Mixed norm regularized recursive total least squares for group sparse system identification

A mixed l_p,0‐regularized recursive total least squares (RTLS) algorithm is considered for group sparse system identification. Regularized recursive least squares (RLS) has been successfully applied to group sparse system identification; however, the estimation performance in regularized RLS‐based algorithms deteriorates when both input and output are contaminated by noise (the error‐in‐variables problem). We propose an l_p,0‐RTLS algorithm to handle group sparse system identification with errors‐in‐variables. The proposed algorithm is an RLS‐like solution that utilizes l_p,0‐regularization. The proposed algorithm provides excellent performance as well as reduces the required complexity by effective inversion matrix handling. Simulations demonstrate the superiority of the proposed l_p,0‐regularized RTLS for a group sparse system identification setting. Copyright © 2015 John Wiley & Sons, Ltd.     

Exponential l2 − l∞ filtering for discrete‐time switched systems under a new framework

In this paper, a robust exponential l₂ ? l_∞ filtering problem is addressed for discrete‐time switched systems with polytopic uncertainties. The purpose of robust exponential l₂ ? l_∞ filtering is to design a filter such that the resulting filtering error system is robustly exponentially stable with a decay rate and a prescribed exponential l₂ ? l_∞ performance index. The robust exponential l₂ ? l_∞ filtering problem is solved via an average dwell time approach. Sufficient conditions in terms of strict LMI are derived for checking the robust exponential stability of a filter. An explicit expression for the desired robust exponential filter is also given. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Fault detection filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time

This paper is concerned with the problem of the fault detection (FD) filter design for discrete‐time switched linear systems with mode‐dependent average dwell‐time. The switching law is mode‐dependent and each subsystem has its own average dwell‐time. The FD filters are designed such that the augmented switched systems are asymptotically stable, and the residual signal generated by the filters achieves a weighted l₂‐gain for some disturbances and guarantees an H _? performance for the fault. By the aid of multiple Lyapunov functions combined with projection lemma, sufficient conditions for the design of the FD filters are formulated by linear matrix inequalities, furthermore, the filters gains are characterized in terms of the solution of a convex optimization problem. Finally, an application to boost convertor is given to illustrate the effectiveness and the applicability of the proposed design method. Copyright © 2013 John Wiley & Sons, Ltd.     

Transient performance improvement of model reference adaptive control: LMI‐based resetting

In this paper, a resetting mechanism is proposed to enhance the transient performance of model reference adaptive control. While the suggested method has a simple structure, it is capable of taking into account both the desired steady‐state behavior and the transient response, simultaneously. Whenever the transient specification is not satisfying, there is a jump in the controller parameters. This jump is determined by designing an optimal reset law. At the reset times, the after‐reset values of parameters are calculated based on a minimization problem. The considered cost function is a mixed H₂/H_∞ criterion, which minimizes the tracking error. The optimization problem is converted to an LMI formulation, and the reset law is designed by solving this LMI at certain reset times. To verify the effectiveness of the proposed approach, simulation results are presented.     

Complex two‐dimensional TNIPM for l1 norm‐based sparse optimization to collocated MIMO radar

In collocated multiple‐input multiple‐output (MIMO) radar, because of the sparse nature of the received signal in the three dimensions of range, angle, and Doppler, accurate estimates of range/angle/Doppler parameters can be achieved using a sparse signal recovery. In this paper, we develop a complex two‐dimensional truncated Newton interior point method (2D TNIPM) for l₁‐norm‐based sparse optimization. Because of the 2D sparse representation of received signal in collocated MIMO radar systems, the performance of proposed algorithm is investigated in order to estimate the target position and velocity. Simulation results show that the 2D TNIPM requires much lower computations compared to the 1D one. Also, it outperforms some other 2D algorithms in the estimation of range, angle, and Doppler parameters under low signal‐to‐noise ratios. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Unitary coherent strategy for spatial sparsity‐based DOA estimation of wideband signals

