Rank deficiency of the dynamic stiffness matrix is an indicator for resonance of a structure at a given frequency. This indicator can be exploited as a heuristic optimization objective to achieve resonance at several ...
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Rank deficiency of the dynamic stiffness matrix is an indicator for resonance of a structure at a given frequency. This indicator can be exploited as a heuristic optimization objective to achieve resonance at several frequencies. Log-det heuristic provides a tractable surrogate function for matrix rank in the case of affine dependency of stiffness and mass matrices on design parameters, which applies to truss structures. Reducing the rank of the dynamic stiffness matrix for higher frequencies implies that the matrix is not semi -positive definite. For this case, the log-det heuristic is valid with a combination of interior -point methods and Fazel's semi -definite embedding via linear matrix inequalities. Further constraints on the fundamental frequency and compliance can be easily added within the framework as linear matrix inequalities. Several successful numerical examples illustrate the performance of the approach.
The global optimum of the optimal power flow (OPF) problem can be sought in various practical settings by adopting the conic relaxations, such as the second order cone programs (SOCPs) and semi-definite programs (SDPs...
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The global optimum of the optimal power flow (OPF) problem can be sought in various practical settings by adopting the conic relaxations, such as the second order cone programs (SOCPs) and semi-definite programs (SDPs). However, the ZIP (constant impedance, constant current, constant power) and exponential load models are not directly amenable with these conic solvers. Thus, these are mostly treated as constant power loads in the literature. In this letter, we propose two simple methods to approximate these static loads with good accuracy. The proposed methods perform much better than the traditional constant power approximation.
Direction of Arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this work, we solve the c...
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ISBN:
(纸本)9781665405409
Direction of Arrival (DOA) estimation is widely applied in acoustic source localization. A multi-frequency model is suitable for characterizing the broadband structure in acoustic signals. In this work, we solve the continuous (gridless) line spectrum estimation problem by incorporating the multi-frequency model into an atomic norm minimization (ANM) framework. We show that our ANM problem is equivalent to a semi-definite program (SDP) which can be solved by an off-the-shelf SDP solver. We also provide the dual certificate that can certify the optimality of the SDP solution, and we localize the sources by finding the peaks of the norm of the dual polynomial. Numerical results support our theoretical findings and demonstrate the effectiveness of the method.
There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches. Each of these two approaches has their own complimentary set of advantages and d...
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There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches. Each of these two approaches has their own complimentary set of advantages and disadvantages, however, only limited attempts have, so far, been developed to bridge the gap between them. To address this issue, this paper introduces a method to bound the worst-case error between feedback control policies based upon model predictive control (MPC) and neural networks (NNs). This result is leveraged into an approach to automatically synthesize MPC policies minimising the worst-case error with respect to a NN. Numerical examples highlight the application of the bounds, with the goal of the paper being to encourage a more quantitative understanding of the relationship between data-driven and model-driven control.
We propose a method called Polynomial Quadratic Convex Reformulation (PQCR) to solve exactly unconstrained binary polynomial problems (UBP) through quadratic convex reformulation. First, we quadratize the problem by a...
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We propose a method called Polynomial Quadratic Convex Reformulation (PQCR) to solve exactly unconstrained binary polynomial problems (UBP) through quadratic convex reformulation. First, we quadratize the problem by adding new binary variables and reformulating (UBP) into a non-convex quadratic program with linear constraints (MIQP). We then consider the solution of (MIQP) with a specially-tailored quadratic convex reformulation method. In particular, this method relies, in a pre-processing step, on the resolution of a semi-definite programming problem where the link between initial and additional variables is used. We present computational results where we compare PQCR with the solvers Baron and Scip. We evaluate PQCR on instances of the image restoration problem and the low auto-correlation binary sequence problem from MINLPLib. For this last problem, 33 instances were unsolved in MINLPLib. We solve to optimality 10 of them, and for the 23 others we significantly improve the dual bounds. We also improve the best known solutions of many instances.
This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic pr...
