gene, <i>dcr-1</i> (F), restored GFP expression in the <i>tam-1(cc567)</i> mutant. <i>dcr-1</i> encodes the C. elegans Dicer protein that is required for <i>RNAi</i> [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-b081" target="_blank">81</a>,<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-b082" target="_blank">82</a>]. Bar: 100 μm.</p><p>(G–H) The relative levels of <i>gfp/lacZ</i> of a transgene <i>ccIs4251 (myo-3::Ngfp-lacZ</i>, <i>myo-3::Mtgfp)</i> [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-b011" target="_blank">11</a>] were measured by qRT-PCR in various genetic background indicated. The level of <i>ama-1</i> mRNA, encoding an RNA PolII, was used as the internal reference. Mean values and ranges of the <i>lacZ/ama-1</i> ratios based on three qRT-PCR trials are shown.</p></div

The SynMuv Suppressor Genes Are Required for Germline Transgene Silencing in WT Animals and for the <i>lag-2::gfp</i> Ectopic Expression in <i>lin-15B(n744)</i>

<div><p>(A–D) DIC (A) and (C) and GFP fluorescence (B) and (D) images of hermaphrodite germline from transgenic strain PD7271 that contains the multicopy <i>let-858::gfp</i> reporters [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-b075" target="_blank">75</a>]. Brackets indicate the region of germ cell nuclei. The transgene was silenced in WT, but desilenced in animals treated with <i>mrg-1(RNAi).</i> RNAi of seven other SynMuv suppressors also displayed a similar effect (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-t003" target="_blank">Table 3</a>). Bar: 10 μm.</p><p>(E–H) GFP fluorescence images of mid-L4 larvae carrying the <i>lag-2::gfp</i> transgene. (E) WT animals display a strong expression of the transgene in distal tip cells (arrowheads) and the vulva (asterisks). (F–G) a strong ectopic expression of the transgene in the intestine (arrows) is seen in two SynMuv mutants. (H) RNAi of <i>isw-1</i> suppressed the ectopic expression of <i>lag-2::gfp</i> in the intestine of the <i>lin-15B(n744)</i> mutant, but not its expression in distal tip cells and vulval cells. RNAi of 14 other SynMuv suppressors also displayed a similar effect (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-t003" target="_blank">Table 3</a>). Bar: 100 μm.</p></div

Functional Analysis of Neuronal MicroRNAs in <i>Caenorhabditis elegans</i> Dauer Formation by Combinational Genetics and Neuronal miRISC Immunoprecipitation

<div><p>Identifying the physiological functions of microRNAs (miRNAs) is often challenging because miRNAs commonly impact gene expression under specific physiological conditions through complex miRNA::mRNA interaction networks and in coordination with other means of gene regulation, such as transcriptional regulation and protein degradation. Such complexity creates difficulties in dissecting miRNA functions through traditional genetic methods using individual miRNA mutations. To investigate the physiological functions of miRNAs in neurons, we combined a genetic “enhancer” approach complemented by biochemical analysis of neuronal miRNA-induced silencing complexes (miRISCs) in <i>C. elegans</i>. Total miRNA function can be compromised by mutating one of the two GW182 proteins (AIN-1), an important component of miRISC. We found that combining an <i>ain-1</i> mutation with a mutation in <i>unc-3</i>, a neuronal transcription factor, resulted in an inappropriate entrance into the stress-induced, alternative larval stage known as dauer, indicating a role of miRNAs in preventing aberrant dauer formation. Analysis of this genetic interaction suggests that neuronal miRNAs perform such a role partly by regulating endogenous cyclic guanosine monophosphate (cGMP) signaling, potentially influencing two other dauer-regulating pathways. Through tissue-specific immunoprecipitations of miRISC, we identified miRNAs and their likely target mRNAs within neuronal tissue. We verified the biological relevance of several of these miRNAs and found that many miRNAs likely regulate dauer formation through multiple dauer-related targets. Further analysis of target mRNAs suggests potential miRNA involvement in various neuronal processes, but the importance of these miRNA::mRNA interactions remains unclear. Finally, we found that neuronal genes may be more highly regulated by miRNAs than intestinal genes. Overall, our study identifies miRNAs and their targets, and a physiological function of these miRNAs in neurons. It also suggests that compromising other aspects of gene expression, along with miRISC, can be an effective approach to reveal miRNA functions in specific tissues under specific physiological conditions.</p></div

