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This paper investigates the output feedback control for nonlinear systems with unknown output functions and unknown growth rates, where the unknown output functions are Lipschitz continuous and the unknown growth rates are time-varying. To deal with this challenging control problem, a time-varying observer is designed and a time-varying scaling transformation is introduced, which can avoid using the derivative information of the output function and can effectively compensate the unknown time-varying growth rate. Then, by combining the time-varying scheme, the backstepping method and the certainty equivalence principle, an output feedback controller is designed to guarantee the boundedness of the closed-loop system states and the global convergence of the original system states. Finally, two simulation examples are given to show the effectiveness of the control scheme.

Identification of structured state-space (gray-box) model is popular for modeling physical and network systems. Due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for successful applications. In this paper, the non-convex gray-box identification problem is reformulated as a structured low-rank matrix factorization problem by exploiting the rank and structured properties of a block Hankel matrix constructed by the system impulse response. To address the low-rank optimization problem, it is first transformed into a difference-of-convex (DC) formulation and then solved using the sequentially convex relaxation method. Compared with the classical gray-box identification methods like the prediction-error method (PEM), the new approach turns out to be more robust against converging to non-global minima, as supported by a simulation study. The developed identification can either be directly used for gray-box identification or provide an initial parameter estimate for the PEM.

The objective of adaptive optics (AO) system control is to design an output feedback controller to reduce the adverse effect of the phase aberration caused by the atmospheric turbulence. As the size of the telescope or AO system becomes larger and larger, how to improve the efficiency of the controller execution becomes an urgent but challenging problem. To this end, this paper presents a structured and sparse controller design method for the large-scale AO systems. A Kronecker structured turbulent phase model, inspired by the frozen-flow movement of the atmospheric turbulence, is developed first, following the design of a sparse controller gain under the $H_{2}$ -norm optimal control framework. Based on the Kronecker structured system matrices and the sparse controller gain, the obtained dynamical controller has a linear execution complexity in the dimension of the turbulent phase, which is even lower than the standard matrix-vector multiplication method. Since the proposed method is a preliminary result, which cannot be directly used in a telescope today, its performance is demonstrated by numerical simulations only.

The inverse optimal control for finite-horizon discrete-time linear quadratic regulators is investigated in this paper, which is to estimate the parameters in the objective function using noisy measurements of partial optimal states only. By the Pontryagin’s minimum principle, the concerned inverse optimal control problem is recast as the identification of a parameterized causal-and-anticausal mixed system excited by boundary conditions. Sufficient identifiability conditions for the unknown parameters are provided in terms of the system model itself, rather than relying on the exact values of optimal states or control inputs. In addition, an elegant algebraic solution is provided for the concerned identification problem that is inherently a challenging optimization problem with trilinear equality constraints, and it can recover the true parameters (up to a scalar ambiguity) in the absence of measurement noise or can consistently identify the parameters (up to a scalar ambiguity) in the presence of white measurement noise. The presented algebraic solution relies on recursive matrix calculations so that its computational burden is much less than directly solving a high-dimensional non-convex optimization problem as done in many existing works. The effectiveness of the proposed method as well as its noise sensitivity issue is illustrated by simulation examples.

In this paper, we study the distributed blind equalization of networked single-input multi-output (SIMO) systems. An indirect distributed equalization framework is presented, which estimates the transfer functions followed by the associated equalizers. Two distributed indirect equalization algorithms are proposed: one depends on multiple average consensus operations, and the other relies on the combination of innovation and one average consensus operation. The former generates an approximate equalizer for which the associated estimation error is determined by the number of average consensus operations, while the latter can provide an accurate equalizer estimation under some mild conditions. The proposed algorithms estimate the desired equalizer recursively and recover the source signal in real time. Furthermore, the distributed equalization under a time-varying topology is investigated as well. Convergence properties of the proposed algorithms are established and numerical simulations are carried out to show the performances of the proposed algorithms.

This paper considers the identification of a network consisting of discrete-time LTI systems that are interconnected by their unmeasurable states. For a large-scale network, the computational burden prevents a centralized solution. To cope with this problem, a subspace-based local identification approach using local observations is presented, which consists of subspace intersection operations in both the temporal and spatial domains. Sufficient conditions are provided for the consistent identification of the presented identification approach. Finally, the implementation of this approach on 1D network is specially investigated and numerical simulations are provided to show its effectiveness.

