Null Controllability Research Articles

Homogeneity for control systems in discrete time

Homogeneity, as a generalization of linearity to nonlinear systems, has proven to be a very powerful in systems and control. Nevertheless, only recently a notion of homogeneity was proposed for discrete-time control systems. However, this so-called D-Homogeneity directly couples the stability behaviour with the degree of homogeneity—in contrast to the continuous-time case. As an alternative, we propose the notion of S-Homogeneity, which avoids this coupling. S-Homogeneity uses a state-dependent time step that is compatible with sampling and discretization in time. We show that this concept preserves a contraction property and null-controllability for state-dependent sampling. For fixed sampling time, it yields (practical/semi-global) null controllability for sufficiently fast sampling, depending on the degree of homogeneity.

Null controllability of a nonlinear age, space and two-sex structured population dynamics model

<p style='text-indent:20px;'>In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problems.</p><p style='text-indent:20px;'>The first problem is related to the total extinction, which means that, we estimate a time <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation. Since the absence of males or females in the population stops births; so, if we have the total extinction of the females at time <inline-formula><tex-math id="M2">\begin{document}$ T, $\end{document}</tex-math></inline-formula> and if <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula> is the life span of the individuals, at time <inline-formula><tex-math id="M4">\begin{document}$ T+A $\end{document}</tex-math></inline-formula> one will get certainly the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after the Schauder's fixed point theorem.</p>

Null Controllability of Hilfer Fractional Stochastic Differential Inclusions

This paper gives the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential. Sufficient conditions for null controllability of nonlocal Hilfer fractional stochastic differential inclusion are established by using the fixed-point approach with the proof that the corresponding linear system is controllable. Finally, the theoretical results are verified with an example.

Null Controllability of Networks Systems

Null Controllability of Networks Systems

Null controllability for a structurally damped stochastic plate equation

In this paper, we obtain a null controllability result for a structurally damped refined stochastic plate equation with two kinds of boundary conditions. The key point is to establish an observability inequality for the backward structurally damped stochastic plate equation. For this purpose, we derive a new global Carleman estimate for the damped stochastic plate operator with homogeneous Dirichlet boundary conditions on the solution and the laplacian of the solution and with homogeneous Neumann boundary conditions of first and third order, respectively. Such an estimate is obtained by using the Carleman estimate for stochastic parabolic operators with complex coefficients in an iteration manner.

Robotic Manipulator’s Expressive Movements Control Using Kinematic Redundancy

In human–robot interaction (HRI), sharing emotions between the human and robot is one of the most important elements. However, market trends suggest that being able to perform productive tasks is more important than being able to express emotions in order for robots to be more accepted by society. In this study, we introduce a method of conveying emotions through a robot arm while it simultaneously executes main tasks. This method utilizes the null space control scheme to exploit the kinematic redundancy of a robot manipulator. In addition, the concept of manipulability ellipsoid is used to maximize the motion in the kinematic redundancy. The “Nextage-Open” robot was used to implement the proposed method, and HRI was recorded on video. Using these videos, a questionnaire with Pleasure–Arousal–Dominance (PAD) scale was conducted via the internet to evaluate people’s impressions of the robot’s emotions. The results suggested that even when industrial machines perform emotional behaviors within the safety standards set by the ISO/TS 15066, it is difficult to provide enough variety for each emotion to be perceived differently. However, people’s reactions to the unclear movements yielded useful and interesting results, showing the complementary roles of motion features, interaction content, prejudice toward robots, and facial expressions in understanding emotion.

Remarks on the Control of Two-Phase Stefan Free-Boundary Problems

This paper concerns the null controllability of the two-phase 1D Stefan problem with distributed controls. This is a free-boundary problem that models solidification or melting processes. In each phase, a parabolic equation, completed with initial and boundary conditions, must be satisfied; the phases are separated by a phase change interface, where an additional free-boundary condition is imposed (the so-called Stefan condition). We assume that two localized sources of heating/cooling controls act on the system (one in each phase). We prove the following local null controllability result: the temperatures can be steered to zero and, simultaneously, the interface can be steered to a prescribed location provided the initial data and the interface position are sufficiently close to the targets. The ingredients of the proofs are a compactness-uniqueness argument (which gives appropriate observability estimates adapted to constraints) and a fixed-point formulation and resolution of the controllability problem (which gives the result for the nonlinear system). We also prove a negative result corresponding to the case where only one control acts on the system and the interface does not collapse to the boundary.

