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Masaaki Nagahara

Publications and source records attributed to Masaaki Nagahara.

At least 37 records · Page 2Linked to original sources
arXiv2017

Min-Max Design of Feedback Quantizers for Netorwked Control Systems

In a networked control system, quantization is inevitable to transmit control and measurement signals. While uniform quantizers are often used in practical systems, the overloading, which is due to the limitation on the number of bits in the quantizer, may significantly degrade the control performance. In this paper, we design an overloading-free feedback quantizer based on a Delta-Sigma modulator,composed of an error feedback filter and a static quantizer. To guarantee no-overloading in the quantizer, we impose an $l_{\infty}$ norm constraint on the feedback signal in the quantizer. Then, for a prescribed $l_{\infty}$ norm constraint on the error at the system output induced by the quantizer, we design the error feedback filter that requires the minimum number of bits that achieves the constraint. Next, for a fixed number of bits for the quantizer, we investigate the achievable minimum $l_{\infty}$ norm of the error at the system output with an overloading-free quantizer. Numerical examples are provided to validate our analysis and synthesis.

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arXiv2016

Continuous Hands-off Control by CLOT Norm Minimization

In this paper, we consider hands-off control via minimization of the CLOT (Combined L-One and Two) norm. The maximum hands-off control is the L0-optimal (or the sparsest) control among all feasible controls that are bounded by a specified value and transfer the state from a given initial state to the origin within a fixed time duration. In general, the maximum hands-off control is a bang-off-bang control taking values of +1, -1, and 0. For many real applications, such discontinuity in the control is not desirable. To obtain a continuous but still relatively sparse control, we propose to use the CLOT norm, a convex combination of L1 and L2 norms. We show by numerical simulation that the CLOT control is continuous and much sparser (i.e. has longer time duration on which the control takes 0) than the conventional EN (elastic net) control, which is a convex combination of L1 and squared L2 norms.

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arXiv2016

Rate-Distortion Analysis of Quantizers with Error Feedback

A Delta-Sigma modulator that is often utilized to convert analog signals into digital signals can be modeled as a static uniform quantizer with an error feedback filter. In this paper, we present a rate-distortion analysis of quantizers with error feedback including the Delta-Sigma modulators, assuming that the error owing to overloading in the static quantizer is negligible. We demonstrate that the amplitude response of the optimal error feedback filter that minimizes the mean squared quantization error can be parameterized by one parameter. This parameterization enables us to determine the optimal error feedback filter numerically. The relationship between the number of bits used for the quantization and the achievable mean squared error can be obtained using the optimal error feedback filter. This clarifies the rate-distortion property of quantizers with error feedback. Then, ideal optimal error feedback filters are approximated by practical filters using the Yule-Walker method and the linear matrix inequality-based method. Numerical examples are provided for demonstrating our analysis and synthesis.

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arXiv2016

Characterization of maximum hands-off control

Maximum hands-off control aims to maximize the length of time over which zero actuator values are applied to a system when executing specified control tasks. To tackle such problems, recent literature has investigated optimal control problems which penalize the size of the support of the control function and thereby lead to desired sparsity properties. This article gives the exact set of necessary conditions for a maximum hands-off optimal control problem using an $L_0$-(semi)norm, and also provides sufficient conditions for the optimality of such controls. Numerical example illustrates that adopting an $L_0$ cost leads to a sparse control, whereas an $L_1$-relaxation in singular problems leads to a non-sparse solution.

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arXiv2015

Maximum Hands-off Control without Normality Assumption

Maximum hands-off control is a control that has the minimum L0 norm among all feasible controls. It is known that the maximum hands-off (or L0-optimal) control problem is equivalent to the L1-optimal control under the assumption of normality. In this article, we analyze the maximum hands-off control for linear time-invariant systems without the normality assumption. For this purpose, we introduce the Lp-optimal control with 0<p<1, which is a natural relaxation of the L0 problem. By using this, we investigate the existence and the bang-off-bang property (i.e. the control takes values of 1, 0 and -1) of the maximum hands-off control. We then describe a general relation between the maximum hands-off control and the L1-optimal control. We also prove the continuity and convexity property of the value function, which plays an important role to prove the stability when the (finite-horizon) control is extended to model predictive control.

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arXiv2015

Multiuser Detection by MAP Estimation with Sum-of-Absolute-Values Relaxation

In this article, we consider multiuser detection that copes with multiple access interference caused in star-topology machine-to-machine (M2M) communications. We assume that the transmitted signals are discrete-valued (e.g. binary signals taking values of $\pm 1$), which is taken into account as prior information in detection. We formulate the detection problem as the maximum a posteriori (MAP) estimation, which is relaxed to a convex optimization called the sum-of-absolute-values (SOAV) optimization. The SOAV optimization can be efficiently solved by a proximal splitting algorithm, for which we give the proximity operator in a closed form. Numerical simulations are shown to illustrate the effectiveness of the proposed approach compared with the linear minimum mean-square-error (LMMSE) and the least absolute shrinkage and selection operator (LASSO) methods.

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arXiv2015

Discrete-Valued Control by Sum-of-Absolute-Values Optimization

In this paper, we propose a new design method of discrete-valued control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. We first formulate the discrete-valued control design as a finite-horizon SOAV optimal control, which is an extended version of L1 optimal control. We then give simple conditions that guarantee the existence, discreteness, and uniqueness of the SOAV optimal control. Also, we give the continuity property of the value function, by which we prove the stability of infinite-horizon model predictive SOAV control systems. We provide a fast algorithm for the SOAV optimization based on the alternating direction method of multipliers (ADMM), which has an important advantage in real-time control computation. A simulation result shows the effectiveness of the proposed method.

