The Classical Continuous Mixed Optimal Control of Couple Nonlinear Parabolic Partial Differential Equations with State Constraints

In this work, the classical continuous mixed optimal control vector (CCMOPCV) problem of couple nonlinear partial differential equations of parabolic (CNLPPDEs) type with state constraints (STCO) is studied. The existence and uniqueness theorem (EXUNTh) of the state vector solution (SVES) of the CNLPPDEs for a given CCMCV is demonstrated via the method of Galerkin (MGA). The EXUNTh of the CCMOPCV ruled with the CNLPPDEs is proved. The Frechet derivative (FÉDE) is obtained. Finally, both the necessary and the sufficient theorem conditions for optimality (NOPC and SOPC) of the CCMOPCV with state constraints (STCOs) are proved through using the Kuhn-Tucker-Lagrange (KUTULA) multipliers theorem (KUTULATH).

Circuit Optimization Study According to the Maximum Principle

The minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behavior of a Hamiltonian for various strategies of optimization. The possibility of applying the maximum principle to the problem of optimization of electronic circuits is analyzed. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

A modified genetic algorithm for system optimization

Purpose In this paper, the previously developed idea of generalized optimization of circuits for deterministic methods has been extended to genetic algorithm (GA) to demonstrate new possibilities for solving an optimization problem that enhance accuracy and significantly reduce computing time. Design/methodology/approach The disadvantages of GAs are premature convergence to local minima and an increase in the computer operation time when setting a sufficiently high accuracy for obtaining the minimum. The idea of generalized optimization of circuits, previously developed for the methods of deterministic optimization, is built into the GA and allows one to implement various optimization strategies based on GA. The shape of the fitness function, as well as the length and structure of the chromosomes, is determined by a control vector artificially introduced within the framework of generalized optimization. This study found that changing the control vector that determines the method for calculating the fitness function makes it possible to bypass local minima and find the global minimum with high accuracy and a significant reduction in central processing unit (CPU) time. Findings The structure of the control vector is found, which makes it possible to reduce the CPU time by several orders of magnitude and increase the accuracy of the optimization process compared with the traditional approach for GAs. Originality/value It was demonstrated that incorporating the idea of generalized optimization into the body of a stochastic optimization method leads to qualitatively new properties of the optimization process, increasing the accuracy and minimizing the CPU time.

Dual-channel digital control of energy consumption and air supply in microclimate systems of livestock premises

The problem of livestock premises air environment parameters ensuring in terms of temperature, humidity and CO2 gas content, established by zoo technical standards, is considered. The problem is formulated as a problem with non-linearity object and consists in its phase (temperature, humidity and CO2 gas content) coordinates stabilizing by the premises heating capacity and its air exchange intensity controlling. A mathematical model of control object’s dynamics parameters based on material flows and energy balance equations is developed. A cyclic algorithm for this problem solving has been developed, it consists of two successive stages: the control search this problem solving, and the found control establishment until any of the coordinates’ phase go beyond the established limits due to disturbances.The search for the control vector consists in periodic relay switching of its coordinates from specified maximum to minimum values so that the phase coordinates remain in the region of permissible variation. It is shown that the control vector corresponding coordinates as their average values for the switching cycle are defined. A block diagram of the control system implementing the developed algorithm is presented. The calculation data are given for a pigsty for 1300 animals.

The Continuous Classical Boundary Optimal Control of Triple Nonlinear Elliptic Partial Differential Equations with State Constraints

Our aim in this work is to study the classical continuous boundary control vector problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector, by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations related with the triple state equations. The Fréchet derivative is obtained. Finally we prove the theorems of both the necessary and sufficient conditions for optimality of the triple nonlinear partial differential equations of elliptic type through the Kuhn-Tucker-Lagrange's Multipliers theorem with equality and inequality constraints.

