The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first dis...The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.展开更多
In this paper,a nonlinear control approach for an unstable networked plant in the presence of actuator and sensor limitations using robust right coprime factorization is proposed.The actuator is limited by upper and l...In this paper,a nonlinear control approach for an unstable networked plant in the presence of actuator and sensor limitations using robust right coprime factorization is proposed.The actuator is limited by upper and lower constraints and the sensor in the feedback loop is subjected to network-induced unknown time-varying delay and noise.With this nonlinear control method,we first employ right coprime factorization based on isomorphism and operator theory to factorize the plant,so that bounded input bounded output(BIBO)stability can be guaranteed.Next,continuous-time generalized predictive control(CGPC)is utilized for the unstable operator of the right coprime factorized plant to guarantee inner stability and enables the closed-loop dynamics of the system with predictive characteristics.Meanwhile,a second-Do F(degrees of freedom)switched controller that satisfies a perturbed Bezout identity and a robustness condition is designed.By using the CGPC controller that possesses predictive behavior and the second-Do F switched stabilizer,the overall stability of the plant subjected to actuator limitations is guaranteed.To address sensor limitations that exist in networked plants in the form of delay and noise which often cause system performance degradation,we implement an identity operator definition in the feedback loop to compensate for these adverse effects.Further,a pre-operator is designed to ensure that the plant output tracks the reference input.Finally,the effectiveness of the proposed design scheme is demonstrated by simulations.展开更多
Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to cert...Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.展开更多
Parallel arrays with coprime subarrays have shown its potential advantages for two dimensional direction of arrival(DOA)estimation.In this paper,by introducing two flexible coprime factors to enlarge the inter-element...Parallel arrays with coprime subarrays have shown its potential advantages for two dimensional direction of arrival(DOA)estimation.In this paper,by introducing two flexible coprime factors to enlarge the inter-element spacing of parallel uniform subarrays,we propose a generalized parallel coprime array(GPCA)geometry.The proposed geometry enjoys flexible array layouts by the coprime factors and enables to extend the array aperture to achieve great improvement of estimation performance.Meanwhile,we verify that GPCA always can obtain M2 degrees of freedom(DOFs)in co-array domain via 2M sensors after optimization,which outperforms sparse parallel array geometries,such as parallel coprime array(PCA)and parallel augmented coprime array(PACA),and is the same as parallel nested array(PNA)with extended aperture.The superiority of GPCA geometry has been proved by numerical simulations with sparse representation methods.展开更多
Nonuniform linear arrays,such as coprime array and nested array,have received great attentions because of the increased degrees of freedom(DOFs)and weakened mutual coupling.In this paper,inspired by the existing copri...Nonuniform linear arrays,such as coprime array and nested array,have received great attentions because of the increased degrees of freedom(DOFs)and weakened mutual coupling.In this paper,inspired by the existing coprime array,we propose a high-order extended coprime array(HoECA)for improved direction of arrival(DOA)estimation.We first derive the closed-form expressions for the range of consecutive lags.Then,by changing the inter-element spacing of a uniform linear array(ULA),three cases are proposed and discussed.It is indicated that the HoECA can obtain the largest number of consecutive lags when the spacing takes the maximum value.Finally,by comparing it with the other sparse arrays,the optimized HoECA enjoys a larger number of consecutive lags with mitigating mutual coupling.Simulation results are shown to evaluate the superiority of HoECA over the others in terms of DOF,mutual coupling leakage and estimation accuracy.展开更多
As the signal bandwidth and the number of channels increase, the synthetic aperture radar （SAR） imaging system produces huge amount of data according to the Shannon-Nyquist theorem, causing a huge burden for data tr...As the signal bandwidth and the number of channels increase, the synthetic aperture radar （SAR） imaging system produces huge amount of data according to the Shannon-Nyquist theorem, causing a huge burden for data transmission. This paper concerns the coprime sampl which are proposed recently but ng and nested sparse sampling, have never been applied to real world for target detection, and proposes a novel way which utilizes these new sub-Nyquist sampling structures for SAR sampling in azimuth and reconstructs the data of SAR sampling by compressive sensing （CS）. Both the simulated and real data are processed to test the algorithm, and the results indicate the way which combines these new undersampling structures and CS is able to achieve the SAR imaging effectively with much less data than regularly ways required. Finally, the influence of a little sampling jitter to SAR imaging is analyzed by theoretical analysis and experimental analysis, and then it concludes a little sampling jitter have no effect on image quality of SAR.展开更多
