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.     

An indirect adaptive pole‐placement control for MIMO discrete‐time stochastic systems

In this paper, an indirect adaptive pole‐placement control scheme for multi‐input multi‐output (MIMO) discrete‐time stochastic systems is developed. This control scheme combines a recursive least squares (RLS) estimation algorithm with pole‐placement control design to produce a control law with self‐tuning capability. A parametric model with a priori prediction outputs is adopted for modelling the controlled system. Then, a RLS estimation algorithm which applies the a posteriori prediction errors is employed to identify the parameters of the model. It is shown that the implementation of the estimation algorithm including a time‐varying inverse logarithm step size mechanism has an almost sure convergence. Further, an equivalent stochastic closed‐loop system is used here for constructing near supermartingales, allowing that the proposed control scheme facilitates the establishment of the adaptive pole‐placement control and prevents the closed‐loop control system from occurring unstable pole‐zero cancellation. An analysis is provided that this control scheme guarantees parameter estimation convergence and system stability in the mean squares sense almost surely. Simulation studies are also presented to validate the theoretical findings. 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.     

On the improvement of l2‐performance by controller resets

In this paper, we propose a state reset algorithm that minimizes the upper bound of the l₂‐norm of an output signal at an arbitrary sampling time. By this means, we attempt to improve the l₂‐performance of a control system. It is shown that the system with the proposed reset algorithm is finite gain l₂‐stable and also asymptotically stable. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

A new model reference adaptive control for linear time‐varying systems

Recent results on the adaptive control of linear time‐varying systems have considered mostly the case in which the range or rate of parameter variations is small. In this paper, a new state feed‐back model reference adaptive control is developed for systems with bounded arbitrary parameter variations. The important feature of the proposed adaptive control is an uncertainty estimation algorithm, which guarantees almost zero tracking error. Note that the conventional parameter estimation algorithm in the adaptive control guarantees only bounded tracking error. Copyright © 2000 John Wiley & Sons, Ltd.     

Global adaptive finite‐time stabilization of a class of switched nonlinear systems with parametric uncertainty

This paper investigates the global adaptive finite‐time stabilization of a class of switched nonlinear systems, whose subsystems are all in p (p≤1) normal form with unknown control coefficients and parametric uncertainties. The restrictions on the power orders and the nonlinear perturbations are relaxed. By using the parameter separation technique, the uncertain parameters are separated from nonlinear functions. A systematic design procedure for a common state feedback controller and a switching adaptive law is presented by employing the backstepping methodology. It is proved that the closed‐loop system is finite‐time stable under arbitrary switching by utilizing the common Lyapunov function. Finally, with the application to finite‐time control of chemical reactor systems, the effectiveness of the proposed method is demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

A novel variable‐length sliding window blockwise least‐squares algorithm for on‐line estimation of time‐varying parameters

Motivated by the advances in computer technology and the fact that the batch/block least‐squares (LS) produces more accurate parameter estimates than its recursive counterparts, several important issues associated with the block LS have been re‐examined in the framework of on‐line identification of systems with abrupt/gradual change parameters in this paper. It is no surprise that the standard block LS performs unsatisfactorily in such a situation. To overcome this deficiency, a novel variable‐length sliding window‐based LS algorithm, known as variable‐length sliding window blockwise least squares, is developed. The algorithm consists of a change detection scheme and a data window with adjustable length. The window length adjustment is triggered by the change detection scheme. Whenever a change in system parameters is detected, the window is shortened to discount ‘old’ data and place more weight on the latest measurements. Several strategies for window length adjustment have been considered. The performance of the proposed algorithm has been evaluated through numerical studies. In comparison with the recursive least squares (RLS) with forgetting factors, superior results have been obtained consistently for the proposed algorithm. Robustness analysis of the algorithm to measurement noise have also been carried out. The significance of the work reported herein is that this algorithm offers a viable alternative to traditional RLS for on‐line parameter estimation by trading off the computational complexity of block LS for improved performance over RLS, because the computational complexity becomes less and less an issue with the rapid advance in computer technologies. Copyright © 2004 John Wiley & Sons, Ltd.     

Adaptive saturated finite‐time control algorithm for buck‐type DC‐DC converter systems

To enhance the convergent rate and robustness of buck‐type DC‐DC converter system, a new finite‐time voltage regulation control algorithm is proposed in this paper. First, an average state space‐based model is analyzed, which considers both the parameters uncertainties and the variations of load and input voltage. By using saturation finite‐time control theory, at the first step, in the absence of disturbance, a new fast voltage regulation control algorithm is designed, which can guarantee that the output voltage converges to the reference voltage in a finite time. Because the saturation constraint is considered during the controller design, the duty ratio function of the converter satisfies the constraint between 0 and 1. Second, in the presence of disturbance, a finite‐time convergent disturbance observer is designed to estimate the unknown disturbances in a finite time. Finally, a disturbance observer‐based finite‐time voltage regulation control algorithm is developed. Compared with PI (Proportional‐Integral) control algorithm, circuit simulations show that the proposed algorithm has a faster regulation performance and stronger robustness performance on disturbance rejection.     