The <i>C. elegans zfp-1</i> Gene

<div><p>(A) Schematic illustration of the transcripts and proteins of <i>zfp-1</i> (<a href="http://www.wormbase.org" target="_blank">http://www.wormbase.org</a>). In <i>zfp-1(ok554)</i> mutant, the fifth and sixth exons were deleted and 2 nucleotides (CG) were inserted. Therefore, the short isoform, ZFP-1S, is unlikely to produce any proteins and the long isoform is expected to generate a truncated protein that lacks the OM-LZ motifs in the mutant.</p><p>(B) Diagram of the functional motifs of the long isoform of ZFP-1 and the sequence alignment of the OM and LZ motifs. C. elegans ZFP-1 and its homologs from human (hAF10) and <i>Drosophila</i> (Alhambra) are compared.</p></div

The SynMuv Suppressor Genes Antagonize the SynMuv B Genes on Germline-Soma Distinction and <i>pgl-1</i> Expression

<div><p>(A) The early larval arrest phenotype associated with the SynMuv B mutation <i>mep-1(lf)</i> was rescued by RNAi of <i>mrg-1.</i> The growth-arrested L1 larvae of <i>mep-1(lf)</i> (arrowheads) and the rescued adults of <i>mep-1(lf)</i> treated with <i>mrg-1(RNAi)</i> (arrow) are indicated. RNAi of 11 other SynMuv suppressor genes displayed a varying degree of rescue (<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.0020074#pgen-0020074-t003" target="_blank">Table 3</a>).</p><p>(B) Quantification of relative mRNA levels of the germline specific gene <i>pgl-1</i> in animals with the genotype indicated. Only three strong larval arrest rescuers, <i>mes-4, mrg-1,</i> and <i>isw-1,</i> were assayed here. <i>rpl-26</i> was used as the internal reference. Mean values and ranges of the <i>pgl-1</i>/<i>rpl-26</i> ratios based on three qRT-PCR trials are shown.</p><p>(C–K) Immunostaining using an anti–PGL-1 antibody shows that <i>mep-1(q660)</i> and <i>mrg-1(RNAi)</i> have opposite effects on ectopic expression of <i>pgl-1</i> in soma. (C–E) Immunofluoresence micrographs of L1 larvae stained with an anti-PGL antibody (red). The genotype of each animal is indicated at the bottom of the corresponding column. (F–H) DAPI staining (blue) of the same animals to indicate nuclei. (I–K) The merged micrographs. White arrowheads indicate germline cells. Arrows indicate the hypodermal cells. The <i>mep-1</i> mutation (D, G, and J) as well as several other SynMuv B genes (not shown, see text) caused ectopic staining of PGL-1 in somatic cells such as hypodermal cells. This ectopic staining was suppressed by <i>mrg-1</i>(RNAi) (E, H, and K) and RNAi of two other SynMuv suppressor genes (<i>isw-1</i> and <i>mes-4</i>)(not shown, text). Bar: 100 μm for A, 10 μm for C-K.</p></div

Neuronal miRNAs act in parallel to UNC-3 to repress undesired dauer formation by potentially affecting IIS and TGF-β signaling.

<p><b>A–D. </b><b>A.</b> Bar graph representing the percent of dauer progeny of indicated genotypes. * indicates that <i>ain-1(lf)</i> mutants were not tested in parallel to these specific experiments. Alleles used are <i>ain-1(ku322 lf), unc-3(e151 lf), and ain-2(tm2432 lf)</i><b>B.</b> Relative dauer rate of <i>unc-3(e151 lf) ain-1(ku322 lf)</i> transgenic mutants carrying the designated extrachromosomal array. Relative dauer rate was determined by normalizing the percent of dauer progeny for transgenic and non-transgenic animals by the percent of dauer progeny of non-transgenic progeny on the same plate. This was done to account for plate-to-plate variation. The AIN-1 protein in each transgene was translationally fused to GFP. <b>C. </b><i>ain-1(tm3681 lf)</i> mutation represses aberrant dauer formation of <i>unc-31(e928 lf)</i> at 27°C. <b>D. </b><i>daf-5(e1386 lf)</i> and <i>daf-16(mu86 lf)</i> suppress aberrant dauer formation phenotype of <i>unc-3(e151 lf) ain-1(ku322 lf)</i>. The percent of dauer progeny is shown relative to the original <i>unc-3(lf) ain-1(lf)</i> mutant. Relative dauer rate was used to account for day-to-day variation. Error bars represent S.E.M. from at least three biological replicates. A student's t-test was used to determine statistical significance for all experiments.</p