Selenoprotein T Protects Endothelial Cells against Lipopolysaccharide-Induced Activation and Apoptosis

Sepsis is an exaggerated immune response upon infection with lipopolysaccharide (LPS) as the main causative agent. LPS-induced activation and apoptosis of endothelial cells (EC) can lead to organ dysfunction and finally organ failure. We previously demonstrated that the first twenty amino acids of the Apurinic/Apyrimidinic Endodeoxyribonuclease 1 (APEX1) are sufficient to inhibit EC apoptosis. To identify genes whose regulation by LPS is affected by this N-terminal APEX1 peptide, EC were transduced with an expression vector for the APEX1 peptide or an empty control vector and treated with LPS. Following RNA deep sequencing, genes upregulated in LPS-treated EC expressing the APEX1 peptide were identified bioinformatically. Selected candidates were validated by semi-quantitative real time PCR, a promising one was Selenoprotein T (SELENOT). For functional analyses, an expression vector for SELENOT was generated. To study the effect of SELENOT expression on LPS-induced EC activation and apoptosis, the SELENOT vector was transfected in EC. Immunostaining showed that SELENOT was expressed and localized in the ER. EC transfected with the SELENOT plasmid showed no activation and reduced apoptosis induced by LPS. SELENOT as well as APEX1(1-20) can protect EC against activation and apoptosis and could provide new therapeutic approaches in the treatment of sepsis.

Optimisation of Parameters in a German Bight Circulation Model by 4DVAR Assimilation of Current and Water Level Observations

Uncertain parameters in a 3D barotropic circulation model of the German Bight are estimated with a variational optimisation approach. Surface current measurements from a high frequency (HF) radar are used in combination with acoustic Doppler current profiler (ADCP) and tide gauge observations as input for a 4DVAR assimilation scheme. The required cost function gradients are estimated using an adjoint model code. The focus of the study is on systematic errors of the model with the control vector including parameters of the bathymetry, bottom roughness, open boundary forcing, meteorological forcing as well as the turbulence model. The model uses the same bathymetry, open boundary forcing, and metereological forcing as the operational model run at the Federal Maritime and Hydrographic Agency (BSH). The baroclinic BSH model is used as a reference to put the performance of the optimised model into perspective. It is shown that the optimised model has better agreement with HF radar data and tide gauge observations both within the fortnight training period and the test period 1 month later. Current profile measurements taken at two platforms indicate that both models have comparable error magnitudes at those locations. The optimised model was also compared with independent drifter data. In this case, drifter simulations based on the BSH model and the respective operational drift model including some surface wave effects were used as a reference. Again, these comparison showed very similar results overall, with some larger errors of the tuned model in very shallow areas, where no observations were used for the tuning and surface wave effects, which are only explicitly considered in the BSH model, play a more important role. The tuned model seems to be slightly more dissipative than the BSH model with more energy entering through the western boundary and less energy leaving toward the north. It also became evident that the 4DVAR cost function minimisation process is complicated by momentum advection, which leads to non-differentiable dependencies of the model with respect to the control vector. It turned out that the omission of momentum advection in the adjoint code still leads to robust estimates of descent directions.

Boundary Optimal Control for Triple Nonlinear Hyperbolic Boundary Value Problem with State Constraints

The paper is concerned with the state and proof of the solvability theorem of unique state vector solution (SVS) of triple nonlinear hyperbolic boundary value problem (TNLHBVP), via utilizing the Galerkin method (GAM) with the Aubin theorem (AUTH), when the boundary control vector (BCV) is known. Solvability theorem of a boundary optimal control vector (BOCV) with equality and inequality state vector constraints (EINESVC) is proved. We studied the solvability theorem of a unique solution for the adjoint triple boundary value problem (ATHBVP) associated with TNLHBVP. The directional derivation (DRD) of the "Hamiltonian"(DRDH) is deduced. Finally, the necessary theorem (necessary conditions "NCOs") and the sufficient theorem (sufficient conditions" SCOs"), together denoted as NSCOs, for the optimality (OP) of the state constrained problem (SCP) are stated and proved.

