Iterative Convex Optimization Research Articles

Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method

Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method

Exponential Local Fisher Discriminant Analysis with Sparse Variables Selection: A Novel Fault Diagnosis Scheme for Industry Application

Local Fisher discriminant analysis (LFDA) has been widely applied to dimensionality reduction and fault classification fields. However, it often suffers from small sample size (SSS) problem and incorporates all process variables without emphasizing the key faulty ones, thus leading to degraded fault diagnosis performance and poor model interpretability. To this end, this paper develops the sparse variables selection based exponential local Fisher discriminant analysis (SELFDA) model, which can overcome the two limitations of basic LFDA concurrently. First, the responsible faulty variables are identified automatically through the least absolute shrinkage and selection operator, and the current optimization problem are subsequently recast as an iterative convex optimization problem and solved by the minimization-maximization method. After that, the matrix exponential strategy is implemented on LFDA, it can essentially overcome the SSS problem by ensuring that the within-class scatter matrix is always full-rank, thus more practical in real industrial practices, and the margin between different categories is enlarged due to the distance diffusion mapping, which is benefit for the enhancement of classification accuracy. Finally, the Tennessee Eastman process and a real-world diesel working process are employed to validate the proposed SELFDA method, experimental results prove that the SELFDA framework is more excellent than the other approaches.

Extreme Sparse-Array Synthesis via Iterative Convex Optimization and Simulated-Annealing Expanded Array

Sparse-array synthesis can considerably reduce the number of sensor elements while optimizing the beam-pattern response performance. The sparsity of an array is related to the degrees of freedom of the array elements. A sparse-array method based on iterative convex optimization and a simulated-annealing expanded array is proposed in this paper. This method transforms the sparse-array problem into a minimum l1 norm problem and obtains the sparse array by solving the convex optimization problem using the primal-dual algorithm. Meanwhile, to improve the degree of freedom, array elements are expanded using stochastic perturbation. According to the simulated-annealing algorithm, the closed array elements are reopened with a specific probability, which is iteratively thinned and expanded. The results show that the proposed method can obtain an extremely sparse array, which is better than that obtained using the existing methods.

Pattern synthesis of dual‐polarised conformal array based on adaptive iterative convex optimisation

Pattern synthesis of dual‐polarised conformal array based on adaptive iterative convex optimisation

Dynamic and Robust Sensor Selection Strategies for Wireless Positioning With TOA/RSS Measurement

Emerging wireless applications are requiring ever more accurate location-positioning from sensor measurements. In this paper, we develop sensor selection strategies for 3D wireless positioning based on time of arrival (TOA) and received signal strength (RSS) measurements to handle two distinct scenarios: (i) known approximated target location, for which we conduct dynamic sensor selection to minimize the positioning error; and (ii) unknown approximated target location, in which the worst-case positioning error is minimized via robust sensor selection. We derive expressions for the Cramér-Rao lower bound (CRLB) as a performance metric to quantify the positioning accuracy resulted from selected sensors. For dynamic sensor selection, two greedy selection strategies are proposed, each of which exploits properties revealed in the derived CRLB expressions. These selection strategies are shown to strike an efficient balance between computational complexity and performance suboptimality. For robust sensor selection, we show that the conventional convex relaxation approach leads to instability, and then develop three algorithms based on (i) iterative convex optimization (ICO), (ii) difference of convex functions programming (DCP), and (iii) discrete monotonic optimization (DMO). Each of these strategies exhibits a different tradeoff between computational complexity and optimality guarantee. Simulation results show that the proposed sensor selection strategies provide significant improvements in terms of accuracy and/or complexity compared to existing sensor selection methods.

Direct Shaping of Minimum and Maximum Singular Values: An 'H_/'H∞ Synthesis Approach for Fault Detection Filters

The performance of fault detection filters relies on a high sensitivity to faults and a low sensitivity to disturbances. The aim of this paper is to develop an approach to directly shape these sensitivities, expressed in terms of minimum and maximum singular values. The developed method offers an alternative solution to the H_/H∞ synthesis problem, building upon traditional multiobjective synthesis results. The result is an optimal filter synthesized via iterative convex optimization and the approach is particularly useful for fault diagnosis as illustrated by a numerical example.

