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We show that global exponential convergence for the augmented primal-dual gradient algorithms can be achieved for partially strongly convex functions. In particular, the objective function only needs to be strongly convex in the subspace satisfying the equality constraint and can be generally convex elsewhere provided the global Lipschitz condition for the gradient is satisfied. This condition also implies that states outside the equality subspace will be driven towards it by the augmented primal-dual algorithm exponentially fast. The analysis is then applied to distributed optimization, where the partially strong convexity can be relaxed to the restricted secant inequality condition, which is not necessarily convex. This work unifies global exponential convergence results for some existing centralized and distributed algorithms., Comment: submitted to ACC2025

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here.

This paper investigates closed-loop stability of a linear discrete-time plant subject to bounded disturbances when controlled according to packetized predictive control (PPC) policies. In the considered feedback loop, the controller is connected to the actuator via a digital communication channel imposing bounded dropouts. Two PPC strategies are taken into account. In both cases, the control packets are generated by solving sparsity-promoting optimization problems. One is based upon an l2-constrained l0 optimization problem. Such problem is relaxed by an l1-l2 optimization problem in the other sparse PPC setting. We utilize effective solving methods for the latter optimization problems. Moreover, we show that in the presence of plant disturbances, the l2-constrained l0 sparse PPC and unconstrained l1-l2 sparse PPC guarantee practical stability for the system if certain conditions are met. More precisely, in each case, we can derive an upper bound on system state if the design parameters satisfy certain conditions. The bounds we derive are increasing with respect to the disturbance magnitude. We show via simulation that in both cases of proposed sparse PPC strategies, larger disturbances bring about performance degradation with no effect on system practical stability.

This article treats optimal sparse control problems with multiple constraints defined at intermediate points of the time domain. For such problems with intermediate constraints, we first establish a new Pontryagin maximum principle that provides first order necessary conditions for optimality in such problems. Then we announce and employ a new numerical algorithm to arrive at, in a computationally tractable fashion, optimal state-action trajectories from the necessary conditions given by our maximum principle. Several detailed illustrative examples are included., Comment: 25 pages, 12 figures

This paper presents analyses for the maximum hands-off control using the geometric methods developed for the theory of turnpike in optimal control. First, a sufficient condition is proved for the existence of the maximum hands-off control for linear time-invariant systems with arbitrarily fixed initial and terminal points using the relation with $L^1$ optimal control. Next, a sufficient condition is derived for the maximum hands-off control to have the turnpike property, which may be useful for approximate design of the control., Comment: Submitted for IEEE Conference on Decision and Control 2020

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 $L^0$-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 $\pm 1$ 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 $L^1$ and $L^2$ norms. We show by numerical simulations 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 $L^1$ and squared $L^2$ norms. We also prove that the CLOT control is continuous in the sense that, if $O(h)$ denotes the sampling period, then the difference between successive values of the CLOT-optimal control is $O(\sqrt{h})$, which is a form of continuity. Also, the CLOT formulation is extended to encompass constraints on the state variable., Comment: 38 pages, 20 figures. enlarged version of arXiv:1611.02071

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.

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., Comment: 8 pages, 18 figures, 3 tables

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.

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., Comment: 6 pages

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

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., Comment: submitted; 6 pages, 7 figures

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., Comment: submitted to IEEE Transactions on Automatic Control; 11 pages with 2 figures

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.

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., Comment: submitted; 6pages, 13 figures. arXiv admin note: text overlap with arXiv:1503.02379

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., Comment: IEEE Signal Processing Letters (to appear)

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., Comment: SICE Journal of Control, Measurement, and System Integration (to appear); 7 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:1412.3238, arXiv:1407.7083

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., Comment: submitted to Automatica, Dec. 2014; 6 pages with 2 figures

In this manuscript, we propose a design method of digital filters which cancel coupling waves generated in single-frequency full-duplex wireless relay stations by using the sampled-data H-infinity control theory. Simulation results show effectiveness of the proposed method to communication performance from a base station to a terminal., Comment: submitted to the SICE International Symposium on Control Systems 2015, Dec. 2014; 2 pages, 4 figures