The robust control issue for uncertain nonlinear system is discussed by using the method of right coprime factorization.As it is difficult to obtain the inverse of the right factor due to the high nonlinearity,the pro...The robust control issue for uncertain nonlinear system is discussed by using the method of right coprime factorization.As it is difficult to obtain the inverse of the right factor due to the high nonlinearity,the proving of the Bezout identity becomes troublesome.Therefore,two sufficient conditions are derived to manage this problem with the nonlinear feedback system as well as that with the uncertain nonlinear feedback system under the definition of Lipschitz norm.A simulation of temperature control is given to demonstrate the validity of the proposed method.展开更多
This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimati...This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.展开更多
It is shown in this paper that any state space realization(A,b,c)of a given transfer function T(s)=β(s)/α(s)withα(s)monic and dim(A)=deg(α(s)),satisfies the identityβ(A)=Qe(A,b)SαQo(A,c)where Qc(A,b)and Qo(A,c)a...It is shown in this paper that any state space realization(A,b,c)of a given transfer function T(s)=β(s)/α(s)withα(s)monic and dim(A)=deg(α(s)),satisfies the identityβ(A)=Qe(A,b)SαQo(A,c)where Qc(A,b)and Qo(A,c)are the controllability matrix and observability matrix of the matrix triple(A,b,c),respectively,and S,~is a nonsingular symmetric matrix.Such an identity gives a deep relationship between the state space description and the transfer function description of single-input single-output(SISO)linear systems.As a direct conclusion,we arrive at the well-known result that a realization of any transfer function is minimal if and only if the numerator and the denominator of the transfer function is coprime.Such a result is also extended to the SISO descriptor linear system case.As an applications,a complete solution to the commuting matrix equation AX---XA is proposed and the minimal realization of multi-input multi-output(MIMO)linear system is considered.展开更多
An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing ...An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing the transmitter and receiver into two sparse subarrays,noncircular property of source can be used to construct new extended received signal model for two sparse subarrays.The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero.To further exploit the multidimensional structure of the noncircular received model,we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor,respectively.Thus,the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained.Then,the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship.Specifically,the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property.Furthermore,a closed-form expression for the deterministic CRB under the NC sources scenario is also derived.Simulation results verify the superiority of the proposed estimator.展开更多
The problem of joint direction of arrival(DOA)and polarization estimation for polarization sensitive coprime planar arrays(PS-CPAs)is investigated,and a fast-convergence quadrilinear decomposition approach is proposed...The problem of joint direction of arrival(DOA)and polarization estimation for polarization sensitive coprime planar arrays(PS-CPAs)is investigated,and a fast-convergence quadrilinear decomposition approach is proposed.Specifically,we first decompose the PS-CPA into two sparse polarization sensitive uniform planar subarrays and employ propagator method(PM)to construct the initial steering matrices separately.Then we arrange the received signals into two quadrilinear models so that the potential DOA and polarization estimates can be attained via quadrilinear alternating least square(QALS).Subsequently,we distinguish the true DOA estimates from the approximate intersecting estimations of the two subarrays in view of the coprime feature.Finally,the polarization estimates paired with DOA can be obtained.In contrast to the conventional QALS algorithm,the proposed approach can remarkably reduce the computational complexity without degrading the estimation performance.Simulations demonstrate the superiority of the proposed fast-convergence approach for PS-CPAs.展开更多
Direction of arrival(DOA)estimation for unfolded coprime array(UFCA)is discussed,and a method based on subspace compensation is proposed.Conventional DOA estimation meth-ods partition the UFCA into two subarrays for s...Direction of arrival(DOA)estimation for unfolded coprime array(UFCA)is discussed,and a method based on subspace compensation is proposed.Conventional DOA estimation meth-ods partition the UFCA into two subarrays for separate estimations,which are then combined for unique DOA determination.However,the DOA estimation performance loss is caused as only the partial array aperture is exploited.We use the estimations from one subarray as initial estimations,and then enhance the estimation results via a compensation based on the whole array,which is im-plemented via a simple least squares(LS)operation constructed from the initial estimation and first-order Taylor expansion.Compared to conventional methods,the DOA estimation performance is improved while the computational complexity is in the same level.Multiple simulations are con-ducted to verify the efficiency of the proposed approach.展开更多
