Three Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control

In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory. The guidance law based on nonsingular terminal sliding mode guarantees finite time convergence of interceptor to the desired impact angle. In order to derive the guidance laws, multi-dimension switching surfaces are used. The stability of the system, with selected switching surfaces, is demonstrated using Lyapunov stability theory. Numerical simulation results are presented to validate the proposed guidance law.

Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

MIMO Decode-and-Forward Relay Beamforming for Secrecy with Cooperative Jamming

In this paper, we consider decode-and-forward (DF) relay beamforming for secrecy with cooperative jamming (CJ) in the presence of multiple eavesdroppers. The communication between a source-destination pair is aided by a multiple-input multiple-output (MIMO) relay. The source has one transmit antenna and the destination and eavesdroppers have one receive antenna each. The source and the MIMO relay are constrained with powers P-S and P-R, respectively. We relax the rank-1 constraint on the signal beamforming matrix and transform the secrecy rate max-min optimization problem to a single maximization problem, which is solved by semidefinite programming techniques. We obtain the optimum source power, signal relay weights, and jamming covariance matrix. We show that the solution of the rank-relaxed optimization problem has rank-1. Numerical results show that CJ can improve the secrecy rate.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Broadcast Control Mechanism for Positional Consensus in Multiagent Systems

In this paper, a strategy for controlling a group of agents to achieve positional consensus is presented. The problem is constrained by the requirement that every agent must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming (LP) formulation that is computationally less intensive than earlier proposed methods. Moreover, a random perturbation input in the control command that helps the agents to come close to each other even for a large number of agents, which was not possible with an existing strategy in the literature, is introduced. The method is extended to achieve positional consensus at a prespecified location. The effectiveness of the approach is illustrated through simulation results. A comparison between the LP approach and the existing second-order cone programming-based approach is also presented. The algorithm was successfully implemented on a robotic platform with three robots.

Anisotropic magnetic couplings and structure-driven canted to collinear transitions in Sr2IrO4 by magnetically constrained noncollinear DFT

We study the canted magnetic state in Sr2IrO4 using fully relativistic density functional theory (DFT) including an on-site Hubbard U correction. A complete magnetic phase diagram with respect to the tetragonal distortion and the rotation of IrO6 octahedra is constructed, revealing the presence of two types of canted to collinear magnetic transitions: a spin-flop transition with increasing tetragonal distortion and a complete quenching of the basal weak ferromagnetic moment below a critical octahedral rotation. Moreover, we put forward a scheme to study the anisotropic magnetic couplings by mapping magnetically constrained noncollinear DFT onto a general spin Hamiltonian. This procedure allows for the simultaneous account and direct control of the lattice, spin, and orbital interactions within a fully ab initio scheme. We compute the isotropic, single site anisotropy and Dzyaloshinskii-Moriya (DM) coupling parameters, and clarify that the origin of the canted magnetic state in Sr2IrO4 arises from the structural distortions and the competition between isotropic exchange and DM interactions.

Novel Relay Selection Rules for Average Interference-Constrained Cognitive AF Relay Networks

Cooperative relaying combined with selection exploits spatial diversity to significantly improve the performance of interference-constrained secondary users in an underlay cognitive radio (CR) network. However, unlike conventional relaying, the state of the links between the relay and the primary receiver affects the choice of the relay. Further, while the optimal amplify-and-forward (AF) relay selection rule for underlay CR is well understood for the peak interference-constraint, this is not so for the less conservative average interference constraint. For the latter, we present three novel AF relay selection (RS) rules, namely, symbol error probability (SEP)-optimal, inverse-of-affine (IOA), and linear rules. We analyze the SEPs of the IOA and linear rules and also develop a novel, accurate approximation technique for analyzing the performance of AF relays. Extensive numerical results show that all the three rules outperform several RS rules proposed in the literature and generalize the conventional AF RS rule.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.

QoS Constrained Optimal Sink and Relay Placement in Planned Wireless Sensor Networks

We are given a set of sensors at given locations, a set of potential locations for placing base stations (BSs, or sinks), and another set of potential locations for placing wireless relay nodes. There is a cost for placing a BS and a cost for placing a relay. The problem we consider is to select a set of BS locations, a set of relay locations, and an association of sensor nodes with the selected BS locations, so that the number of hops in the path from each sensor to its BS is bounded by h(max), and among all such feasible networks, the cost of the selected network is the minimum. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard, and is hard to even approximate within a constant factor. For this problem, we propose a polynomial time approximation algorithm (SmartSelect) based on a relay placement algorithm proposed in our earlier work, along with a modification of the greedy algorithm for weighted set cover. We have analyzed the worst case approximation guarantee for this algorithm. We have also proposed a polynomial time heuristic to improve upon the solution provided by SmartSelect. Our numerical results demonstrate that the algorithms provide good quality solutions using very little computation time in various randomly generated network scenarios.