An Effective Optimization Methods for the Suppression of Edge Effects in Ultrawideband Tightly Coupled Antenna Arrays

An effective optimization method is proposed for the suppression of edge effects in finite ultrawideband tightly coupled antenna arrays (TCAAs). By designing a practical finite TCAAs, the influences of edge effects on active voltage standing wave ratio (VSWR) are analyzed. Meanwhile, both the active VSWR and the array gain pattern are formulated as analytical expressions with respect to amplitude and phase excitations for analyzing the design freedom of edge effects. Aimed at suppressing the edge effects within an ultrawideband operation band, a nonconvex optimization problem is established for the synthesis of tightly coupled dipole arrays (TCDAs), where array gains at considered scanning angles and frequencies satisfying given maximum active VSWR and amplitude dynamic range ratio (DRR) are maximized. The nonconvex problem is transformed into an iterative convex optimization problem by the use of an iterative way, and the amplitude and phase excitations are efficiently solved by the convex optimization algorithm accordingly. By comparing to the traditional uniform amplitude and progressive phase excitation (UAPPE) method, the simulated and measured results of the ultrawideband TCDA show that the proposed method can slightly improve array gains at most frequencies, while the active VSWRs are suppressed to 3 over a 10:1 bandwidth when scanning up to 45°.

Synthesis of Difference Patterns for 3-D Conformal Beam-Scanning Arrays With Asymmetric Radiation Aperture

Due to the asymmetry of the elements’ position distribution and polarization direction, it is a challenge to synthesize difference patterns with large slope and symmetric main-lobe on 3-D conformal beam-scanning arrays with asymmetric radiation aperture. In this article, an approach to synthesize the optimal difference patterns for 3-D conformal arrays with asymmetric radiation aperture is proposed. To determine the limitation region of the main-lobe and sidelobe for a 3-D conformal array, an initial difference pattern is generated by the joint multidimensional vector clustering method. Then, an auxiliary phase function is introduced to convert the nonconvex constraint of the symmetry of the difference beam into a convex one. Finally, an iterative convex optimization is applied to obtain the optimal difference pattern. The optimization progress is finished by extracting the vector field patterns of a simulated antenna element. Two design examples employing hemispherical conformal array (HCA) and conical conformal array (CCA) with asymmetric radiation aperture are implemented to demonstrate the effectiveness of the proposed method. Difference patterns with −20 dB sidelobe level (SLL) and large slope are obtained in both numerical and simulated results of the two design examples.

Synthesis of Modular Subarrayed Phased-Array With Shaped-Beams by Means of Sequential Convex Optimization

In this letter, an efficient method based on sequential convex optimization is proposed to synthesize modular subarrayed phased-arrays with shaped beams. The proposed method consists of two steps. In the first step, the subarray configuration with exact tiling is acquired through solving iterative convex optimization problems. To obtain the arrangement of subarrays with exact tiling, the binary vector sparsity problem is relaxed to be a reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{l}}_1}$</tex-math></inline-formula> -norm minimization problem which can be solved efficiently by interior point method. In general, there are plenty of exact tiling configurations. To obtain the subarray configuration which is more conductive to radiating the target shaped-beam, the limiting conditions of the shaped-beam are added to the solution process of exact tiling. In the abovementioned solution process, the excitations of the subarrays can be obtained at the same time. However, due to the exact tiling constraints in the solution process, the obtained excitations are usually not the optimal solution for the obtained exact tiling configuration. Therefore, in the second step of the proposed method, the convex optimization method is used again to recompute the excitations of the modular subarrayed phased-array. Two numerical examples are implemented to verify the validity and reliability of the proposed method.

Fault Diagnostics and Tolerance Analysis of a Microgrid System Using Hamilton-Jacobi-Isaacs Equation and Game Theoretic Estimations in Sliding Mode Observers.

This paper focuses on robustness and sensitivity analysis for sensor fault diagnosis of a voltage source converter based microgrid model. It uses robust control parameters such as minimum sensitivity parameter , maximum robustness parameter , and compromised both , being incorporated in the sliding mode observer theory using the game theoretic saddle point estimation achieved through convex optimization of constrained LMIs. The approach used works in a way that the mentioned robust control parameters are embedded in Hamilton–Jacobi–Isaacs-Equation (HJIE) and are also used to determine the inequality version of HJIE, which is, in terms of the Lyapunov function, faults/disturbances and augmented state/output estimation error as its variables. The stability analysis is also presented by negative definiteness of the same inequality version of HJIE, and additionally, it also gives linear matrix inequalities (LMIs), which are optimized using iterative convex optimization algorithms to give optimal sliding mode observer gains enhanced with robustness to maximal preset values of disturbances and sensitivity to minimal preset values of faults. The enhanced sliding mode observer is used to estimate states, faults, and disturbances using sliding mode observer theory. The optimality of sliding mode observer gains for sensitivity of the observer to minimal faults and robustness to maximal disturbance is a game theoretic saddle point estimation achieved through convex optimization of LMIs. The paper includes results for state estimation errors, faults’ estimation/reconstruction, fault estimation errors, and fault-tolerant-control performance for current and potential transformer faults. The considered faults and disturbances in current and potential transformers are sinusoidal nature composite of magnitude/phase/harmonics at the same time.

