Educação matemática pela arte
Gusmão, Lucimar Donizete
2013-08-28
Search results
10 records were found.
In this paper, we give a causal solution to the problem of spline interpolation using H∞ optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to reconstruct the inter-sample values. This leads to non-causality of the filter, and this becomes a critical issue for real-time applications. Our objective here is to derive a causal system which approximates spline interpolation by H∞ optimization for the filter. The advantage of H∞ optimization is that it can address uncertainty in the input signals to be interpolated in design, and hence the optimized system has robustness property against signal uncertainty. We give a closed-form solution to the H∞ optimization in the case of the cubic splines. For higher-order splines, the optimal filter can be effectively solv...
In this letter, we propose control theoretic smoothing splines with L^1 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 L^1 optimality, that is, we use the L^1 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.
In remote control systems, efficient representation of control signals is one of the crucial issues because of bandwidth-limitedness of the communication channel, such as a wireless communication link, between the controller and the controlled object. Recently, a new method based on compressed sensing has been proposed, in which control signals are sparsely representation based on l^1-l^2 optimization. There exist however so many methods other than l^1-l^2 optimization for compressed sensing. In this study, we perform a comparative study of sparsity-promoting methods in compressed sensing, and reveal their advantages and disadvantages by simulation in view of remote control over rate-limited networks.
本稿では，制御におけるスパース性の利用について考察する．すなわち，スパースな信号を用いた制御の利点とその導出法について考える．もし制御信号がスパースであれば，ある時間区間で制御信号が完全に0となるので，その区間でアクチュエータを休止させることができる．この性質により，制御データの伝送負荷を削減でき，また省エネが達成されるといった利点が生まれる．本稿では，これらの利点について概説した後，連続時間のL0ノルムを定義し，ある種のL1最適制御問題の解が最もスパースな許容解(L0最適解)でもあることを示す．
In this article, we consider sparsity-optimal control that minimizes the L0 norm of a continuous-time control signal. The L0 norm of a control signal is defined by the length of its support (the time intervals where the control is exactly zero), and sparse control is a control whose L0 norm is much less than the signal length. In sparse control, actuators are stopped on a relatively long time interval, on which the consumption of fuel or electric power is cut and the emission of CO2, the noise sound, and the vibration are reduced. Therefore, sparse control is a control suited to energy consumption. In this article, we give a sufficient condition such that the L0-optimal controls are equivalent to the L1-optimal controls. We also consider an extension to feedback control based on the self-triggered control method.
In this article, we show the L^0 optimality of the minimum-fuel control (or L^1-optimal control) under the normality assumption of the control problem. Based on this property, we can compute the L^0- optimal (or the sparsest) control via L^1 optimization.
L^1-optimal control, also known as minimum-fuel control, is a classical control problem, which has been researched since 1960’s. In contrast, compressed sensing, which is based on L^1 optimization, has been recently studied in signal processing. Motivated this, sparsity promoting methods based on L^1 optimization have been also proposed for rate-limited networked control systems. However, the theoretical relationship between sparsity and L^1-optimal control has not been studied. In this article, we first show an example of control of a double-integrator system and illustrate that the L^1-optimal control is sparse. Then we prove that the solutions of an L^1-optimal control problem are the sparsest among the admissible controls. We also discuss the effectiveness of L^1 optimal control in networked control systems.
In this article, we consider the problem of coupling waves in a single-frequency full-duplex relay station. Conventional design methods give a digital filter or an adaptive array antenna that cancels the effect of coupling waves on the sampling instants. However, they ignore intersample oscillations that may be gained in the positive feedback loop, and thus degrade the performance. To solve this problem, we propose sampled-data H∞ design of digital filters that cancel the continuous-time effect of coupling waves. Simulation results are shown to illustrate the effectiveness of the proposed method.
In this article, we propose H∞ optimal design of digital filters that cancel the continuous-time effect of coupling waves in a single frequency full-duplex relay station from the transmitter to the receiving antenna. In this study, we model a relay station as a continuoustime system while conventional researches treat it as a discrete-time system. For this model, we design digital filters via the theory of sampled-data H∞ control for cancellation of coupling waves. Numerical experiments show the effectiveness of the proposed method.
In this paper, we consider digital control of two-wheel self-balancing robots. Conventionally, a continuous-time controller is first designed and then discretized to implement it on a digital controller. In this case, intersample behavior is often ignored. Alternatively, we propose sampled-data control for self-balancing robots to improve intersample behavior. We show simulation and experimental results to illustrate the effectiveness of the proposed method.