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arXiv2015

Symbol Detection for Frame-Based Faster-than-Nyquist Signaling via Sum-of-Absolute-Values Optimization

In this letter, we propose a new symbol detection method for faster-than-Nyquist signaling (FTNS) systems. Based on frame theory, we formulate a symbol detection problem as a under-determined linear equation on a finite set. The problem is reformulated as a sum-of-absolute-values (SOAV) optimization that can be efficiently solved by the fast iterative shrinkage thresholding algorithm (FISTA). The proximity operator for the convex optimization is derived analytically. Simulation results are given to show that the proposed method can successfully detect symbols in faster-than-Nyquist signaling systems and has lower complexity in terms of computation time.

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arXiv2015

Loop-Back Interference Suppression for OFDM Signals via Sampled-Data Control

In this article, we consider the problem of loop-back interference suppression for orthogonal frequency division multiplexing (OFDM) signals in amplify-and-forward single-frequency full-duplex relay stations. The loop-back interference makes the system a closed-loop system, and hence it is important not only to suppress the interference but also to stabilize the system. For this purpose, we propose sampled-data $H^{\infty}$ design of digital filters that ensure the stability of the system and suppress the continuous-time effect of interference at the same time. Simulation results are shown to illustrate the effectiveness of the proposed method.

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arXiv2015

Digital Cancelation of Self-Interference for Single-Frequency Full-Duplex Relay Stations via Sampled-Data Control

In this article, we propose sampled-data design of digital filters that cancel the continuous-time effect of coupling waves in a single-frequency full-duplex relay station. In this study, we model a relay station as a continuoustime system while conventional researches treat it as a discrete-time system. For a continuous-time model, we propose digital feedback canceler based on the sampled-data H-infinity control theory to cancel coupling waves taking intersample behavior into account. We also propose robust control against unknown multipath interference. Simulation results are shown to illustrate the effectiveness of the proposed method.

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arXiv2015

Sampled-data $H^{\infty}$ Optimization for Self-interference Suppression in Baseband Signal Subspaces

In this article, we propose a design method of selfinterference cancelers for wireless relay stations taking account of the baseband signal subspace. The problem is first formulated as a sampled-data $H^{\infty}$ control problem with a generalized sampler and a generalized hold, which can be reduced to a discretetime $\ell^2$-induced norm minimization problem. Taking account of the implementation of the generalized sampler and hold, we adopt the filter-sampler structure for the generalized sampler, and the uspampler-filter-hold structure for the generalized hold. Under these implementation constraints, we reformulate the problem as a standard discrete-time $H^{\infty}$ control problem by using the discrete-time lifting technique. A simulation result is shown to illustrate the effectiveness of the proposed method.

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arXiv2015

Discrete Signal Reconstruction by Sum of Absolute Values

In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the reconstruction is exponential as it is. To overcome this difficulty, we extend the idea of compressed sensing, and propose to solve the problem by minimizing the sum of weighted absolute values. We assume that the probability distribution defined on an alphabet is known, and formulate the reconstruction problem as linear programming. Examples are shown to illustrate that the proposed method is effective.

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arXiv2014

Value Function in Maximum Hands-off Control

In this brief paper, we study the value function in maximum hands-off control. Maximum hands-off control, also known as sparse control, is the L0-optimal control among the admissible controls. Although the L0 measure is discontinuous and non- convex, we prove that the value function, or the minimum L0 norm of the control, is a continuous and strictly convex function of the initial state in the reachable set, under an assumption on the controlled plant model. This property is important, in particular, for discussing the sensitivity of the optimality against uncertainties in the initial state, and also for investigating the stability by using the value function as a Lyapunov function in model predictive control.

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arXiv2014

Continuity of the Value Function in Sparse Optimal Control

We prove the continuity of the value function of the sparse optimal control problem. The sparse optimal control is a control whose support is minimum among all admissible controls. Under the normality assumption, it is known that a sparse optimal control is given by L^1 optimal control. Furthermore, the value function of the sparse optimal control problem is identical with that of the L1-optimal control problem. From these properties, we prove the continuity of the value function of the sparse optimal control problem by verifying that of the L1-optimal control problem.

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arXiv2014

Sparsity Methods for Networked Control

In this presentation, we introduce sparsity methods for networked control systems and show the effectiveness of sparse control. In networked control, efficient data transmission is important since transmission delay and error can critically deteriorate the stability and performance. We will show that this problem is solved by sparse control designed by recent sparse optimization methods.

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arXiv2014

Sampled-Data H-infinity Design of Coupling Wave Cancelers in Single-Frequency Full-Duplex Relay Stations

In this article, we propose sampled-data H-infinity design of digital filters that cancel the continuous-time effect of coupling waves in a single-frequency full-duplex relay station. In this study, we model a relay station as a continuous-time system while conventional researches treat it as a discrete-time system. For a continuous-time model, we propose digital feedforward and feedback cancelers based on the sampled-data control theory to cancel coupling waves taking intersample behavior into account. Simulation results are shown to illustrate the effectiveness of the proposed method.

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arXiv2014

L1 Control Theoretic Smoothing Splines

In this paper, we propose control theoretic smoothing splines with L1 optimality for reducing the number of parameters that describes the fitted curve as well as removing outlier data. A control theoretic spline is a smoothing spline that is generated as an output of a given linear dynamical system. Conventional design requires exactly the same number of base functions as given data, and the result is not robust against outliers. To solve these problems, we propose to use L1 optimality, that is, we use the L1 norm for the regularization term and/or the empirical risk term. The optimization is described by a convex optimization, which can be efficiently solved via a numerical optimization software. A numerical example shows the effectiveness of the proposed method.

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