The coherent l₁‐singular value decomposition (l₁‐SVD) uses a non‐unitary coherent strategy for transferring different frequency bin data to a reference bin, which decreases the signal‐to‐error ratio (SER) in transferring, thereby leading to a decrease in accuracy in the direction of arrival (DOA) estimation. To cope with this problem, in this paper we propose a unitary coherent strategy that uses unitary focusing matrices for transferring data. Simulation results show that the proposed method outperforms the coherent l₁‐SVD method in accurate DOA estimation. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Output‐feedback H∞ quadratic tracking control of linear systems using reinforcement learning

This paper presents an online learning algorithm based on integral reinforcement learning (IRL) to design an output‐feedback (OPFB) H_∞ tracking controller for partially unknown linear continuous‐time systems. Although reinforcement learning techniques have been successfully applied to find optimal state‐feedback controllers, in most control applications, it is not practical to measure the full system states. Therefore, it is desired to design OPFB controllers. To this end, a general bounded L₂ ‐gain tracking problem with a discounted performance function is used for the OPFB H_∞ tracking. A tracking game algebraic Riccati equation is then developed that gives a Nash equilibrium solution to the associated min‐max optimization problem. An IRL algorithm is then developed to solve the game algebraic Riccati equation online without requiring complete knowledge of the system dynamics. The proposed IRL‐based algorithm solves an IRL Bellman equation in each iteration online in real time to evaluate an OPFB policy and updates the OPFB gain using the information given by the evaluated policy. An adaptive observer is used to provide the knowledge of the full states for the IRL Bellman equation during learning. However, the observer is not needed after the learning process is finished. A simulation example is provided to verify the convergence of the proposed algorithm to a suboptimal OPFB solution and the performance of the proposed method.     

Quantized H∞ filtering for state‐delayed systems with finite frequency specifications

This paper presents a novel design approach for the finite frequency (FF) H_∞ filtering problem for discrete‐time state‐delayed systems with quantized measurements. The system state and output are assumed affected by FF external noises. Attention is focused on the design of a stable filter that guarantees the stability and a prescribed ?₂ gain performance level for the filtering error system in the FF domain of input noises. Sufficient conditions for the solvability of this problem are developed by choosing an appropriate Lyapunov‐Krasovskii functional based on the delay partitioning technique and using the FF ?₂ gain definition combined with the generalized S‐procedure. Then, by means of Finsler's lemma, the derived conditions are linearized and additional slack variables are further introduced to more flexible result. Final filter design conditions are consequently established in terms of linear matrix inequalities in three different frequency ranges, ie, low‐, middle‐ and high‐frequency range. Finally, a simulation example is presented to illustrate the effectiveness and the merits of the proposed approach.     

Energy model based loss‐minimized speed control of induction motor with a full‐order observer

In this paper, a loss‐minimization algorithm is developed to achieve maximum efficiency in terms of slip frequency. The optimal value of slip frequency can be obtained by minimizing all controllable losses of the induction motor (IM). The ratio of magnetic energy converted to torque (W_T) to magnetic energy stored in the rotating field (W_q) is defined in terms of slip frequency to obtain an error function that is used to design a controller to achieve the desired speed. Since the energy model of the IM can be expressed by the multi‐input and multi‐output (MIMO) system, an MIMO optimal regulator is proposed to achieve the desired speed with maximum efficiency. To design an optimal regulator, it is necessary to measure all state quantities. But W_T and W_q cannot be measured directly. Therefore, a full‐order observer is proposed to estimate these state quantities. The gains of the observer system are calculated by using the pole placement technique. Consequently, the observer system becomes stable. The performance of the proposed controller and observer system are verified by using simulation. With regard to the simulation results, it can be concluded that the desired speed can be achieved by using the proposed controller and the unknown state quantities can be estimated properly by using the proposed observer system. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Coherent l1‐SVD method for DOA estimation of wideband signals

The l₁‐SVD is an efficient method for spatial sparsity based direction of arrival (DOA) estimation of narrowband signals. We propose a coherent strategy for extension of the l₁‐SVD method to wideband signals. In this method, focusing matrices are used for transferring different frequency bins data to the reference bin, and then the transformed data are combined. Finally the l₁‐SVD is applied for the combined data. The proposed method outperforms the non‐coherent strategy with a lower computational burden. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Kernelized relative entropy for direct fault detection in industrial rotary kilns