The concept of difference and sum(diff-sum)coarray has attracted a lot of attentions in the estimation of direction-of-arrival(DOA)for the past few years,due to its high degrees-of-freedom(DOFs).A vectorized conjugate...The concept of difference and sum(diff-sum)coarray has attracted a lot of attentions in the estimation of direction-of-arrival(DOA)for the past few years,due to its high degrees-of-freedom(DOFs).A vectorized conjugate augmented MUSIC(VCA-MUSIC)algorithm is applied to generate an equivalent signal model which contains the virtual sensor positions of both the difference and sum of the physical sensors in the two-dimensional(2D)arrays,by utilizing both the spatial and temporal information.Besides,an augmented 2D coprime array configuration is presented with the basis on the concept of difference and sum coarray.By compressing the inter-element spacing of one subarray and introducing the proper separation between the two subarrays of 2D coprime array,the redundancy between the difference coarray and the sum one can be reduced so that more virtual sensors in both coarrays can make contributions to the DOFs.As a result,a much larger consecutive area in the diff-sum coarray can be achieved,which can significantly increase the DOFs.Numerical simulations verify the superiority of the proposed array configuration.展开更多
Let a finite group A act on a finite group G via automorphism and let s be a positive integer.In this paper,we introduce the probabilistic zeta function of ordered s-tuples from G which A-generate G,denoted by P^(A)(G...Let a finite group A act on a finite group G via automorphism and let s be a positive integer.In this paper,we introduce the probabilistic zeta function of ordered s-tuples from G which A-generate G,denoted by P^(A)(G,s).When(|A|,|G|)=1,it is proved that G is solvable if and only if P^(A)(G,s)has an Euler product expansion with all factors of the form 1-c/q^(s),where each q is a prime power.This is a generalization of Detomi and Lucchini's result in 2003.展开更多
Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We show that if 4 divides no A-invariant conjugacy class size of G, then G is solvable. We also characterize the A-invariant struc...Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We show that if 4 divides no A-invariant conjugacy class size of G, then G is solvable. We also characterize the A-invariant structure of G under certain arithmetical conditions on the set of A-invariant class sizes of G by means of the fixed point subgroup, some of which imply the solvability of G. Thus, we extend, for coprime action, several results appeared in the literature on class sizes.展开更多
Blade Tip Timing(BTT)enables non-contact measurements of rotating blades by placing probes strategically.Due to the uneven probe layout,BTT signals exhibit periodic irregularities.While recovering parameters like freq...Blade Tip Timing(BTT)enables non-contact measurements of rotating blades by placing probes strategically.Due to the uneven probe layout,BTT signals exhibit periodic irregularities.While recovering parameters like frequency from such signals is possible,achieving high-precision vibration parameters remains challenging.This paper proposed a novel two-stage off-grid estimation method.It leverages a unique array layout(coprime array)to obtain a regular augmented covariance matrix.Subsequently,parameters in the matrix are recovered using the sparse iterative covariance-based estimation method based on covariance fitting criteria.Finally,high-precision estimates of imprecise parameters are obtained using unconditional maximum likelihood estimation,effectively eliminating the effects of basis mismatch.Through substantial numerical and experimental validation,the proposed method demonstrates significantly higher accuracy compared to classical BTT parameter estimation methods,approaching the lower bound of unbiased estimation variance.Furthermore,due to its immunity to frequency gridding,it can track minor frequency deviations,making it more suitable for indicating blade condition.展开更多
In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is c...In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.展开更多
In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering th...In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.展开更多
In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decre...In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decrease the cost of their production.Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily,the vibration suppression control is needed for realizing the above purpose.Incidentally,the use of various smart materials in actuators has grown.In particular,a shape memory alloy(SMA)is applied widely and has several advantages:light weight,large displacement by temperature change,and large force to mass ratio.However,the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature.The hysteretic behavior of the SMA actuators affects their control performance.In previous research,an operator-based control system including a hysteresis compensator has been proposed.The vibration of a flexible arm is dealt with as the controlled object;one end of the arm is clamped and the other end is free.The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments.Nevertheless,the feedback signal of the previous designed system has increased exponentially.It is difficult to use the system in the long-term because of the phenomenon.Additionally,the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat,and strain on the SMA actuator is generated.With long-time use of the SMA actuator,the environmental temperature around the SMA actuator varies through radiation of the heat.There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator.In this research,a design method of the operator-based control system is proposed considering the long-term use of the system.In the method,the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered.The effectiveness of the proposed method is verified by simulations and experiments.展开更多