Null Controllability for a Degenerate Population Equation with Memory

In this paper we consider the null controllability for a population model depending on time, on space and on age. Moreover, the diffusion coefficient degenerate at the boundary of the space domain. The novelty of this paper is that for the first time we consider the presence of a memory term, which makes the computations more difficult. However, under a suitable condition on the kernel we deduce a null controllability result for the original problem via new Carleman estimates for the adjoint problem associated to a suitable nonhomogeneous parabolic equation.

Null Boundary Controllability of the Linear Kuramoto–Sivashinsky Equation with Variable Coefficients

Null Boundary Controllability of the Linear Kuramoto–Sivashinsky Equation with Variable Coefficients

Composite Nonlinear Path-Following Control for Unmanned Ground Vehicles With Anti-Windup ESO

In this article, a composite nonlinear feedback (CNF) controller with anti-windup extended state observer (ESO) is proposed for path-following control of unmanned ground vehicles (UGVs). To describe steering dynamics accurately, a saturation model with bounded disturbances is developed subject to path-following, lateral dynamic, and steering capability. The anti-windup ESO is investigated for real-time disturbance estimation under saturated input. The CNF controller is designed for path-following. In terms of asymptotically null controllability, a practical semiglobal stabilization result is derived for the closed-loop system with saturated input and bounded disturbances. Experimental results show that the proposed strategy is effective for UGVs.

Synthesis of frequency diverse array with large null depths via a hybrid optimisation approach of mayfly algorithm and convex programing

By controlling the null distribution in the range-angle dimension, the frequency diverse array (FDA) can handle range-dependent interference, which is usually difficult to solve for the traditional phased array. However, the current investigations focus more on the design of weights for null control, ignoring the unique design dimension of FDA, that is, the frequency offsets. Therefore, the array potential cannot be fully exploited to maximise the range-dependent interference suppression capability. In this paper, a novel FDA synthesis method with large null depth is proposed. By incorporating the mayfly algorithm and convex programing, frequency offsets and transmit weights are jointly optimised to generate maximum null depths in a given region while maintaining the specified array response of the desired target. Other null control methods for FDA are listed as comparison, including weights-only optimisation method, frequency offsets-only optimisation and frequency offsets and weights sequentially optimisation method. Numerical examples demonstrate the superiority of the proposed algorithm.

Multi-Omic Analysis of Two Common P53 Mutations: Proteins Regulated by Mutated P53 as Potential Targets for Immunotherapy.

Simple SummaryTP53 is the most frequently mutated gene in many cancers, but it has failed to be a very effective target for treatment to date. To overcome this, we have examined what else changes in cells when the TP53 gene is mutated. We modified cells that had no TP53 expression to have one of the two most common mutations, either R175H or R273H. We examined how the presence of these TP53 mutations caused cellular changes including microscopic, gene expression and peptide presentation to the immune system. This has allowed us to identify new (secondary) targets that could be used to facilitate the treatment of tumors that harbor p53 mutations.The p53 protein is mutated in more than 50% of human cancers. Mutated p53 proteins not only lose their normal function but often acquire novel oncogenic functions, a phenomenon termed mutant p53 gain-of-function. Mutant p53 has been shown to affect the transcription of a range of genes, as well as protein–protein interactions with transcription factors and other effectors; however, no one has intensively investigated and identified these proteins, or their MHC presented epitopes, from the viewpoint of their ability to act as targets for immunotherapeutic interventions. We investigated the molecular changes that occurred after the TP53 null osteosarcoma cells, SaOS-2, were transfected with one of two conformational p53-mutants, either R175H or R273H. We then examined the phenotypic and functional changes using macroscopic observations, proliferation, gene expression and proteomics alongside immunopeptidome profiling of peptide antigen presentation in the context of major histocompatibility complex (MHC) class I molecules. We identified several candidate proteins in both TP53 mutant cell lines with differential expression when compared to the TP53 null vector control, SaOS-V. Quantitative SWATH proteomics combined with immune-peptidome analysis of the class-I eluted peptides identified several epitopes presented on pMHC and in silico analysis shortlisted which antigens were expressed in a range of cancerous but not adjacent healthy tissues. Out of all the candidates, KLC1 and TOP2A showed high levels of expression in every tumor type examined. From these proteins, three A2 and four pan HLA-A epitopes were identified in both R175H and R273H from TOP2A. We have now provided a short list of future immunotherapy targets for the treatment of cancers harboring mutated TP53.