Constructive approximation of non‐linear discrete‐time systems

It is known that large classes of approximately‐finite‐memory maps can be uniformly approximated arbitrarily well by the maps of certain non‐linear structures. As an application, it was proved that time‐delay networks can be used to uniformly approximate arbitrarily well the members of a large class of causal nonlinear dynamic discrete‐time input–output maps. However, the proof is non‐constructive and provides no information concerning the determination of a structure that corresponds to a prescribed bound on the approximation error. Here we give some general results concerning the problem of finding the structure. Our setting is as follows. There is a large family 𝒢 of causal time‐invariant approximately‐finite‐memory input‐output maps G from a set S of real d‐vector‐valued discrete‐time inputs (with d⩾1) to the set of ℝ‐valued discrete‐time outputs, with both the inputs and outputs defined on the non‐negative integers 𝒵₊. We show that for each ϵ>0, any Gϵ𝒢 can be uniformly approximated by a structure map H(G, ·) to within tolerance ϵ, and we give analytical results and an example to illustrate how such a H(G, ·) can be determined in principle. Copyright © 2000 John Wiley & Sons, Ltd.     

Generalized forgetting functions for on‐line least‐squares identification of time‐varying systems

The problem of on‐line identification of a parametric model for continuous‐time, time‐varying systems is considered via the minimization of a least‐squares criterion with a forgetting function. The proposed forgetting function depends on two time‐varying parameters which play crucial roles in the stability analysis of the method. The analysis leads to the consideration of a Lyapunov function for the identification algorithm that incorporates both prediction error and parameter convergence measures. A theorem is proved showing finite time convergence of the Lyapunov function to a neighbourhood of zero, the size of which depends on the evolution of the time‐varying error terms in the parametric model representation. Copyright © 2001 John Wiley & Sons, Ltd.     

Accurate one‐terminal fault location algorithm based on the principle of short‐circuit calculation

An alternative method to find the line fault distance in a transmission network employing only one‐terminal measured data is presented. The proposed method applies Z_bus for short‐circuit calculation to find the fault location on a transmission line without the necessity to know the fault type a priori. The well‐known drawback of the standard simple‐reactance one‐terminal algorithm, which neglects the effect of fault impedance, will be minimized by estimating the voltage drop at the fault location by employing the Z_bus technique. Accuracy the proposed method is demonstrated using the short‐circuit simulation of the modified IEEE‐14 bus test system on MATLAB/Simulink and the Simpower Toolbox. Compared to the accuracy obtained from the standard one‐terminal algorithm, test results confirm substantially improved accuracy of the proposed method in all cases of the four types of fault categories: single line‐to‐ground fault; double line‐to‐ground fault; line‐to‐line fault; and balance three‐phase fault. While the accuracy has been significantly improved, especially for the case with a relatively high fault impedance, also the simplicity in the involved computation is well preserved when compared to other iterative‐based techniques. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

A wave‐front‐time dependent corona model for transmission‐line surge calculations

For transmission‐line surge studies, the inclusion of corona discharge due to high voltage surges is important as well as the inclusion of frequency‐dependent effects. Because the charge‐voltage (q‐v) curve of a lightning surge is different from that of a switching surge, a corona model should reproduce different q‐v curves for different wave‐front times. The present paper proposes a wave‐front time dependent corona model which can express the dependence by a simple calculation procedure as accurately as a rigorous finite‐difference method which requires an enormous calculation time. The simplicity enhances the incorporation of the corona model into a line model, because a large number of models are to be inserted into the line model by discretization. The q‐v curves calculated by the proposed method agrees well with field tests. This paper also proposes an efficient method to deal with nonlinear corona branches in distributed‐parameter line model using the trapezoidal rule of integration and the predictor‐corrector method. © 1999 Scripta Technica, Electr Eng Jpn, 129(1): 29–38, 1999     

Set theoretic performance verification of low‐frequency learning adaptive controllers

Although adaptive control has been used in numerous applications, the ability to obtain a predictable transient and steady‐state closed‐loop performance is still a challenging problem from the verification and validation standpoint. To that end, we considered a recently developed robust adaptive control methodology called low‐frequency learning adaptive control and utilized a set of theoretic analysis to show that the transitory performance of this approach can be expressed, analyzed, and optimized via a convex optimization problem based on linear matrix inequalities. This key feature of this design and analysis framework allows one to tune the adaptive control parameters rigorously so that the tracking error components of the closed‐loop nonlinear system evolve in a priori specified region of the state space whose size can be minimized by selecting a suitable cost function. Simulation examples are provided to demonstrate the efficacy of the proposed verification and validation architecture showing the possibility of performing parametric studies to analyze the interplay between the size of the tracking error residual set and important design parameters such as the adaptation rate and the low‐pass filters time constant of the weights adaptation algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

