This article deals with the problem of adaptive target detection in the presence of homogeneous Gaussian interference with frequency diverse array multiple-input multiple-output radar. Adaptive ...detectors are devised according to the generalized likelihood ratio test criterion, where the position of the target within each range cell is assumed unknown. To obtain the maximum likelihood estimate of the target incremental range under the H_1 hypothesis, three different optimization strategies are pursued. They are, respectively, based on semidefinite programming, discrete grid search, and Newton method. At the analysis stage, a detection performance comparison is carried on among the new proposed adaptive detectors, benchmark, and mismatched receivers. Numerical results corroborate the effectiveness of the developed receivers.
This paper addresses target localization problems in both noncooperative and cooperative 3-D wireless sensor networks (WSNs), for both cases of known and unknown sensor transmit power, i.e., PT . We ...employ a hybrid system that fuses distance and angle measurements, extracted from the received signal strength and angle-of-arrival information, respectively. Based on range and angle measurement models, we derive a novel nonconvex estimator based on the least squares criterion. The derived nonconvex estimator tightly approximates the maximum-likelihood estimator for small noise. We then show that the developed estimator can be transformed into a generalized trust region subproblem framework, by following the squared range approach, for noncooperative WSNs. For cooperative WSNs, we show that the estimator can be transformed into a convex problem by applying appropriate semidefinite programming relaxation techniques. Moreover, we show that the generalization of the proposed estimators for known PT is straightforward to the case where PT is not known. Our simulation results show that the new estimators have excellent performance and are robust to not knowing PT . The new estimators for noncooperative localization significantly outperform the existing estimators, and our estimators for cooperative localization show exceptional performance in all considered settings.
Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a ...guarantee, one must be able to bound the output of neural networks when their input changes within a bounded set. In this article, we propose a semidefinite programming (SDP) framework to address this problem for feed-forward neural networks with general activation functions and input uncertainty sets. Our main idea is to abstract various properties of activation functions (e.g., monotonicity, bounded slope, bounded values, and repetition across layers) with the formalism of quadratic constraints. We then analyze the safety properties of the abstracted network via the S -procedure and SDP. Our framework spans the tradeoff between conservatism and computational efficiency and applies to problems beyond safety verification. We evaluate the performance of our approach via numerical problem instances of various sizes.
For objects belonging to a known model set and observed through a prescribed linear process, we aim at determining methods to recover linear quantities of these objects that are optimal from a ...worst-case perspective. Working in a Hilbert setting, we show that, if the model set is the intersection of two hyperellipsoids centered at the origin, then there is an optimal recovery method which is linear. It is specifically given by a constrained regularization procedure whose parameters can be precomputed by semidefinite programming. This general framework can be applied to several scenarios, including the two-space problem and problems involving ℓ2-inaccurate data. It can also be applied to the problem of recovery from ℓ1-inaccurate data. For the latter, we reach the conclusion of existence of an optimal recovery method which is linear, again given by constrained regularization, under a computationally verifiable sufficient condition.
To ensure grid efficiency and reliability, power system operators continuously monitor the operational characteristics of the grid through a critical process called state estimation (SE), which ...performs the task by filtering and fusing various measurements collected from grid sensors. This study analyzes the vulnerability of the key operation module, namely ac-based SE, against potential cyber attacks on data integrity, also known as false data injection attack (FDIA). A general form of FDIA can be formulated as an optimization problem, whose objective is to find a stealthy and sparse data injection vector on the sensor measurements with the aim of making the state estimate spurious and misleading. Due to the nonlinear ac measurement model and the cardinality constraint, the problem includes both continuous and discrete nonlinearities. To solve the FDIA problem efficiently, we propose a novel convexification framework based on semidefinite programming (SDP). By analyzing a globally optimal SDP solution, we delineate the "attackable region" for any given set of measurement types and grid topology, where the spurious state can be falsified by FDIA. Furthermore, we prove that the attack is stealthy and sparse, and derive performance bounds. Simulation results on various IEEE test cases indicate the efficacy of the proposed convexification approach. From the grid protection point of view, the results of this study can be used to design a security metric for the current practice against cyber attacks, redesign the bad data detection scheme, and inform proposals of grid hardening. From a theoretical point of view, the proposed framework can be used for other nonconvex problems in power systems and beyond.