Equivalent one-dimensional first-order linear hyperbolic systems and range of the minimal null control time with respect to the internal coupling matrix

In this paper, we are interested in the minimal null control time of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls. Our main result is an explicit characterization of the smallest and largest values that this minimal null control time can take with respect to the internal coupling matrix. In particular, we obtain a complete description of the situations where the minimal null control time is invariant with respect to all the possible choices of internal coupling matrices. The proof relies on the notion of equivalent systems, in particular the backstepping method, a canonical LU-decomposition for boundary coupling matrices and a compactness-uniqueness method adapted to the null controllability property.

"Feedback null controllability for a class of semilinear control systems"

"For a class of semilinear control systems we get null controllability results and estimates for the minimum time function by considering appropriate feedback laws."

Abstract 795: Entinostat restores responsiveness to Olaparib in ID8 TP53 null and ID8 TP53 null/BRCA2 null mouse ovarian cancer cell lines

Abstract Poly (adenosine diphosphate [ADP]-ribose) polymerase inhibitors (PARPi) reduce disease progression in patients diagnosed with ovarian cancer. The anticancer effects of PARPi are most effective in tumors with BRCA mutations and homologous recombination (HR) deficiency (HRD). One mechanism of PARPi resistance is through restoration of HR repair. Our group has shown that entinostat (an HDACi) potentiates the effects of olaparib (a PARPi). The objective of this study was to investigate mechanisms of intrinsic PARPi resistance by studying the combination of entinostat and olaparib in HR proficient and HR deficient mouse ovarian cancer cell lines. We used the ID8 TP53 null (HR proficient) and ID8 TP53 null/BRCA2 null (HR deficient) mouse ovarian cancer cell lines that harbor molecular features consistent with human high-grade serous ovarian cancer. To recapitulate an ongoing clinical trial using this drug combination, cells were pre-treated with 0.25 µM Entinostat or control for 24 hours, followed by 24 or 72 hours of drug treatment [0.5 µM Entinostat, 10 µM of Olaparib, the combination of both, or control]. Clonogenicity assays were used to assess colony formation and MTS assays were used to measure cell viability and proliferation. We then performed immunofluorescence (IF) staining for RAD51 (a marker for HR repair), γH2AX (a marker of DNA damage) and Ki67 (a marker of proliferation). As expected in the clonogenicity assay, there was no statistically significant difference in cell survival between the olaparib treated ID8 TP53 null (HR proficient) cells and vehicle-treated controls (p= 0.0993; paired t test). Alternatively, the ID8 TP53 null/BRCA2 null (HR deficient) cell line treated with olaparib alone reduced cell viability compared to control (p=0.0245; paired t test). Clonogenicity assays also demonstrated that the combination of entinostat and olaparib reduced colony formation compared to control in the ID8 TP53 null cell line (p<0.0001; one-way ANOVA). MTS assays corroborated this treatment effect (p< 0.0001; two way ANOVA). Preliminary data suggests that compared to controls and each drug alone, IF staining for RAD51 and Ki67 expression was reduced in cells treated with combination therapy. Also preliminarily, there was increased number of γH2AX foci in combination treatment compared to controls and each drug alone. Entinostat restores responsiveness to olaparib in ID8 TP53 null HR proficient mouse ovarian cancer cells that molecularly resemble high-grade serous ovarian carcinoma. These results suggest this drug combination can overcome intrinsic resistance to PARPi and provide additional preclinical support for clinical investigation of this combination for the treatment of HR proficient ovarian cancer. Citation Format: Tyler Woodard, Viju Gupta, Simona Miceska, Bisiayo Fashemi, Wendy Zhang, Dineo Khabele. Entinostat restores responsiveness to Olaparib in ID8 TP53 null and ID8 TP53 null/BRCA2 null mouse ovarian cancer cell lines [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 795.