Irregular Subarray Design Strategy Based on Weighted L1 Norm Iterative Convex Optimization

Subarray technology is an effective tradeoff between the sensor array radiation performance and manufacturing cost control. This letter proposes an irregular subarray tiling strategy based on the weighted L1 norm iterative convex optimization (WL1X) method. We first establish a subarray partition model and solve the L0 norm constraint problem by weighted L1 norm iterative convex optimization and then the optimal solution is selected based on the radiation performance. Further, We adopt a good initial point for the local optimization to improve scheme acquisition and selection efficiency. The proposed method can quickly obtain a subarray partition structure with better performance. The effectiveness and potential of the proposed methods are verified by various numerical examples.

UAV trajectory optimization using chance-constrained second-order cone programming

It is challenging to generate optimal trajectories for nonlinear dynamic systems under external disturbances. In this brief, we present a novel approach for planning safe trajectories of the chance-constrained trajectory optimization problems with nonconvex constraints. First, the chance constraints are handled by deterministic ones which show its availability. We derive an iterative convex optimization method to solve the optimal control problem. Then the chance-constrained optimal control (CCOCP) problem is reformed to be a nonlinear programming problem (NLP) through the hp-adaptive pseudospectral method. An iterative successive linearization algorithm is detailed to convex the NLP to be a convex optimization one which described as a second-order cone programming problem. We demonstrate the proposed approach on a 3-DoF of unmanned aerial vehicle system under chance-constrained. The simulation results show reliable solutions for the UAV chance-constrained trajectory optimization problem.

Synthesis of Sparse Antenna Arrays Subject to Constraint on Directivity via Iterative Convex Optimization

An effective optimization method is proposed for the synthesis of sparse antenna arrays subject to constraint on directivity in this letter. Based on the framework of thinned arrays synthesis, a real-value mixed integer programming problem for the minimization of the number of elements under given maximum sidelobe level, scan range, and minimum directivity in a limited array aperture is established. In order to solve this problem efficiently, an iterative convex optimization method is proposed, where the strategies of weighted l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm minimization and the polygonal expansion and contraction of the element position are integrated together organically. Owing to the adoption of such two strategies, both the search space regarding the element positions and the convergence speed can be controlled flexibly. Several representative numerical examples are presented in comparison with reported advanced methods to demonstrate the effectiveness of the proposed method.

Optimal Trajectory Generation for Intelligent Vehicles in Complex Traffic Based on Iteration Convex Optimization

Intelligent vehicles face considerable challenges in the complex traffic environment since they need to deal with various constraints and elements. This dissertation puts forward a novel trajectory planning framework for intelligent vehicles to generate safe and optimal driving trajectories. First, we design a spatiotemporal occupancy framework to deal with all kinds of elements in the complex driving environment based on the Frenét frame. This framework unifies various constraints on the road in the three-dimensional spatiotemporal representation and clearly describes the collision-free configuration space. Then we use the convex approximation method to construct a time-varying convex feasible region based on the above accurate temporal and spatial description. We formulate the trajectory planning problem as a standard quadratic programming formulation with collision-free and dynamics constraints. Finally, we apply the iterative convex optimization algorithm to solve the quadratic programming problem in the time-varying convex feasible region. Moreover, we design several typical experimental scenarios and have verified that the proposed method has good effectiveness and real-time.

Pattern Synthesis for Dual-Polarized Conformal Arrays via Iterative Convex Optimization

An iterative convex optimization (ICO) algorithm is proposed to solve pattern synthesis problem under the framework of dual-polarized conformal arrays in this paper. The subproblems of shaping main lobe, optimizing side lobe, and suppressing cross-polarization component are summarized as a joint optimization problem. To solve this problem, the nonconvex constraint about main lobe is rewritten as a convex constraint, which will bring error. And an auxiliary phase function is introduced to correct this error alternatively. Due to the deviation between auxiliary phase and real phase of pattern function, a method minimizing the peak of the synthesis error over observation angles is effectively applied to further improve the performance of the method. Numerical examples show good pattern synthesis ability and convergence performance of the ICO method.