In this study,the passivity-based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator-based robust right coprime factorisation method is concerned.For the system with u...In this study,the passivity-based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator-based robust right coprime factorisation method is concerned.For the system with unknown perturbations,a design scheme is proposed to guarantee the uncertain non-linear systems to be robustly stable while the equivalent non-linear systems is passive,meanwhile the asymptotic tracking property of the plant output is discussed.Moreover,the design scheme can be also used into the general Hamiltonian systems while the simulation is used to further demonstrate the effectiveness of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(12271154)the Natural Science Foundation of Hunan Province(2022JJ30234)the Postgraduate Scientific Research Innovation Project of Hunan Province(CX20231032)。
文摘The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence,and is closely related to zero coprime equivalence of multivariate polynomial matrices.We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices.Then,we investigate the zero coprime equivalence problem for several classes of polynomial matrices,some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained.Finally,an example is provided to illustrate the main results.
文摘In this paper,a nonlinear control approach for an unstable networked plant in the presence of actuator and sensor limitations using robust right coprime factorization is proposed.The actuator is limited by upper and lower constraints and the sensor in the feedback loop is subjected to network-induced unknown time-varying delay and noise.With this nonlinear control method,we first employ right coprime factorization based on isomorphism and operator theory to factorize the plant,so that bounded input bounded output(BIBO)stability can be guaranteed.Next,continuous-time generalized predictive control(CGPC)is utilized for the unstable operator of the right coprime factorized plant to guarantee inner stability and enables the closed-loop dynamics of the system with predictive characteristics.Meanwhile,a second-Do F(degrees of freedom)switched controller that satisfies a perturbed Bezout identity and a robustness condition is designed.By using the CGPC controller that possesses predictive behavior and the second-Do F switched stabilizer,the overall stability of the plant subjected to actuator limitations is guaranteed.To address sensor limitations that exist in networked plants in the form of delay and noise which often cause system performance degradation,we implement an identity operator definition in the feedback loop to compensate for these adverse effects.Further,a pre-operator is designed to ensure that the plant output tracks the reference input.Finally,the effectiveness of the proposed design scheme is demonstrated by simulations.
基金Supported by the Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0884)。
文摘Graph labeling is the assignment of integers to the vertices,edges,or both,subject to certain conditions.Accordingly,hypergraph labeling is also the assignment of integers to the vertices,edges,or both,subject to certain conditions.This paper is to generalize the coprime labelings of graph to hypergraph.We give the definition of coprime labelings of hypergraph.By using Rosser-Schoenfeld's inequality and the coprime mapping theorem of Pomerance and Selfridge,we prove that some linear hypergraphs are prime.
文摘Parallel arrays with coprime subarrays have shown its potential advantages for two dimensional direction of arrival(DOA)estimation.In this paper,by introducing two flexible coprime factors to enlarge the inter-element spacing of parallel uniform subarrays,we propose a generalized parallel coprime array(GPCA)geometry.The proposed geometry enjoys flexible array layouts by the coprime factors and enables to extend the array aperture to achieve great improvement of estimation performance.Meanwhile,we verify that GPCA always can obtain M2 degrees of freedom(DOFs)in co-array domain via 2M sensors after optimization,which outperforms sparse parallel array geometries,such as parallel coprime array(PCA)and parallel augmented coprime array(PACA),and is the same as parallel nested array(PNA)with extended aperture.The superiority of GPCA geometry has been proved by numerical simulations with sparse representation methods.
基金supported by the National Natural Science Foundation of China(62071476,62022091,61801488,61921001)the China Postdoctoral Science Foundation(2021T140788,2020M683728)+1 种基金the Science and Technology Innovation Program of Hunan Province(2020RC2041)the Research Program of National University of Defense Technology(ZK19-10,ZK20-33).