Abstract 3543: Altering tumor immunophenotypes with PD-L1 engineered toxin bodies

Abstract Targeting of PD-L1 checkpoint has shown clinical efficacy in multiple solid tumor indications. Currently approved PD-L1 targeted approaches rely on the blocking activity of monoclonal antibodies (mAbs) which sterically inhibit PD-L1 thus preventing PD-1 mediated immune checkpoint activity. Although these mAbs have shown activity in the clinic, the need for pre-existing tumor specific immunity and tumor immune infiltration precludes responses in some patients and leads to resistance in others. Therefore, there remains a need for new modalities and treatment paradigms. Molecular Templates has developed MT-6402, an engineered toxin body (ETB) targeting PD-L1 designed to overcome the challenges of current PD-L1 targeting approaches by 1) directly depleting PD-L1 positive tumor or immunosuppressive immune cells displaying PD-L1 and 2) alteration of the tumor immunophenotype through the cytoplasmic delivery of an HLA:A*02 restricted cytomegalovirus (CMV) antigen. Delivery of this antigen is meant to leverage recruitment of existing CMV-restricted cytotoxic T lymphocytes (CTLs) for cell-mediated cytotoxic depletion (antigen seeding technology, AST) of CMV antigen presenting tumor cells. MT-6402 is currently in a phase I open-label, dose escalation and expansion study in subjects with advanced solid cancers that express PD-L1 (NCT04795713). Initial assessment of pharmacodynamic markers for PD-L1 and CMV-mediated ETB activity in a subject with confirmed PD-L1+ tumor cells, CMV positivity, and HLA:A*02 restriction has shown serum phenotypes associated with robust checkpoint inhibitor activity and full extravasation of circulating CMV-specific T cells. In addition to assessing early clinical data from the HLA: A*02 restricted MT-6402 trials, expansion of ETB AST to a broader patient population requires testing of ETBs engineered with the ability to deliver CMV antigens across a broad range of HLA restriction, including HLA:A*01, HLA:A*03, and HLA:A*24. To this end, ETBs were benchmarked against MT-6402 to identify candidates that retain comparable specificity, selectivity, and activity. Substitution of peptide antigens did not alter specificity or selectivity of ETBs compared to MT-6402. Candidate ETB binding profiles and potency were comparable to MT-6402. ETBs delivered an antigen seeding response in a PD-L1 dependent and HLA specific manner. In vivo efficacy of candidate ETBs was comparable in a murine efficacy xenograft model with MT-6402. An ex vivo cytokine release assay in a co-culture setting using HLA matched CTLs and PD-L1+ target cells, treatment with AST capable ETBs resulted in secretion of antigen specific T cell mediated immune cytokines compared to AST null controls. These cytokines overlap with cytokine signatures observed after dosing MT-6402 in HLA:A*02 patients. Preclinical assessment of the safety profile of candidates is ongoing and further development is slated for 2021. Citation Format: Swati Khanna, Elizabeth M. Kapeel, Lauren R. Byrne, Elizabeth Saputra, Steven Rivera, Lindsey Aschenbach, Lilia A. Rabia, Garrett L. Cornelison, Rachael M. Orlandella, Brigitte Brieschke, Michaela Sousares, Jay Zhao, Garrett L. Robinson, Chris Moore, Joseph D. Dekker. Altering tumor immunophenotypes with PD-L1 engineered toxin bodies [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 3543.

Null Controllability for Fourth Order Stochastic Parabolic Equations

Null Controllability for Fourth Order Stochastic Parabolic Equations

Exterior controllability properties for a fractional Moore–Gibson–Thompson equation

The three concepts of exact, null and approximate controllabilities are analyzed from the exterior of the Moore–Gibson–Thompson equation associated with the fractional Laplace operator subject to the nonhomogeneous Dirichlet type exterior condition. Assuming that \(b>0\) and \(\alpha -\frac{\tau c^2}{b}>0\), we show that if \(0<s<1\) and \(\varOmega \subset {\mathbb {R}}^N\) (\(N\ge 1\)) is a bounded domain with a Lipschitz continuous boundary \(\partial \varOmega \), then there is no control function g such that the following system $$\begin{aligned} {\left\{ \begin{array}{ll} \tau u_{ttt} + \alpha u_{tt}+c^2(-\varDelta )^{s} u + b(-\varDelta )^{s} u_{t}=0 &{} \text{ in } \; \varOmega \times (0,T),\\ u=g\chi _{{\mathcal {O}}} &{} \text{ in } \; ({\mathbb {R}}^N\setminus \varOmega )\times (0,T) ,\\ u(\cdot ,0) = u_0, u_t(\cdot ,0) = u_1, u_{tt}(\cdot ,0)=u_2 &{} \text{ in } \; \varOmega , \end{array}\right. } \end{aligned}$$is exactly or null controllable in time \(T>0\). However, we prove that for \(0<s<1\), the system is approximately controllable for every \(g\in H^1((0,T);L^{2}({\mathcal {O}}))\), where \(\mathcal O\subset {\mathbb {R}}^N\setminus {\overline{\varOmega }}\) is an arbitrary non-empty open set.