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., Comment: Submitted to ASCC2015

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., Comment: 10th Asian Control Conference 2015 (ASCC 2015), 2015; 4 pages, 10 figures

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., Comment: Submitted to IEICE SmartCom2014 Conference

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., Comment: SICE Annual Conference 2014 (6 pages, 12 figures)

FIR (finite impulse response) digital filter design is a fundamental problem in signal processing. In particular, FIR approximation of analog filters (or systems) is ubiquitous not only in signal processing but also in digital implementation of controllers. In this article, we propose a new design method of an FIR digital filter that optimally approximates a given analog filter in the sense of minimizing the H-infinity norm of the sampled-data error system. By using the lifting technique and the KYP (Kalman-Yakubovich-Popov) lemma, we reduce the H-infinity optimization to a convex optimization described by an LMI (linear matrix inequality). We also extend the method to multi-rate and multi-delay systems. A design example is shown to illustrate the effectiveness of the proposed method., Comment: The 19th IFAC World Congress; 6 pages, 8 figures

In this article, we introduce a new paradigm of control, called hands-off control, which can save energy and reduce CO2 emissions in control systems. A hands-off control is defined as a control that has a much shorter support than the horizon length. The maximum hands-off control is the minimum support (or sparsest) control among all admissible controls. With maximum hands-off control, actuators in the feedback control system can be stopped during time intervals over which the control values are zero. We show the maximum hands-off control is given by L1 optimal control, for which we also show numerical computation formulas., Comment: SICE Control Division Multi Symposium 2014 (Japanese domestic conference); English translation from Japanese article

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., Comment: Accepted for publication in IEEE Signal Processing Letters. 4 pages (twocolumn), 5 figures

In this thesis, we present a new method for designing multirate signal processing and digital communication systems via sampled-data H-infinity control theory. The difference between our method and conventional ones is in the signal spaces. Conventional designs are executed in the discrete-time domain, while our design takes account of both the discrete-time and the continuous-time signals. Namely, our method can take account of the characteristic of the original analog signal and the influence of the A/D and D/A conversion. While the conventional method often indicates that an ideal digital low-pass filter is preferred, we show that the optimal solution need not be an ideal low-pass when the original analog signal is not completely band-limited. This fact can not be recognized only in the discrete-time domain. Moreover, we consider quantization effects. We discuss the stability and the performance of quantized sampled-data control systems. We justify H-infinity control to reduce distortion caused by the quantizer. Then we apply it to differential pulse code modulation. While the conventional Delta modulator is not optimal and besides not stable, our modulator is stable and optimal with respect to the H-infinity-norm. We also give an LMI (Linear Matrix Inequality) solution to the optimal H-infinity approximation of IIR (Infinite Impulse Response) filters via FIR (Finite Impulse Response) filters. A comparison with the Nehari shuffle is made with a numerical example, and it is observed that the LMI solution generally performs better. Another numerical study also indicates that there is a trade-off between the pass-band and stop-band approximation characteristics., Comment: PHD Thesis, Kyoto University, 2003

YY filter, named after the founder Prof. Yutaka Yamamoto, is a digital filter designed by sampled-data control theory, which can optimize the analog performance of the signal processing system with AD/DA converters. This article discusses problems in conventional signal processing and introduces advantages of the YY filter.

Analysis and design of filtered-x adaptive algorithms are conventionally done by assuming that the transfer function in the secondary path is a discrete-time system. However, in real systems such as active noise control, the secondary path is a continuous-time system. Therefore, such a system should be analyzed and designed as a hybrid system including discrete- and continuous- time systems and AD/DA devices. In this article, we propose a hybrid design taking account of continuous-time behavior of the secondary path via lifting (continuous-time polyphase decomposition) technique in sampled-data control theory.