In this paper, we propose multi-input multi-output (MIMO) beamforming designs towards joint radar sensing and multi-user communications. We employ the Cramér-Rao bound (CRB) as a performance metric ...of target estimation, under both point and extended target scenarios. We then propose minimizing the CRB of radar sensing while guaranteeing a pre-defined level of signal-to-interference-plus-noise ratio (SINR) for each communication user. For the single-user scenario, we derive a closed form for the optimal solution for both cases of point and extended targets. For the multi-user scenario, we show that both problems can be relaxed into semidefinite programming by using the semidefinite relaxation approach, and prove that the global optimum can be generally obtained. Finally, we demonstrate numerically that the globally optimal solutions are reachable via the proposed methods, which provide significant gains in target estimation performance over state-of-the-art benchmarks.
Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, ...quantum metrology for non-Markovian processes is much less explored. In this Letter, we establish a general framework of non-Markovian quantum metrology. For any parametrized non-Markovian process on a finite-dimensional system, we derive a formula for the maximal amount of quantum Fisher information that can be extracted from it by an optimally controlled probe state. In addition, we design an algorithm that evaluates this quantum Fisher information via semidefinite programming. We apply our framework to noisy frequency estimation, where we find that the optimal performance of quantum metrology is better in the non-Markovian scenario than in the Markovian scenario and explore the possibility of efficient sensing via simple variational circuits.
This article presents an efficient and comprehensive method to find out the minimum number of and the corresponding locations of phasor measurement units (PMUs) guaranteeing full numerical ...observability of a power system as well as maximize the measurement redundancy in conjunction with preexisting conventional measurements. Furthermore, the effect of number of available channels of PMUs on their optimal placement can be taken into account. The proposed optimal PMU placement (OPP) formulation is extended to consider the case of two types of contingencies, single PMU loss and single branch outage. The objective of the OPP method is the numerical observability, unlike the majority of earlier works which are based on topological observability and do not always ensure numerical observability required for the successful execution of state estimation (SE). The problem is formulated as a binary semidefinite programming (BSDP) model with binary decision variables, minimizing a linear objective function subject to linear matrix inequality (LMI) observability constraints. The BSDP problem is solved using an outer approximation scheme based on binary integer linear programming. The effectiveness of the proposed method is verified on different IEEE test systems.
A new cooperative received signal strength-based localization algorithm is proposed which employs relative error estimation and semidefinite programming (SDP). First, the log-normal shadowing RSS ...measurement model is transformed into an equivalent multiplicative model. Then, a relative error estimation criterion is used with this model to develop a nonconvex estimator to approximate the maximum likelihood solution. Finally, semidefinite relaxation is applied to the nonconvex estimator to obtain an SDP estimator. The proposed algorithm is first derived for noncooperative RSS-based localization and then extended to the cooperative case. The Cramer-Rao lower bound is derived for cooperative RSS-based localization. Performance results are presented, which demonstrate that the proposed SDP estimator provides a significant improvement over existing localization methods.
In this paper, the problem of designing static output feedback (SOF)
negative imaginary controller has been studied. Because the constraints brought by negative imaginary (NI) property and
...performance are a set of bilinear matrix inequalities (BMIs), designing an SOF NI controller with
performance is a non-trivial problem. To overcome the difficulty of solving BMIs, a linearisation-based method is proposed. First, a necessary and sufficient condition is established, where the constraints of NI property and
performance are reformulated as similar forms. Second, inspired by the semidefinite programming, the derived condition is converted to the difference between two convex functions. Then a linearised iterative algorithm with initialisation process is provided to compute the desired SOF
NI controller. Finally, two numerical examples are presented to illustrate the proposed results.
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