Entropy Constrained Exemplar-based Image Inpainting

Image inpainting is the process of filling the unwanted region in an image marked by the user. It is used for restoring old paintings and photographs, removal of red eyes from pictures, etc. In this paper, we propose an efficient inpainting algorithm which takes care of false edge propagation. We use the classical exemplar based technique to find out the priority term for each patch. To ensure that the edge content of the nearest neighbor patch found by minimizing L-2 distance between patches, we impose an additional constraint that the entropy of the patches be similar. Entropy of the patch acts as a good measure of edge content. Additionally, we fill the image by considering overlapping patches to ensure smoothness in the output. We use structural similarity index as the measure of similarity between ground truth and inpainted image. The results of the proposed approach on a number of examples on real and synthetic images show the effectiveness of our algorithm in removing objects and thin scratches or text written on image. It is also shown that the proposed approach is robust to the shape of the manually selected target. Our results compare favorably to those obtained by existing techniques

Prior image based temporally constrained reconstruction algorithm for magnetic resonance guided high intensity focused ultrasound

Purpose: A prior image based temporally constrained reconstruction ( PITCR) algorithm was developed for obtaining accurate temperature maps having better volume coverage, and spatial, and temporal resolution than other algorithms for highly undersampled data in magnetic resonance (MR) thermometry. Methods: The proposed PITCR approach is an algorithm that gives weight to the prior image and performs accurate reconstruction in a dynamic imaging environment. The PITCR method is compared with the temporally constrained reconstruction (TCR) algorithm using pork muscle data. Results: The PITCR method provides superior performance compared to the TCR approach with highly undersampled data. The proposed approach is computationally expensive compared to the TCR approach, but this could be overcome by the advantage of reconstructing with fewer measurements. In the case of reconstruction of temperature maps from 16% of fully sampled data, the PITCR approach was 1.57x slower compared to the TCR approach, while the root mean square error using PITCR is 0.784 compared to 2.815 with the TCR scheme. Conclusions: The PITCR approach is able to perform more accurate reconstructions of temperature maps compared to the TCR approach with highly undersampled data in MR guided high intensity focused ultrasound. (C) 2015 American Association of Physicists in Medicine.

CheepSync: A Time Synchronization Service for Resource Constrained Bluetooth LE Advertisers

Clock synchronization is highly desirable in distributed systems, including many applications in the Internet of Things and Humans. It improves the efficiency, modularity, and scalability of the system, and optimizes use of event triggers. For IoTH, BLE - a subset of the recent Bluetooth v4.0 stack - provides a low-power and loosely coupled mechanism for sensor data collection with ubiquitous units (e.g., smartphones and tablets) carried by humans. This fundamental design paradigm of BLE is enabled by a range of broadcast advertising modes. While its operational benefits are numerous, the lack of a common time reference in the broadcast mode of BLE has been a fundamental limitation. This article presents and describes CheepSync, a time synchronization service for BLE advertisers, especially tailored for applications requiring high time precision on resource constrained BLE platforms. Designed on top of the existing Bluetooth v4.0 standard, the CheepSync framework utilizes low-level time-stamping and comprehensive error compensation mechanisms for overcoming uncertainties in message transmission, clock drift, and other system-specific constraints. CheepSync was implemented on custom designed nRF24Cheep beacon platforms (as broadcasters) and commercial off-the-shelf Android ported smartphones (as passive listeners). We demonstrate the efficacy of CheepSync by numerous empirical evaluations in a variety of experimental setups, and show that its average (single-hop) time synchronization accuracy is in the 10 mu s range.

The Feedback Capacity of the Binary Erasure Channel With a No-Consecutive-Ones Input Constraint

The input-constrained erasure channel with feedback is considered, where the binary input sequence contains no consecutive ones, i.e., it satisfies the (1, infinity)-RLL constraint. We derive the capacity for this setting, which can be expressed as C-is an element of = max(0 <= p <= 0.5) (1-is an element of) H-b (p)/1+(1-is an element of) p, where is an element of is the erasure probability and Hb(.) is the binary entropy function. Moreover, we prove that a priori knowledge of the erasure at the encoder does not increase the feedback capacity. The feedback capacity was calculated using an equivalent dynamic programming (DP) formulation with an optimal average-reward that is equal to the capacity. Furthermore, we obtained an optimal encoding procedure from the solution of the DP, leading to a capacity-achieving, zero-error coding scheme for our setting. DP is, thus, shown to be a tool not only for solving optimization problems, such as capacity calculation, but also for constructing optimal coding schemes. The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.