The objective of this work is to use a 1‐dimensional signal that reflects the dissimilarity between multidimensional probability densities for detection. With the modified Kullback‐Leibler divergence, faults can be directly detected without any normality assumption or joint monitoring of related test statistics in different subspaces such as the T² and SPE in principal component analysis–based methods. To relieve the difficulty associated with asymptotic high‐dimensional density estimates, we have estimated the density ratio rather than the densities themselves. This can be done by approximating the density ratio with kernel basis functions and learn the weights from the available data. The developed algorithm is generic and can be applied to any industrial system as long as process historical data is available. As a case study, we apply this algorithm to a real rotary kiln in operation, which is an integral part of the cement manufacturing plant of Ain El Kebira, Algeria.     

Synthesis and application of a real‐time model‐free behavioral controller with bumpless switching mechanism

The aims of this paper are twofold. Firstly, we present a model‐free algorithm for synthesizing an online controller. Secondly, this algorithm also addresses the issue of switching this controller in a closed loop with a bumpless interconnection mechanism. The novelty of this algorithm lies in the fact that we do not use any a priori knowledge of the model of the plant in real time. We use the mathematical framework of behavioral system theory to demonstrate the online controller synthesis and its implementation mechanism. The effectiveness of the proposed algorithm is demonstrated on the experimental three‐tank system. Copyright © 2015 John Wiley & Sons, Ltd.     

A robust adaptive pole‐placement controller without strictly positive real condition

This paper considers the adaptive pole‐placement control problem for system (1) with unmodelled dynamics η_n dominated by a small constant ε multiplied by a quantity independent of ε but tending to infinity as the past input, output, and noise grow. Using bounded external excitation and randomly varying truncation techniques, we give a design method of adaptive pole‐placement controller. It is shown that the closed‐loop system is globally stable, the estimation error for the parameter contained in the modelled part is of order ε, and the closed‐loop system under the adaptive pole‐placement control law is suboptimal in the sense of $$\mathop{\lim\sup}\limits_{{n\to\infty }}{1\over n}\mathop{\sum}\limits_{i=0}^n{\left({A^{*}(z)y_{n}‐L(z)C(z)w_{n}‐B(z)R(z)y_{n}^{*}}\right)^{2}{\leq}O({\varepsilon}^{2})+\gamma^{2}\mathop{\sum}\limits_{j=1}^q{b_{j}^{2}}}$$\nopagenumbers\end while the SPR condition used usually in other papers is replaced by a stability condition. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of geometry parameters of saw‐tooth surface on the feeding velocity of microparts

In this paper, we study experimentally the effect of the geometry parameters of a saw‐tooth surface and a micropart on the motion of the micropart. The experiments are performed for a range of the saw‐tooth pitch p, micropart length l, and exciting frequency f applied to the surface. By the use of particle tracking velocimetry method, we obtain the time‐dependent velocity and then the ensemble‐averaged velocity of the microparts. The results show that the velocity of the micropart increases up to a certain value of pf and then decreases with increasing pf. The widths of the profiles are similar for the same value of the relative scale l/p but the peaks of the profiles are slightly larger and the profiles are shifted leftward for larger pitches of the saw‐tooth surface. It implies that the motion of the micropart depends more on the characteristic surface velocity pf than on the relative scale l/p and that a larger pitch of the sawtooth creates a larger asymmetric force on the micropart. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

An efficient preconditioning technique for numerical simulation of hydrodynamic model semiconductor devices

We investigate the application of preconditioned generalized minimal residual (GMRES) algorithm to the equations of hydrodynamic model of semiconductor devices. An introduction to such a model is presented. We use finite‐element method P₁‐isoP₂ element to discretize the equations. A preconditioning technique is proposed. The CPU times are presented for n⁺‐n‐n⁺ diodes and 0.25 μm gate length Si MESFETs by using the preconditioned GMRES algorithm and the GMRES algorithm. The numerical results show that the preconditioning technique accelerates effectively the velocity of convergence. Copyright © 2003 John Wiley & Sons, Ltd.     