In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with complex-valued coefficients. While the conventional method assumes band limitation of signals, we propose a new method by sampled-data H-infinity optimization. By this method, we can remove the band-limiting assumption and the optimal filter can be with real-valued coefficients. Moreover, we show that without band-limited assumption, there can be the optimal decimation patterns among ones with the same ratio. By examples, we show the effectiveness of our method.

In this paper, we give a causal solution to the problem of spline interpolation using H-infinity 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-infinity optimization for the filter. The advantage of H-infinity 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-infinity optimization in the case of the cubic splines. For higher-order splines, the optimal filter can be effectively solved by a numerical computation. We also show that the optimal FIR (Finite Impulse Response) filter can be designed by an LMI (Linear Matrix Inequality), which can also be effectively solved numerically. A design example is presented to illustrate the result.

In this article, we consider remote-controlled systems, where the command generator and the controlled object are connected with a bandwidth-limited communication link. In the remote-controlled systems, efficient representation of control commands is one of the crucial issues because of the bandwidth limitations of the link. We propose a new representation method for control commands based on compressed sensing. In the proposed method, compressed sensing reduces the number of bits in each control signal by representing it as a sparse vector. The compressed sensing problem is solved by an L1-L2 optimization, which can be effectively implemented with an iterative shrinkage algorithm. A design example also shows the effectiveness of the proposed method.

We investigate the use of compressive sampling for networked feedback control systems. The method proposed serves to compress the control vectors which are transmitted through rate-limited channels without much deterioration of control performance. The control vectors are obtained by an L1-L2 optimization, which can be solved very efficiently by FISTA (Fast Iterative Shrinkage-Thresholding Algorithm). Simulation results show that the proposed sparsity-promoting control scheme gives a better control performance than a conventional energy-limiting L2-optimal control.

This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H-infinity performance criterion naturally takes intersample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction.

In this article we consider two problems: FIR (Finite Impulse Response) approximation of IIR (Infinite Impulse Response) filters and inverse FIR filtering of FIR or IIR filters. By means of Kalman-Yakubovich-Popov (KYP) lemma and its generalization (GKYP), the problems are reduced to semidefinite programming described in linear matrix inequalities (LMIs). MATLAB codes for these design methods are given. An design example shows the effectiveness of these methods., Comment: MATLAB codes are available at http://www-ics.acs.i.kyoto-u.ac.jp/mat/fdf/

We investigate a networked control architecture for LTI plant models with a scalar input. Communication from controller to actuator is over an unreliable network which introduces packet dropouts. To achieve robustness against dropouts, we adopt a packetized predictive control paradigm wherein each control packet transmitted contains tentative future plant input values. The novelty of our approach is that we seek that the control packets transmitted be sparse. For that purpose, we adapt tools from the area of compressed sensing and propose to design the control packets via on-line minimization of a suitable L1/L2 cost function. We then show how to choose parameters of the cost function to ensure that the resultant closed loop system be practically stable, provided the maximum number of consecutive packet dropouts is bounded. A numerical example illustrates that sparsity reduces bit-rates, thereby making our proposal suited to control over unreliable and bit-rate limited networks., Comment: arXiv admin note: text overlap with arXiv:1307.8242

In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by the second-order integrator, but not for other cases. The difficulty in the problem is that the monotonicity constraint should be satisfied over an interval which has the cardinality of the continuum. To solve this problem, we first formulate the problem as a semi-infinite quadratic programming, and then we adopt a discretization technique to obtain a finite-dimensional quadratic programming problem. It is shown that the solution of the finite-dimensional problem always satisfies the infinite-dimensional monotonicity constraint. It is also proved that the approximated solution converges to the exact solution as the discretization grid-size tends to zero. An example is presented to show the effectiveness of the proposed method.

