An efficient method for multiobjective optimal control and optimal control subject to integral constraints

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget" remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian "marching" method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced "weighted sum" based algorithm for the same problem. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.Comment: The final version accepted by J. Comp. Math. : 41 pages, 14 figures. Since the previous version: typos fixed, formatting improved, one mistake in bibliography correcte

Investigating Unipolar Switching in Niobium Oxide Resistive Switches: Correlating Quantized Conductance and Mechanism

Memory devices based on resistive switching (RS) have not been fully realised due to lack of understanding of the underlying switching mechanisms. Nature of ion transport responsible for switching and growth of conducting filament in transition metal oxide based RS devices is still in debate. Here, we investigated the mechanism in Niobium oxide based RS devices, which shows unipolar switching with high ON/OFF ratio, good endurance cycles and high retention times. We controlled the boundary conditions between low-conductance insulating and a high-conductance metallic state where conducting filament (CF) can form atomic point contact and exhibit quantized conductance behaviour. Based on the statistics generated from quantized steps data, we demonstrated that the CF is growing atom by atom with the applied voltage sweeps. We also observed stable quantized states, which can be utilized in multistate switching

Controlled inter-state switching between quantized conductance states in resistive devices for multilevel memory

A detailed understanding of quantization conductance (QC), their correlation with resistive switching phenomena and controlled manipulation of quantized states is crucial for realizing atomic-scale multilevel memory elements. Here, we demonstrate highly stable and reproducible quantized conductance states (QC-states) in Al/Niobium oxide/Pt resistive switching devices. Three levels of control over the QC-states, required for multilevel quantized state memories, like, switching ON to different quantized states, switching OFF from quantized states, and controlled inter-state switching among one QC states to another has been demonstrated by imposing limiting conditions of stop-voltage and current compliance. The well defined multiple QC-states along with a working principle for switching among various states show promise for implementation of multilevel memory devices

Robust Resource Allocation Techniques on Homogeneous Distributed System

Distributed computing systems utilize various resources with different capabilities to satisfy the requirements of diverse task mixtures and to maximize the system performance. Such systems often operate in an environment where certain desired performance features degrade due to unpredictable circumstances, such as higher than expected work load or inaccuracies in the estimation of task and system parameters. Thus, when resources are allocated to tasks it is desirable to do this in a way that makes the system performance on these tasks robust against unpredictable changes. The system is considered robust if the actual makespan under the perturbed conditions does not exceed the required time constraint. The goal is to maximize the collective allowable error in execution time estimation for the tasks that can occur without the makespan exceeding the constraint

Water flow and transport of chloride in unsaturated concrete

Concrete structures deteriorate in their operating environment under the combined action of harsh environmental conditions and external loading. Although the applied load can lead to a certain degradation of the structure, the main long-term deterioration mechanism involves moisture movement and the transport of chlorides within concrete. In order to build durable and reliable structures, it is necessary to be able to accurately predict the movement of moisture and chlorides within concrete. In the case of unsaturated concrete, the transport of chloride ions is integrally associated with prediction of moisture fluxes in concrete. Even the diffusion of chloride ions depends on the degree of saturation of the concrete since concrete must have a continuous liquid phase for diffusion to occur. Therefore, simple diffusion theory, used in the current literature, is not sufficient to predict the diffusion of chloride ions in the case of unsaturated concrete. Most diffusion models described in the current published literature are applicable to concrete structures that are permanently wet and invariably underestimate the amount of chlorides penetrating the concrete of structures subjected to wetting and drying cycles. The research presented in this thesis reviews current knowledge, mathematical models and test methods pertinent to the movement of moisture and transport of chloride ions in unsaturated concrete. A laboratory testing program was established to characterize the material properties of concrete mixes with water-cement ratios 0.4, 0.5 and 0.6. Concrete was characterized by its saturated hydraulic conductivity, moisture retention function and dependence of diffusion coefficient on degree of saturation. A geotechnical centrifuge was used to determine the saturated hydraulic conductivity of the concrete samples. Values of the saturated hydraulic conductivity of the samples were in the range of 10-11-10-12 m/s. The moisture retention function of concrete samples was determined using a vapour equilibrium technique. The experimental moisture retention data was used to determine van Genuchten parameters for each of the concrete mixtures and subsequently used to determine the capillary pressure-degree of saturation relationship and relative permeability-degree of saturation relationship as a ``closed- form`` analytical expression. An electrical resistivity technique was used to determine the dependence of the chloride diffusion coefficient on the degree of saturation of the concrete. The result was compared with the Millington and Quirk model. Most of the experimental results should be useful to researchers in the field, as well as the engineering community at large, considering that they are rarely found in the concrete literature. Simulations were made to determine the influence of various parameters measured during experiment on movement of moisture and transport of chloride ions in unsaturated concrete using TOUGH2, a multiphase, multicomponent, model that simulates coupled heat, moisture and salt transport in saturated and unsaturated rocks

Cross-layer Based MANET Performance Optimization for Different Traffic and Mobility Scenario

The self configuring dexterous autonomy of MANET imposes some network challenges constrained to traditional dynamic routing behaviour. So as working with different mobility and traffic patterns with normal management schemes may lead some minor pitfalls to some important network performance parameters and hence can degrade the whole network performance. Here,  Our aim is to make some DSR and MAC based cross layer optimizations and testify it on different mobility and traffic scenarios so as to justify the robustness of our proposed improvement. Keywords— Cross- Layer, DSR, MAC, MANET, Optimizatio

Further Constructions of AMUBs for Non-prime power Composite Dimensions

Construction of a large class of Mutually Unbiased Bases (MUBs) for non-prime power composite dimensions ($d = k\times s$) is a long standing open problem, which leads to different construction methods for the class Approximate MUBs (AMUBs) by relaxing the criterion that the absolute value of the dot product between two vectors chosen from different bases should be $\leq \frac{\beta}{\sqrt{d}}$. In this chapter, we consider a more general class of AMUBs (ARMUBs, considering the real ones too), compared to our earlier work in [Cryptography and Communications, 14(3): 527--549, 2022]. We note that the quality of AMUBs (ARMUBs) constructed using RBD$(X,A)$ with $|X|= d$, critically depends on the parameters, $|s-k|$, $\mu$ (maximum number of elements common between any pair of blocks), and the set of block sizes. We present the construction of $\mathcal{O}(\sqrt{d})$ many $\beta$-AMUBs for composite $d$ when $|s-k|< \sqrt{d}$, using RBDs having block sizes approximately $\sqrt{d}$, such that $|\braket{\psi^l_i|\psi^m_j}| \leq \frac{\beta}{\sqrt{d}}$ where $\beta = 1 + \frac{|s-k|}{2\sqrt{d}}+ \mathcal{O}(d^{-1}) \leq 2$. Moreover, if real Hadamard matrix of order $k$ or $s$ exists, then one can construct at least $N(k)+1$ (or $N(s)+1$) many $\beta$-ARMUBs for dimension $d$, with $\beta \leq 2 - \frac{|s-k|}{2\sqrt{d}}+ \mathcal{O}(d^{-1})< 2$, where $N(w)$ is the number of MOLS$(w)$. This improves and generalizes some of our previous results for ARMUBs from two points, viz., the real cases are now extended to complex ones too. The earlier efforts use some existing RBDs, whereas here we consider new instances of RBDs that provide better results. Similar to the earlier cases, the AMUBs (ARMUBs) constructed using RBDs are in general very sparse, where the sparsity $(\epsilon)$ is $1 - \mathcal{O}(d^{-\frac{1}{2}})$