PRDM16 expression and function in mammalian cochlear development.

PR domain containing 16 (PRDM16) is a key transcriptional regulator in the development of craniofacial, adipose, and neural tissues. Our lab identified PRDM16 expression in the epithelial cells of the Kölliker's organ (KO) that starts at ~E13.5 and is maintained until KO disappearance. A transgenic mouse model that carries a gene trap null allele of Prdm16 (Prdm16cGT ) was used to characterize the impact of Prdm16 loss on cochlear development. At P0 Prdm16cGT null cochlea exhibited hypoplastic KO, shortened cochlear duct, increased density of hair cells (HCs) and supporting cells (SCs) in the apical turn as well as multiple isolated ectopic HCs within the KO domain. KO epithelial cells proliferation rate was reduced in the apical turn of the developing Prdm16cGT null cochlea vs controls. Bulk RNA sequencing of cochlear duct cells at E14.5 followed by quantitative real time PCR and mRNA Fluorescence in-situ hybridization (FISH) validation identified differentially expressed genes in Prdm16cGT null vs littermate control cochleae. Upregulated genes at E14.5 included Fgf20, as well as several Notch pathway genes (Lfng, Hes1, and Jag1). This study characterizes Prdm16 expression during cochlear development and establishes its requirement for KO development.

IMP1/IGF2BP1 alters extracellular vesicle cargo in colorectal cancer

BackgroundColorectal cancer (CRC) is the third leading cause of cancer‐related death worldwide. There is an urgent need for new therapeutic targets and methods of early detection to improve patient outcomes. Extracellular Vesicles (EVs) and EV cargo are promising new biomarkers and therapeutic targets. EVs are secreted nanoparticles that carry DNA, RNA, and proteins. EVs can target specific cell types and once taken up by a destination cell, EV cargo can shape cell gene expression and physiology. EVs can shape the tumor microenvironment (TME) (i.e., stromal, immune, and endothelial cells), which plays critical roles in patient survival and disease outcomes. Our current understanding of how EV cargo is determined and how it influences the CRC cell TME is limited. One promising but understudied molecular aspect of EVs is RNA binding proteins (RNAbps). RNAbps are post‐transcriptional regulators of gene expression and could provide a link between host cell gene expression and EV cargo. Insulin‐like growth factor 2 RNA binding protein 1 (IMP1, IGF2BP1) is an RNAbp with a critical role in CRC development and progression. IMP1 is expressed highly in CRC tumors, expression correlates with worse prognosis, and IMP1 binds/potently regulates tumor‐associated transcripts. How EV cargo is influenced by IMP1 and effects on EV targeting to destination cells and on target cell gene expression and function is not known. Understanding how IMP1 shapes EV cargo and which TME cells are targeted, will identify new mechanisms of cancer development/progression through IMP1‐EV‐mediated alteration of the TME and novel EV cargo as candidates for early detection biomarkers.HypothesisWe hypothesize that IMP1 facilitates the packaging of tumor‐promoting EV cargo that interact and communicate with the TME to enhance tumor progression.MethodsEVs were isolated from IMP1 null and IMP1‐overexpressing (IMP1OE) CRC cell lines, HT‐29, SW480, as well as wildtype Caco2 cells (express high levels of IMP1) by size‐exclusion chromatography. EVs were assessed by nanoparticle tracking analysis, western blot, electron microscopy, and qPCR.ResultsWe found that IMP1 enters EVs from Caco2 and SW480 IMP1OE cell lines, but not HT‐29 IMP1OE or corresponding null controls. IMP1 did not alter EV secretion in CRC cell lines. We found that IMP1 target mRNAs, such as KRAS, cMYC are present within EVs, but not the IMP1 target PTGS2.ConclusionsOur novel findings suggest that IMP1 enters the EV to directly influence EV cargo in specific CRC cell lines. Our findings have implications for the development of novel early detection biomarkers and therapeutic approaches in CRC.