On the assignability of LTI systems with arbitrary control structures

ABSTRACT In this paper, the assignability of linear time-invariant (LTI) systems with respect to arbitrary control structures is addressed. It is well established that the closed-loop spectrum of an LTI system with an arbitrary control structure is confined to the set containing the fixed-modes of the system with respect to that control structure. However, the assignment of the closed-loop spectrum is not merely limited by the existence of fixed-modes in practical scenarios. The pole assignment may require excessive control effort or even become infeasible due to the presence of small perturbations in the system dynamics. To offer more insights in such more realistic scenarios, a continuous measure known as fixed-mode radius is developed. However, its evaluation is confronted with a highly non-convex optimization problem combined with the need for a combinatorial search. This study utilises properties of positive-definite cones and duality theory to formulate the assignability assessment as an optimization problem with linear matrix inequality (LMI) constraints. Based on the suggested formulation, three alternative methods are proposed to evaluate the distance to unassignability. The first two methods offer alternative non-iterative and convex programs. The third method proposes an iterative convex optimization while updating the binary variables based on the dual variables. All the proposed methods rely on convex optimization, do not involve gridding over the complex plane and circumvent the combinatorial nature of the problem by using properties of positive definite cones. Simulation results confirm the effectiveness of the proposed methods in the assessment of fixed-mode radius with respect to arbitrary control structures.

Research on Multibeam Pattern Synthesis of Time Modulated Array Based on Convex Optimization

An efficient multibeam pattern synthesis method for time modulated array (TMA) is proposed in this paper. The aim of this method is to generate a beam pattern on the specified sideband of TMA. The pattern synthesis problem is divided into two stages. In the first stage, the sequential convex optimization method is used to suppress the sidelobe of the center frequency and reduce the amplitude dynamic range ratios (DRR). In the second stage, the iterative convex optimization method is used to realize the multibeam pattern synthesis in the sideband. Owing to the introduction of convex optimization, the proposed method could be more efficient than approaches using a global optimization algorithm. The proposed method is capable of realizing pattern synthesis under different DRR constraints and different beam radiation directions. Numerical examples of two beams and four beams patterns of 1000-element time modulated linear array verify the effectiveness of the proposed method.

Concentric Ring Array Synthesis for Low Side Lobes: An Overview and a Tool for Optimizing Ring Radii and Angle of Rotation

A comprehensive review on the approaches for synthesizing low side lobe concentric ring array (CRA) antennas is given. An Iterative Convex Optimization (ICO) based array layout synthesis technique is proposed for peak side-lobe level (PSLL) minimization over a given circular field-of-view in steerable uniform-amplitude concentric ring array (UA-CRA) antennas. For a given number of rings and number of uniformly-distributed elements in each ring, the ICO algorithm optimizes the ring radii and angle of rotation, with possible constraints on the minimum element separation and largest array size. As compared to the existing UA-CRA synthesis techniques, the proposed method presents unique features as it combines the capability of optimization of angle of rotation of the rings and PSLL minimization for multiple elevation scan angles in a computationally-efficient and easy-to-solve procedure. Through numerical design examples, it is demonstrated how the ICO technique can be effectively used (i) to synthesize sparse UA-CRA topologies generating low PSLL steerable beams, and (ii) to assess and improve the PSLL suppression performance of various known optimization algorithms. Based on the UA-CRA topologies synthesized via competitive methods in the recent literature, a new set of improved array topologies are presented.

Research on Pattern Synthesis of Time Modulated Sparse Array Based on Discrete Variable Convex Optimization

Effective resource utilization is an important problem in the application of array, especially for the new time modulated array. Considering the problem of full utilization of array elements in time modulated array, a sparse optimization algorithm based on discrete variable convex optimization is proposed in this paper. The pattern optimization of equal excitation time modulation array is realized in two stages: In the first stage, the number of working array elements is as low as possible under the condition of suppressing the sidelobe of the central frequency. In the second stage, the sideband is suppressed by iterative convex optimization. The numerical simulation results are compared with other methods to verify the effectiveness of the proposed method in pattern optimization of equal excitation time modulation array. Finally, the optimization performance of the algorithm with different array parameters is verified.

A Novel Subchannel and Power Allocation Algorithm in V2V Communication

This paper investigates resource allocation of latency constrained vehicle‐to‐vehicle (V2V) communication. When a subchannel of a vehicle‐to‐infrastructure (V2I) link can be reused by multiple V2V links, a nonlinear mixed integer optimization problem with the goal of maximizing the spectral efficiency of the system is derived under the constraints of minimum transmission rate of V2I links and transmission latency of V2V links. The subchannel allocation problem is solved by means of two‐sided exchange matching theory, optimal transmission power of V2I and V2V links is solved based on the poly‐block approximation (PBA) algorithm, and the system spectrum efficiency is maximized through loop iteration. In order to reduce the computational complexity of power allocation problem, a power allocation algorithm based on iterative convex optimization (ICO) is proposed. The convergence of the resource allocation algorithm is also proved. The simulation results show that the proposed algorithms can guarantee transmission latency requirements of V2V links and improve the system sum rate and access ratio of V2V links. Compared with two traditional algorithms, latency of poly‐block approximation combined with many to one matching (PBAMTO) is reduced by 30.41% and 20.43%, respectively.