文摘Nonuniform linear arrays,such as coprime array and nested array,have received great attentions because of the increased degrees of freedom(DOFs)and weakened mutual coupling.In this paper,inspired by the existing coprime array,we propose a high-order extended coprime array(HoECA)for improved direction of arrival(DOA)estimation.We first derive the closed-form expressions for the range of consecutive lags.Then,by changing the inter-element spacing of a uniform linear array(ULA),three cases are proposed and discussed.It is indicated that the HoECA can obtain the largest number of consecutive lags when the spacing takes the maximum value.Finally,by comparing it with the other sparse arrays,the optimized HoECA enjoys a larger number of consecutive lags with mitigating mutual coupling.Simulation results are shown to evaluate the superiority of HoECA over the others in terms of DOF,mutual coupling leakage and estimation accuracy.
基金supported by the National Natural Science Foundation of China(61571388U1233109)
文摘As the signal bandwidth and the number of channels increase, the synthetic aperture radar （SAR） imaging system produces huge amount of data according to the Shannon-Nyquist theorem, causing a huge burden for data transmission. This paper concerns the coprime sampl which are proposed recently but ng and nested sparse sampling, have never been applied to real world for target detection, and proposes a novel way which utilizes these new sub-Nyquist sampling structures for SAR sampling in azimuth and reconstructs the data of SAR sampling by compressive sensing （CS）. Both the simulated and real data are processed to test the algorithm, and the results indicate the way which combines these new undersampling structures and CS is able to achieve the SAR imaging effectively with much less data than regularly ways required. Finally, the influence of a little sampling jitter to SAR imaging is analyzed by theoretical analysis and experimental analysis, and then it concludes a little sampling jitter have no effect on image quality of SAR.
基金supported by the National Natural Science Foundation of China(61304093,61472195)
文摘The robust control issue for uncertain nonlinear system is discussed by using the method of right coprime factorization.As it is difficult to obtain the inverse of the right factor due to the high nonlinearity,the proving of the Bezout identity becomes troublesome.Therefore,two sufficient conditions are derived to manage this problem with the nonlinear feedback system as well as that with the uncertain nonlinear feedback system under the definition of Lipschitz norm.A simulation of temperature control is given to demonstrate the validity of the proposed method.
基金supported by the National Natural Science Foundations of China (Nos.61371169,61601167, 61601504)the Natural Science Foundation of Jiangsu Province (No.BK20161489)+1 种基金the Open Research Fund of State Key Laboratory of Millimeter Waves, Southeast University (No. K201826)the Fundamental Research Funds for the Central Universities (No. NE2017103)
文摘This paper presents a low?complexity method for the direction?of?arrival(DOA)estimation of noncircular signals for coprime sensor arrays.The noncircular property is exploited to improve the performance of DOA estimation.To reduce the computational complexity,the rotational invariance propagator method(RIPM)is included in the algorithm.First,the extended array output is reconstructed by combining the array output and its conjugated counterpart.Then,the RIPM is utilized to obtain two sets of DOA estimates for two subarrays.Finally,the true DOAs are estimated by combining the consistent results of the two subarrays.This illustrates the potential gain that both noncircularity and coprime arrays provide when considered together.The proposed algorithm has a lower computational complexity and a better DOA estimation performance than the standard estimation of signal parameters by the rotational invariance technique and Capon algorithm.Numerical simulation results illustrate the effectiveness and superiority of the proposed algorithm.
基金the Chinese Outstanding Youth Foundation(No.69925308)Program for Changjiang Scholars and Innovative Research Team in University.
文摘It is shown in this paper that any state space realization(A,b,c)of a given transfer function T(s)=β(s)/α(s)withα(s)monic and dim(A)=deg(α(s)),satisfies the identityβ(A)=Qe(A,b)SαQo(A,c)where Qc(A,b)and Qo(A,c)are the controllability matrix and observability matrix of the matrix triple(A,b,c),respectively,and S,~is a nonsingular symmetric matrix.Such an identity gives a deep relationship between the state space description and the transfer function description of single-input single-output(SISO)linear systems.As a direct conclusion,we arrive at the well-known result that a realization of any transfer function is minimal if and only if the numerator and the denominator of the transfer function is coprime.Such a result is also extended to the SISO descriptor linear system case.As an applications,a complete solution to the commuting matrix equation AX---XA is proposed and the minimal realization of multi-input multi-output(MIMO)linear system is considered.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61701507,61890542,and 61890540).