Innovative dual system approach for selective eradication of cancer cells using viral-based delivery of natural bacterial toxin–antitoxin system

The inactivation of p53, a tumor suppressor, and the activation of the RAS oncogene are the most frequent genetic alterations in cancer. We have shown that a unique E. coli MazF-MazE toxin–antitoxin (TA) system can be used for selective and effective eradication of RAS-mutated cancer cells. This out of the box strategy holds great promise for effective cancer treatment and management. We provide proof of concept for a novel platform to selectively eradicate cancer cells using an adenoviral delivery system based on the adjusted natural bacterial system. We generated adenoviral vectors carrying the mazF toxin (pAdEasy-Py4-SV40mP-mCherry-MazF) and the antitoxin mazE (pAdEasy-RGC-SV40mP-MazE-IRES-GFP) under the regulation of RAS and p53, resp. The control vector carries the toxin without the RAS-responsive element (pAdEasy-ΔPy4-SV40mP-mCherry-MazF). In vitro, the mazF-mazE TA system (Py4-SV40mP-mCherry-MazF+RGC-SV40mP-MazE-IRES-GFP) induced massive, dose-dependent cell death, at 69% compared to 19% for the control vector, in a co-infected HCT116 cell line. In vivo, the system caused significant tumor growth inhibition of HCT116 (KRASmut/p53mut) tumors at 73 and 65% compared to PBS and ΔPY4 control groups, resp. In addition, we demonstrate 65% tumor growth inhibition in HCT116 (KRASmut/p53wt) cells, compared to the other two control groups, indicating a contribution of the antitoxin in blocking system leakage in WT RAS cells. These data provide evidence of the feasibility of using mutations in the p53 and RAS pathway to efficiently kill cancer cells. The platform, through its combination of the antitoxin (mazE) with the toxin (mazF), provides effective protection of normal cells from basal low activity or leakage of mazF.

Memory CD8 T Cells Generated by Cytomegalovirus Vaccine Vector Expressing NKG2D Ligand Have Effector-Like Phenotype and Distinct Functional Features

Viral vectors have emerged as a promising alternative to classical vaccines due to their great potential for induction of a potent cellular and humoral immunity. Cytomegalovirus (CMV) is an attractive vaccine vector due to its large genome with many non-essential immunoregulatory genes that can be easily manipulated to modify the immune response. CMV generates a strong antigen-specific CD8 T cell response with a gradual accumulation of these cells in the process called memory inflation. In our previous work, we have constructed a mouse CMV vector expressing NKG2D ligand RAE-1γ in place of its viral inhibitor m152 (RAE-1γMCMV), which proved to be highly attenuated in vivo. Despite attenuation, RAE-1γMCMV induced a substantially stronger CD8 T cell response to vectored antigen than the control vector and provided superior protection against bacterial and tumor challenge. In the present study, we confirmed the enhanced protective capacity of RAE-1γMCMV as a tumor vaccine vector and determined the phenotypical and functional characteristics of memory CD8 T cells induced by the RAE-1γ expressing MCMV. RNAseq data revealed higher transcription of numerous genes associated with effector-like CD8 T cell phenotype in RAE-1γMCMV immunized mice. CD8 T cells primed with RAE-1γMCMV were enriched in TCF1 negative population, with higher expression of KLRG1 and lower expression of CD127, CD27, and Eomes. These phenotypical differences were associated with distinct functional features as cells primed with RAE-1γMCMV showed inferior cytokine-producing abilities but comparable cytotoxic potential. After adoptive transfer into naive hosts, OT-1 cells induced with both RAE-1γMCMV and the control vector were equally efficient in rejecting established tumors, suggesting the context of latent infection and cell numbers as important determinants of enhanced anti-tumor response following RAE-1γMCMV vaccination. Overall, our results shed new light on the phenotypical and functional distinctness of memory CD8 T cells induced with CMV vector expressing cellular ligand for the NKG2D receptor.