Fault detection for discrete‐time switched singular time‐delay systems: an average dwell time approach

In this paper, the fault detection problem is investigated for a class of discrete‐time switched singular systems with time‐varying state delays. The residual generator is firstly constructed based on a switched filter, and the design of fault detection filter is formulated as an H _∞ filtering problem, that is, minimizing the error between residual and fault in the H _∞ sense. Then, by constructing an appropriate decay‐rate‐dependent piecewise Lyapunov function and using the average dwell time scheme, a sufficient condition for the residual system to be regular, causal, and exponential stable while satisfying a prescribed H _∞ performance is derived in terms of linear matrix inequalities (LMIs). The corresponding solvability condition for the desired fault detection filters is also established via LMI approach. Finally, a numerical example is presented to show the effectiveness of the developed theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient estimation of adjoint‐variable S‐parameter sensitivities with time domain TLM

We present a novel algorithm for efficient estimation of S‐parameter sensitivities with the time‐domain transmission line modelling (TLM) method. The original electromagnetic structure is simulated using TLM to obtain the S‐parameters in the desired frequency band. For each port, an adjoint TLM simulation that runs backward in time is derived and solved. The sensitivities of the S‐parameters in the desired frequency band are estimated using only the original and adjoint simulations. For a structure with N_p ports and n designable parameters, our approach requires only N_p additional simulations regardless of n. This can be easily contrasted with the 2nN_p additional simulations required by the central difference approximation. Our algorithm is illustrated through the estimation of S‐parameter sensitivities with respect to the dimensions of waveguide discontinuities. Very good match is obtained between our sensitivity estimates and those obtained using central difference approximation. Copyright © 2005 John Wiley & Sons, Ltd.     

Online concurrent reinforcement learning algorithm to solve two‐player zero‐sum games for partially unknown nonlinear continuous‐time systems

Online adaptive optimal control methods based on reinforcement learning algorithms typically need to check for the persistence of excitation condition, which is necessary to be known a priori for convergence of the algorithm. However, this condition is often infeasible to implement or monitor online. This paper proposes an online concurrent reinforcement learning algorithm (CRLA) based on neural networks (NNs) to solve the H _∞ control problem of partially unknown continuous‐time systems, in which the need for persistence of excitation condition is relaxed by using the idea of concurrent learning. First, H _∞ control problem is formulated as a two‐player zero‐sum game, and then, online CRLA is employed to obtain the approximation of the optimal value and the Nash equilibrium of the game. The proposed algorithm is implemented on actor–critic–disturbance NN approximator structure to obtain the solution of the Hamilton–Jacobi–Isaacs equation online forward in time. During the implementation of the algorithm, the control input that acts as one player attempts to make the optimal control while the other player, that is, disturbance, tries to make the worst‐case possible disturbance. Novel update laws are derived for adaptation of the critic and actor NN weights. The stability of the closed‐loop system is guaranteed using Lyapunov technique, and the convergence to the Nash solution of the game is obtained. Simulation results show the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple characteristic model‐based golden‐section adaptive control: Stability and optimization

The characteristic model‐based golden‐section adaptive control (CM‐GSAC) law has been developed for over 20 years in China with a broad range of applications in various fields. However, quite a few theoretical problems remain open despite its satisfying performance in practice. This paper revisits the stability of the CM‐GSAC from its very beginning and explores the underlying implications of the so‐called golden‐section parameter l₂≈0.618. The closed‐loop system, which consists of the CM and the GSAC, is a discrete time‐varying system, and its stability is discussed from three perspectives. First, attentions have been paid to select the optimal controller coefficients such that the closed‐loop system exhibits the best transient performance in the worst case. Second, efforts are made to improve the robustness in the presence of parameter estimation errors, which provide another choice when designing the adaptive controller. Finally, by measuring the slowly time‐varying nature in an explicit inequality form, a bridge is built between the instantaneous stability and the time‐varying stability. In order to relax the constraints on the parameter bounds of the CM, the GSAC is further extended to multiple CMs, which shows more satisfying tracking performance than that of the traditional multiple model adaptive control method. Copyright © 2014 John Wiley & Sons, Ltd.