This paper studies the blind identification of multi-channel FIR systems using precise and quantized observations. First, a new deterministic blind identification (DBI) algorithm is presented for multi-channel FIR systems using precise observations, in which the system parameters can be consistently estimated and the common source signal can be stably recovered. When the observed samples are quantized by a static finite-level quantizer, an iterative deterministic blind identification (IDBI) method is then provided. The asymptotic characters of the proposed IDBI method are discussed and the quantization effect on the identification performance is analyzed. Numerical simulations are given to support the developed DBI method and IDBI method.

This paper presents a second-order statistics based method for blind identification of non-minimum phase single-input-single-output (SISO) auto-regression moving-average (ARMA) systems. By holding the system input while sampling the system output at the normal rate, the SISO system is transformed into an equivalent single-input-multi-output (SIMO) ARMA model. Theoretical analysis is conducted to exploit the system auto-regressive information contained in the autocorrelation matrices of the over-sampled output and to derive expressions for constructive estimation of the ARMA system parameters. The developed systematic identification method has flexibility in choosing the over-sampling rate which can be as low as two. The effectiveness of the proposed method is demonstrated by simulation results.

This paper develops a Kalman smoother to estimate white noise input for systems with random parametric uncertainties in the observation equation. The derived input estimator is optimal in terms of the mean square error (MSE) criterion. Convergence analysis for the derived Kalman smoother is provided, which shows that stability of the Kalman filter cannot guarantee that of the designed fixed-point Kalman smoother. Furthermore, the designed smoothing estimator is applied to the semi-blind deconvolution problem, and an optimal solution is obtained. Numerical examples are given to demonstrate the performance of the proposed method in comparison with two typical deconvolution methods.

This correspondence presents a new second-order statistical approach to blind identification of single-input multiple-output (SIMO) autoregressive and moving average (ARMA) system models. The proposed approach exploits the dynamical autoregressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block Toeplitz structure of the channel convolution matrix used by classical subspace methods. For the multi-channel model with the same autoregressive (AR) polynomial, sufficient conditions and an efficient identification algorithm are given such that the multi-channel model can be uniquely identified up to a constant scaling factor. Furthermore, an extension of the result to blind identification of multi-channel models with different AR polynomials is presented. Simulation results are given to show the effectiveness of the proposed approach.

To improve the quality of medical ultrasound images, a number of restoration methods based on demodulated signals have been proposed in the literature. However, due to the shift of center frequency of transmitted ultrasound pulses at different penetration depth in a lossy medium, it is hard to determine the exact center frequency at a specified position so to achieve satisfactory demodulation. In this paper, this problem is dealt with by a novel restoration method based on envelope models of the radio frequency (RF) and the point spread function (PSF) signals. To cope with the ill inverse problem caused by the narrow band PSF, an envelop signal based sparse regularized deconvolution model is derived under a sparsity assumption of the tissue reflectivity function (TRF). Furthermore, a two-step iterative shrinkage/thresholding (TwIST) method based alternating minimization approach is applied to compute the optimal solution of the proposed deconvolution problem. Finally, the robustness and the practicability of the proposed method are demonstrated by a series of experiments on both numerical simulation and in vivo data. The experimental results show that the proposed method can achieve significant improvement of the ultrasound images in terms of the resolution gain and signal-to-noise ratio (SNR).

Medical ultrasound imaging is a non-invasive technique for clinical diagnosis, but its applications are limited by the low image quality. In this paper, the problem of ultrasound imaging is dealt with by a novel deconvolution method which utilizes the envelope of the point spread function (EPSF) instead of the commonly used point spread function (PSF). The EPSF is estimated based on minimum phase assumption without considering phase unwrapping and linear phase elimination, thus it is much efficient and reliable. After obtaining the EPSF, an l 1 -norm regularized optimization model is derived and efficiently solved by an augmented Lagrangian method (ALM). Experiments are conducted on both simulated and in vivo data. The results show that the proposed deconvolution method can provide significantly improved ultrasound images in terms of resolution gain and signal to noise ratio.

This paper studies the identification of ARMA systems with colored measurement noises using finite-level quantized observations. Compared with the case under colorless noises, this problem is more challenging. Our approach is to jointly design an adaptive quantizer and a recursive estimator to identify system parameters. Specifically, the quantizer uses the latest estimate to adjust its thresholds, and the estimator is updated by using quantized observations. To accommodate the temporal correlations of quantization errors and measurement noises, we construct a second-order statistics equivalent system, from which the original ARMA system is identified. The associated identifiability problem and convergence are analyzed as well. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed algorithm.