文摘An effective method via tensor decomposition is proposed to deal with the joint direction-of-departure(DOD)and direction-of-arrival(DOA)estimation of noncircular sources in colocated coprime MIMO radar.By decomposing the transmitter and receiver into two sparse subarrays,noncircular property of source can be used to construct new extended received signal model for two sparse subarrays.The new received model can double the virtual array aperture due to the elliptic covariance of imping sources is nonzero.To further exploit the multidimensional structure of the noncircular received model,we stack the subarray output and its conjugation according to mode-1 unfolding and mode-2 unfolding of a third-order tensor,respectively.Thus,the corresponding extended tensor model consisted of noncircular information for DOA and DOD can be obtained.Then,the higher-order singular value decomposition technique is utilized to estimate the accurate signal subspace and angular parameter can be automatically paired via the rotational invariance relationship.Specifically,the ambiguous angle can be eliminated and the true targets can be achieved with the aid of the coprime property.Furthermore,a closed-form expression for the deterministic CRB under the NC sources scenario is also derived.Simulation results verify the superiority of the proposed estimator.
基金supported by the Open Research Fund of the State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System(No.CEMEE2019Z0104B)。
文摘The problem of joint direction of arrival(DOA)and polarization estimation for polarization sensitive coprime planar arrays(PS-CPAs)is investigated,and a fast-convergence quadrilinear decomposition approach is proposed.Specifically,we first decompose the PS-CPA into two sparse polarization sensitive uniform planar subarrays and employ propagator method(PM)to construct the initial steering matrices separately.Then we arrange the received signals into two quadrilinear models so that the potential DOA and polarization estimates can be attained via quadrilinear alternating least square(QALS).Subsequently,we distinguish the true DOA estimates from the approximate intersecting estimations of the two subarrays in view of the coprime feature.Finally,the polarization estimates paired with DOA can be obtained.In contrast to the conventional QALS algorithm,the proposed approach can remarkably reduce the computational complexity without degrading the estimation performance.Simulations demonstrate the superiority of the proposed fast-convergence approach for PS-CPAs.
基金the Fund of State Key Laboratory of Com-plex Electromagnetic Environment Effects on Electronics and Information System(CEMEE 2021Z0101B)the Na-tional Natural Science Foundation of China(No.61601167).
文摘Direction of arrival(DOA)estimation for unfolded coprime array(UFCA)is discussed,and a method based on subspace compensation is proposed.Conventional DOA estimation meth-ods partition the UFCA into two subarrays for separate estimations,which are then combined for unique DOA determination.However,the DOA estimation performance loss is caused as only the partial array aperture is exploited.We use the estimations from one subarray as initial estimations,and then enhance the estimation results via a compensation based on the whole array,which is im-plemented via a simple least squares(LS)operation constructed from the initial estimation and first-order Taylor expansion.Compared to conventional methods,the DOA estimation performance is improved while the computational complexity is in the same level.Multiple simulations are con-ducted to verify the efficiency of the proposed approach.
基金Supported by the National Natural Science Foundation of China(61801024)。
文摘The concept of difference and sum(diff-sum)coarray has attracted a lot of attentions in the estimation of direction-of-arrival(DOA)for the past few years,due to its high degrees-of-freedom(DOFs).A vectorized conjugate augmented MUSIC(VCA-MUSIC)algorithm is applied to generate an equivalent signal model which contains the virtual sensor positions of both the difference and sum of the physical sensors in the two-dimensional(2D)arrays,by utilizing both the spatial and temporal information.Besides,an augmented 2D coprime array configuration is presented with the basis on the concept of difference and sum coarray.By compressing the inter-element spacing of one subarray and introducing the proper separation between the two subarrays of 2D coprime array,the redundancy between the difference coarray and the sum one can be reduced so that more virtual sensors in both coarrays can make contributions to the DOFs.As a result,a much larger consecutive area in the diff-sum coarray can be achieved,which can significantly increase the DOFs.Numerical simulations verify the superiority of the proposed array configuration.
