Mixed linear regression (MLR) is a powerful model to characterize nonlinear relationships among observed data while still being simple and computationally efficient. This paper investigates the online learning and dat...
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Mixed linear regression (MLR) is a powerful model to characterize nonlinear relationships among observed data while still being simple and computationally efficient. This paper investigates the online learning and data clustering problem for MLR model with an arbitrary number of sub-models and arbitrary mixing weights. Previous investigations mainly focus on offline learning algorithms, and the convergence results are established under the independent and identically distributed (i.i.d.) input data assumption. To overcome these fundamental limitations, we propose a novel online learning algorithm for parameter estimation based on the EM principle. By using Ljung's ODE method and Lyapunov stability theorem, we first establish the almost sure convergence results of the proposed algorithm without the traditional i.i.d. assumption on the input data. Furthermore, by using the stochastic Lyapunov function method, we also provide its convergence rate analysis for the first time. Finally, we analyze the performance of online data clustering based on the parameter estimates, which is asymptotically the same as that in the case of known parameters. Copyright 2024 by the author(s)
This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances. A switched Koopman modeling...
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This paper proposes a data-driven learning-based approach to predictive control for switched nonlinear systems subject to state and control constraints and external stochastic disturbances. A switched Koopman modeling framework is developed, where a multi-mode neural network for state lifting is trained simultaneously with Koopman operators and state reconstruction matrices for all *** framework facilitates the construction of the switched linear Koopman model in a transformed space and effectively captures the dynamics of the original nonlinear system. A switched predictive control strategy is then designed to regulate the switched Koopman model with constrained states and control inputs against both the stochastic disturbances and the uncertainties introduced by the lifting neural network. The proposed control scheme ensures mean-square stability and guarantees boundedness during the online phase. Furthermore, boundedness analysis is performed to determine the bounded set of the original system state across all admissible switching sequences. The effectiveness of the proposed methodology is demonstrated through a case study of a gene regulatory network.
controller optimization has mostly been done by minimizing a certain single cost *** practice,however,engineers must contend with multiple and conflicting considerations,denoted as design indices(DIs)in this *** to ac...
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controller optimization has mostly been done by minimizing a certain single cost *** practice,however,engineers must contend with multiple and conflicting considerations,denoted as design indices(DIs)in this *** to account for such complexity and nuances is detrimental to the applications of any advanced control *** paper addresses this challenge heads on,in the context of active disturbance rejection controller(ADRC)and with four competing DIs:stability margins,tracking,disturbance rejection,and noise *** this end,the lower bound for the bandwidth of the extended state observer is first established for guaranteed closed-loop ***,one by one,the mathematical formula is meticulously derived,connecting each DI to the set of controller *** our best knowledge,this has not been done in the context of *** formulas allow engineers to see quantitatively how the change of each tuning parameter would impact all of the DIs,thus making the guesswork *** example is given to show how such analytical methods can help engineers quickly determine controller parameters in a practical scenario.
In this paper, we consider a model which is derived from a class of the 2-dimensional Kolmogorov systems. Our purpose is to investigate the continuity of periodic solutions for this model in coefficient functions with...
In this paper, we consider a model which is derived from a class of the 2-dimensional Kolmogorov systems. Our purpose is to investigate the continuity of periodic solutions for this model in coefficient functions with respect to weak topologies. Finally, we provide an example as an application to Lotka-Volterra systems.
The aim of quantum metrology is to exploit quantum effects to improve the precision of parameter estimation beyond its classical limit. In this paper, we investigate the quantum parameter estimation problem with multi...
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The aim of quantum metrology is to exploit quantum effects to improve the precision of parameter estimation beyond its classical limit. In this paper, we investigate the quantum parameter estimation problem with multiple channels. It is related but not limited to the following two important and practical quantum metrology problems:(i) Quantum enhanced metrology with control, whose aim is to improve the precision of quantum sensing by utilizing feedback or open-loop control;(ii) Practical quantum metrology where the underlying evolution of quantum probes may change from a unitary dynamics to an open system dynamics,owing to the inevitable decoherence during the quantum sensing operation. For various kinds of quantum multiple channels, the corresponding quantum channel Fisher information is derived. To demonstrate the results, some illustrative examples are given.
In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any ...
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In this paper,we present a novel penalty model called ExPen for optimization over the Stiefel *** from existing penalty functions for orthogonality constraints,ExPen adopts a smooth penalty function without using any first-order derivative of the objective *** show that all the first-order stationary points of ExPen with a sufficiently large penalty parameter are either feasible,namely,are the first-order stationary points of the original optimization problem,or far from the Stiefel ***,the original problem and ExPen share the same second-order stationary ***,the exact gradient and Hessian of ExPen are easy to *** a consequence,abundant algorithm resources in unconstrained optimization can be applied straightforwardly to solve ExPen.
The paper considers the control problem for uncertain nonlinear systems with unknown control input gain. Based on the information of control direction rather than the nominal value of control input gain, a new active ...
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The paper considers the control problem for uncertain nonlinear systems with unknown control input gain. Based on the information of control direction rather than the nominal value of control input gain, a new active disturbance rejection control design is proposed. In the proposed design, the extended state observer(ESO) is constructed to estimate the total disturbance containing the uncertainty of control input. Via the estimations from ESO, the control input is generated by a designed dynamical system, which can force the actual input to track the ideal input. Moreover, for a wide class of nonlinear uncertainties, the transient performance of the proposed design is investigated. The theoretical results show that the tracking and estimating errors, as well as the difference between the actual and ideal inputs, can be sufficiently small by tuning the parameter of ESO despite various uncertainties. The experiment of a permanent magnet linear synchronous motor servo system illustrates the effectiveness of the proposed design.
VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and *** calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to v...
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VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and *** calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2(AIVISS)to verify the existence of a double solution(a singular solution of an arbitrary multiplicity)of a slightly perturbed polynomial system.
An equivalent definition of hypermatrices is *** matrix expression of hypermatrices is *** permu-tation matrices,the conversion between different matrix expressions is *** various kinds of contracted products of hyper...
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An equivalent definition of hypermatrices is *** matrix expression of hypermatrices is *** permu-tation matrices,the conversion between different matrix expressions is *** various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.
We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering probl...
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We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition.A Nystr¨om method is proposed for the scattering problem based on the integral equation *** of the Nystr¨om method is established with convergence rate depending on the smoothness of the rough *** doing so,a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral *** experiments are presented to demonstrate the effectiveness of the *** subject classification:35P25,45P05.
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