In remote control, efficient compression or representation of control signals is essential to send them through rate-limited channels. For this purpose, we propose an approach of sparse control signal representation using the compressive sampling technique. The problem of obtaining sparse representation is formulated by cardinality-constrained L2 optimization of the control performance, which is reducible to L1-L2 optimization. The low rate random sampling employed in the proposed method based on the compressive sampling, in addition to the fact that the L1-L2 optimization can be effectively solved by a fast iteration method, enables us to generate the sparse control signal with reduced computational complexity, which is preferable in remote control systems where computation delays seriously degrade the performance. We give a theoretical result for control performance analysis based on the notion of restricted isometry property (RIP). An example is shown to illustrate the effectiveness of the proposed approach via numerical experiments.

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data H-infinity optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time H-infinity optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method., Comment: To appear in IEEE Transactions on Signal Processing

This paper proposes a min-max design of noise-shaping delta-sigma modulators. We first characterize the all stabilizing loop-filters for a linearized modulator model. By this characterization, we formulate the design problem of lowpass, bandpass, and multi-band modulators as minimization of the maximum magnitude of the noise transfer function (NTF) in fixed frequency band(s). We show that this optimization minimizes the worst-case reconstruction error, and hence improves the SNR (signal-to-noise ratio) of the modulator. The optimization is reduced to an optimization with a linear matrix inequality (LMI) via the generalized KYP (Kalman-Yakubovich-Popov) lemma. The obtained NTF is an FIR (finite-impulse-response) filter, which is favorable in view of implementation. We also derive a stability condition for the nonlinear model of delta-sigma modulators with general quantizers including uniform ones. This condition is described as an H-infinity norm condition, which is reduced to an LMI via the KYP lemma. Design examples show advantages of our design.

We study packetized predictive control, known to be robust against packet dropouts in networked systems. To obtain sparse packets for rate-limited networks, we design control packets via an L0 optimization, which can be effectively solved by orthogonal matching pursuit. Our formulation ensures asymptotic stability of the control loop in the presence of bounded packet dropouts., Comment: 3-page extended abstract for MTNS 2012 with 3 figures

In this article, we propose optimal discretization of analog filters (or controllers) based on the theory of sampled-data H-infinity control. We formulate the discretization problem as minimization of the H-infinity norm of the error system between a (delayed) target analog filter and a digital system including an ideal sampler, a zero-order hold, and a digital filter. The problem is reduced to discrete-time H-infinity optimization via the fast sample/hold approximation method. We also extend the proposed method to multirate systems. Feedback controller discretization by the proposed method is discussed with respect to stability. Numerical examples show the effectiveness of the proposed method., Comment: submitted to the 2013 IEEE Multi-Conference on Systems and Control (MSC 2013), Aug. 2013

In this article, we consider control theoretic splines with L1 optimization for rejecting outliers in data. Control theoretic splines are either interpolating or smoothing splines, depending on a cost function with a constraint defined by linear differential equations. Control theoretic splines are effective for Gaussian noise in data since the estimation is based on L2 optimization. However, in practice, there may be outliers in data, which may occur with vanishingly small probability under the Gaussian assumption of noise, to which L2-optimized spline regression may be very sensitive. To achieve robustness against outliers, we propose to use L1 optimality, which is also used in support vector regression. A numerical example shows the effectiveness of the proposed method., Comment: Submitted to the 59th World Statistics Congress (WSC), Aug. 2013

We study a networked control architecture for linear time-invariant plants in which an unreliable data-rate limited network is placed between the controller and the plant input. The distinguishing aspect of the situation at hand is that an unreliable data-rate limited network is placed between controller and the plant input. To achieve robustness with respect to dropouts, the controller transmits data packets containing plant input predictions, which minimize a finite horizon cost function. In our formulation, we design sparse packets for rate-limited networks, by adopting an an ell-0 optimization, which can be effectively solved by an orthogonal matching pursuit method. Our formulation ensures asymptotic stability of the control loop in the presence of bounded packet dropouts. Simulation results indicate that the proposed controller provides sparse control packets, thereby giving bit-rate reductions for the case of memoryless scalar coding schemes when compared to the use of, more common, quadratic cost functions, as in linear quadratic (LQ) control., Comment: 9 pages, 7 figures. arXiv admin note: text overlap with arXiv:1307.8242