基金supported by Shanghai Sailing Program(20YF1413400)Young Scientists Fund of the National Natural Science Foundation of China(12001359)supported by the National Natural Science Foundation of China(12171302).
文摘Let a finite group A act on a finite group G via automorphism and let s be a positive integer.In this paper,we introduce the probabilistic zeta function of ordered s-tuples from G which A-generate G,denoted by P^(A)(G,s).When(|A|,|G|)=1,it is proved that G is solvable if and only if P^(A)(G,s)has an Euler product expansion with all factors of the form 1-c/q^(s),where each q is a prime power.This is a generalization of Detomi and Lucchini's result in 2003.
基金supported by National Natural Science Foundation of China(Grant No.11301218)the Nature Science Fund of Shandong Province(Grant No.ZR2014AM020)+4 种基金University of Jinan Research Funds for Doctors(Grant Nos.XBS1335 and XBS1336)the Valencian GovernmentProyecto PROMETEO/2011/30the Spanish GovernmentProyecto(Grant No.MTM2010-19938-C03-02)
文摘Let A and G be finite groups and suppose that A acts coprimely on G via automorphisms. We show that if 4 divides no A-invariant conjugacy class size of G, then G is solvable. We also characterize the A-invariant structure of G under certain arithmetical conditions on the set of A-invariant class sizes of G by means of the fixed point subgroup, some of which imply the solvability of G. Thus, we extend, for coprime action, several results appeared in the literature on class sizes.
基金the National Natural Science Foundation of China(Nos.52105117,52222504&51875433)the Funds for Distinguished Young talent of Shaanxi Province,China(No.2019JC-04)。
文摘Blade Tip Timing(BTT)enables non-contact measurements of rotating blades by placing probes strategically.Due to the uneven probe layout,BTT signals exhibit periodic irregularities.While recovering parameters like frequency from such signals is possible,achieving high-precision vibration parameters remains challenging.This paper proposed a novel two-stage off-grid estimation method.It leverages a unique array layout(coprime array)to obtain a regular augmented covariance matrix.Subsequently,parameters in the matrix are recovered using the sparse iterative covariance-based estimation method based on covariance fitting criteria.Finally,high-precision estimates of imprecise parameters are obtained using unconditional maximum likelihood estimation,effectively eliminating the effects of basis mismatch.Through substantial numerical and experimental validation,the proposed method demonstrates significantly higher accuracy compared to classical BTT parameter estimation methods,approaching the lower bound of unbiased estimation variance.Furthermore,due to its immunity to frequency gridding,it can track minor frequency deviations,making it more suitable for indicating blade condition.
基金supported by the National Natural Science Foundation of China(61203229)
文摘In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.
文摘In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.
文摘In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decrease the cost of their production.Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily,the vibration suppression control is needed for realizing the above purpose.Incidentally,the use of various smart materials in actuators has grown.In particular,a shape memory alloy(SMA)is applied widely and has several advantages:light weight,large displacement by temperature change,and large force to mass ratio.However,the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature.The hysteretic behavior of the SMA actuators affects their control performance.In previous research,an operator-based control system including a hysteresis compensator has been proposed.The vibration of a flexible arm is dealt with as the controlled object;one end of the arm is clamped and the other end is free.The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments.Nevertheless,the feedback signal of the previous designed system has increased exponentially.It is difficult to use the system in the long-term because of the phenomenon.Additionally,the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat,and strain on the SMA actuator is generated.With long-time use of the SMA actuator,the environmental temperature around the SMA actuator varies through radiation of the heat.There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator.In this research,a design method of the operator-based control system is proposed considering the long-term use of the system.In the method,the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered.The effectiveness of the proposed method is verified by simulations and experiments.
基金National Natural Science Foundation of China,Grant/Award Number:61304093Natural Science Foundation of Shandong Province,Grant/Award Number:ZR2021MF047。
文摘In this study,the passivity-based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator-based robust right coprime factorisation method is concerned.For the system with unknown perturbations,a design scheme is proposed to guarantee the uncertain non-linear systems to be robustly stable while the equivalent non-linear systems is passive,meanwhile the asymptotic tracking property of the plant output is discussed.Moreover,the design scheme can be also used into the general Hamiltonian systems while the simulation is used to further demonstrate the effectiveness of the proposed method.