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This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic process. Under such sporadically available measurement streams, a regulator consisting of a hybrid observer, continuous-time post-processing internal model, and stabilizer are proposed, which resets with the arrival of new measurements. The resulting system exhibits a deterministic behavior except for the jumps that occur at random sampling times and therefore the overall closed-loop system can be categorized as a piecewise deterministic Markov process (PDMP). In existing works on ORPs with aperiodic sampling, the requirement of boundedness on inter-sampling intervals precludes extending the solution to the random sampling intervals with possibly unbounded support. Using the Lyapunov-like theorem for the stability analysis of stochastic systems, we offer sufficient conditions to ensure that the overall closed-loop system is mean exponentially stable (MES) and the objectives of the ORP are achieved under stochastic sampling of measurement streams. The resulting LMI conditions lead to a numerically tractable design of the hybrid regulator. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are verified.(c) 2023 European Control Association. Published by Elsevier Ltd. All rights reserved.
A recent result on the potential of Delta \!\Sigma modulators ( Delta \!\Sigma Ms) as heuristic optimizers for circulant unconstrained discrete quadratic programming (C-UDQP) is revisited, bridging it with current dev...
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A recent result on the potential of Delta \!\Sigma modulators ( Delta \!\Sigma Ms) as heuristic optimizers for circulant unconstrained discrete quadratic programming (C-UDQP) is revisited, bridging it with current developments on the design of Delta \!\Sigma Ms by semi-definite programming (SDP). This provides an efficient strategy by which one can design a Delta \!\Sigma \text{M} and its input signal from a C-UDQP specification so that the solution of the C-UDQP problem can be found in the Delta \!\Sigma \text{M} output, all with almost no manual intervention. The proposed concept is validated by simulation-based experiments on a benchmark case, comparing the new strategy to previous results and exact optimization techniques.
This paper presents exact semi-definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectra...
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This paper presents exact semi-definite Program (SDP) reformulations for infinite-dimensional moment optimization problems involving a new class of piecewise Sum-of-Squares (SOS)-convex functions and projected spectrahedral support sets. These reformulations show that solving a single SDP finds the optimal value and an optimal probability measure of the original moment problem. This is done by establishing an SOS representation for the non-negativity of a piecewise SOS-convex function over a projected spectrahedron. Finally, as an application and a proof-of-concept illustration, the paper presents numerical results for the Newsvendor and revenue maximization problems with higher-order moments by solving their equivalent SDP reformulations. These reformulations promise a flexible and efficient approach to solving these models. The main novelty of the present work in relation to the recent research lies in finding the solution to moment problems, for the first time, with piecewise SOS-convex functions from their numerically tractable exact SDP reformulations.
In this paper, we consider a multi-tag symbiotic radio backscatter system, where a multi-antenna source node transmits its own message to a multi-antenna destination, while multiple backscatter tags transmit informati...
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In this paper, we consider a multi-tag symbiotic radio backscatter system, where a multi-antenna source node transmits its own message to a multi-antenna destination, while multiple backscatter tags transmit information to the destination by directly reflecting the incident signals from the source. We investigate the optimal beamforming design to minimize the transmit power at the source, subject to the signal-to-interference-plus -noise ratio (SINR) constraints for the signals of the source and the tags, and the harvested power constraints at the tags. The formulated min-power optimization problem is non-convex, and we propose a semi-definite programming (SDP) based alternating optimization algorithm to optimize the transmit beamforming vector at the source and the receive beamforming vector at the destination. Numerical results show that the proposed beamforming design algorithm converges fast and outperforms the counterpart scheme significantly.
Eclipsing is the designation for the attendant loss that occurs for return echoes that arrive when the receiver is turned off during the transmission of a long pulse. Assuming unknown knowledge about the target echo d...
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Eclipsing is the designation for the attendant loss that occurs for return echoes that arrive when the receiver is turned off during the transmission of a long pulse. Assuming unknown knowledge about the target echo delay (TED), this paper presents a robust design approach to jointly optimize the transmit sequence and receive filter for the detection of radar targets in the presence of return echo eclipsing loss and signal-dependent interference. The worst-case signal-to-interference-plus-noise-ratio (SINR) at the output of the filter is considered as the performance measure of the system. The robust design problem is formulated as a non-convex max-min optimization problem to robustify the system SINR with respect to the unknown target eclipsing loss condition. In addition to an energy constraint, an upper bound to the peak-to-average-power ratio (PAR) is imposed on the transmit sequence. The original non convex optimization problem is solved using relaxation methods and an iterative optimization process alternating between two sequential semi-definite programming (SDP) problems. Then, the randomization methods are utilized to synthesize the transmit sequence and the corresponding filter sharing the robust response. Finally, the effectiveness of the proposed procedure is demonstrated through experimental results, underlining the performance enhancement offered by a robust joint design. (C) 2020 Elsevier B.V. All rights reserved.
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