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We develop several efficient algorithms for the classical Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input n× n matrix A, this problem asks to find diagonal (scaling) matrices X and Y (if they exist), so that X A Y ε-approximates a doubly stochastic matrix, or more generally a matrix...
This paper contributes to the convergence analysis of iterative learning control (ILC) for a linear time-varying system with measurement data dropouts, where the data dropout problem is formulated by a Markov chain model. The widely used Bernoulli model for data dropout is a special case of the Markov chain model. A regulating parameter is added to the classic P-type update law. The mean square and...
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method...
The approximation of stable linear time-invariant systems is a central task in many applications. Therefore, it is important to know if a given approximation process is stable and converges for all signals from the signal space or if it is unstable and diverges for certain signals. Further, in the case of divergence, it is interesting to know whether the set of signals with divergent approximation...
In this note, we investigate the problem of stabilization for second order switched systems by means of output feedback control and switching design. Under mild conditions, we design the output feedback and switching signal to exponentially stabilize the switched systems. Meanwhile, we optimize the switching signal to achieve nonovershooting of the output.
The number of crossband filters controls convergence rate and steady-state MSE of LMS algorithm in subband in the short-time Fourier domain, which necessitates a compromise between them due to its fixed value. Therefore, a decision to adaptively control the number of crossband filters is proposed to provide both fast convergence rate and small steady-state MSE. The advantage of the proposed algorithm...
Iterative learning control (ILC) is an important method for networked control systems and it uses the control information several times before to form the current control input signal [1]. Nowadays, ILC has developed maturely, but its output signal may cannot track the desired trajectory accurately because of the channel noise of wireless transmission. In this paper, we introduce the Adaptive Fourier...
In this paper, an implicit iterative algorithm is proposed to obtain the unique positive definite solution of the continuous algebraic Riccati matrix equation. In this proposed algorithm, there exists a tuning parameter which can be appropriately chosen such that the algorithm achieves better convergence performance. A sufficient condition is given for the convergence of the proposed algorithm. Moreover,...
We consider generalized resistive systems, comprising linear Kirchhoff equations and non-linear element equations, depending on the flow through the element and on two adjacent nodal variables. The derivatives of the element equation should possess a special signature. For such systems we prove the global non-degeneracy of the Jacobi matrix and the applicability of globally convergent solution tracing...
This contribution identifies an often ignored source of uncertainty in the accuracy of the adaptive cross approximation algorithm, and proposes a combination of adaptations that reduce this uncertainty with negligible additional computational cost.
The paper exploits the convergence characteristics of the first- and second-order PI-type iterative learning control (ILC) schemes for linear time-invariant (LTI) systems with direct-through terms. The aim is to investigate the effects of the integration embedments into the conventional P-type ILC rule. In the exploitation, the tracking errors are assessed in the form of the Lebesgue-p norm and the...
The goal of this paper is to study the state-feedback stabilization of controlled discrete-time switched linear systems (SLSs), where the discrete switching control input and the continuous control input coexist. We propose a periodic hybrid-control policies, periodic control Lyapunov functions (PCLFs), and prove that the existence of a quadratic PCLF is a necessary and sufficient condition for the...
A time-invariant, linear, distributed observer is described for estimating the state of an m > 0 channel, n-dimensional continuous-time linear system of the form ẋ = Ax, yi = Cix, i 2 ∈ {1, 2, …, m}. The state x is simultaneously estimated by m agents assuming each agent i senses yi and receives the state zj of each of its neighbors' estimators. Neighbor relations are characterized by a constant...
Iterative Learning Control (ILC) enables performance improvement by learning from previous tasks. The aim of this paper is to develop an ILC approach for Linear Parameter Varying (LPV) systems to enable improved performance and increased convergence speed compared to the linear time-invariant approach. This is achieved through dedicated analysis and norm-optimal synthesis of LPV learning filters....
This paper addresses the problem of multiple model adaptive estimation (MMAE) for discrete-time linear parameter varying (LPV) systems that are affected by parametric uncertainty. The MMAE system relies on a finite number of local observers, each designed using a selected model (SM) from the set of possible plant models. Each local observer is an LPV Kalman filter, obtained as a linear combination...
A new approach to the solution of the causal output tracking problem for discrete-time linear systems is presented. A dynamic steady state estimator is proposed in the form of a state observer taking as output, the reference to be tracked. Once the steady state has been estimated, the output tracking problem is converted into a stabilization problem and a control law is designed such that the output...
This paper presents the design of an impulsive observer based correction scheme to achieve the output regulation of a linear system having additive disturbances at the input. The sampled measurement is only available for the plant and the reference signal to achieve the output regulation. Impulsive observer could estimate the states in finite time for any applicable non-pathological sampling time...
This paper deals with the problem of the iterative learning tracking control (ILC) for continuous-time linear systems (LTI) operating in a repetitive manner. The design of iterative learning control law is developped by using the stability along the pass theory of 2D-repetitif systems. In this case, the convergence of the tracking error has been performed for a given learning controller gains. The...
In this paper we analyze the convergence behavior of a sampling based system approximation process, where the time variable is in the argument of the signal and not in the argument of the bandlimited impulse response. We consider the Paley-Wiener space PWπ2 of bandlimited signals with finite energy and stable linear time-invariant (LTI) systems, and show that there are signals and systems such that...
First order ordinary differential equations are associated to a system of linear algebraic equations with a positive definite matrix. Vector solutions of the differential systems are expressed in the form of infinite series in terms of the system matrix. They represent the parametric equations of the orthogonal trajectories to hypersurfaces defined by a related quadratic functional. The convergence...
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