An extension of the FFT‐based algorithm for the match‐count problem to weighted scores

The match‐count problem on strings is the basic problem of counting the matches of characters between two strings for every possible alignment. The problem is classically computed in O (σ n log m ) time using a fast Fourier transform (FFT) for two strings of lengths m and n (m ≤ n ) over an alphabet of size σ . This paper extends the target of this FFT‐based algorithm to a weighted version of the problem, which computes the sum of similarities between characters instead of the number of matches. The algorithm extended in this paper can solve the weighted match‐count problem in O (dn log m ) time by mapping characters to numerical vectors of dimensionality d . This paper also evaluates the usefulness of the extended algorithm by applying it to plagiarism detection in documents. The experimental results show that the proposed algorithm is applicable to general vector representation of words and that the obtained plagiarism detection method can extremely reduce the processing time with a slight decrease of accuracy from the method based on the normal match‐count problem.     

Modeling of unbalanced three‐phase driving‐point impedance with application to control of grid‐connected power converters

The dq transformation is widely used in the analysis and control of three‐phase symmetrical and balanced systems. The transformation is the real counterpart of the complex transformations derived from the symmetrical component theory. The widespread distributed generation and dynamically connected unbalanced loads in a three‐phase system inherently create unbalanced voltages to the point of common coupling. The unbalanced voltages will always be transformed as coupled positive‐sequence and negative‐sequence components with double‐frequency ripples that can be removed by some filtering algorithms in the dq frame. However, a technique for modeling unbalanced three‐phase impedance between voltages and currents of same sequences or of opposite sequences is still missing. We propose an effective method for modeling unbalanced three‐phase impedance using a decoupled zero‐sequence impedance and two interacting positive‐sequence and negative‐sequence balanced impedances in the dq frame. The proposed method can decompose a system with unbalanced resistance, inductance, or capacitance into a combination of independent reciprocal bases (IRB). Each IRB basis belongs to one of the positive‐sequence, negative‐sequence, or zero‐sequence system components to facilitate further analysis. The effectiveness of this approach is verified with a case study of an unbalanced load and another case study of an unbalanced voltage compensator in a microgrid application. Copyright © 2015 John Wiley & Sons, Ltd.     

Self‐adjoint S‐parameter sensitivities for lossless homogeneous TLM problems

We present a novel efficient algorithm for the estimation of S‐parameter sensitivities in homogeneous and lossless transmission line modelling (TLM) problems. Our approach estimates S‐parameter adjoint‐based sensitivities without actually carrying out any adjoint simulation. By applying a transformation to the original TLM simulation we establish an isomorphism between the original and the adjoint problem. The unique properties of the TLM node in a lossless and homogeneous problem are also exploited in establishing the isomorphism. For an electromagnetic structure with N_p ports, only the N_p original simulations utilized in evaluating the S‐parameters are required to estimate their sensitivities as well. Our novel approach is illustrated through estimating S‐parameter sensitivities with respect to waveguide discontinuities. Good match is obtained between our sensitivity estimates and those calculated using finite differences at the response level. Copyright © 2005 John Wiley & Sons, Ltd.     

Predictor‐based iterative neural dynamic surface control for three‐phase voltage source PWM rectifier

This paper addresses the control problem of a three‐phase voltage source pulse width modulation rectifier in the presence of parametric uncertainties and external time‐varying disturbances. An adaptive controller is designed by combining a modified dynamic surface control method and a predictor‐based iterative neural network control algorithm. Especially, neural networks with iterative update laws based on prediction errors are employed to identify the lumped uncertainties. Besides, a finite‐time‐convergent differentiator, instead of a first‐order filter, is used to obtain the time derivative of the virtual control law. Using a Lyapunov–Krasovskii functional, it is proved that all signals in the closed‐loop system are ultimately uniformly bounded. Both simulation and experimental studies are provided to show the effectiveness of the proposed approach. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

A Five‐Element Multiplex Resonant Full‐Bridge DC‐DC Converter with a Variable Inductive Reactance

A five‐element multiplex resonant (LLCLC) full‐bridge DC‐DC converter controlled by pulse frequency modulation (PFM) is proposed in this paper. The high frequency (HF)‐link resonant DC‐DC converter proposed herein can perform wide‐range output power and voltage regulation with a narrow frequency range due to an antiresonant tank that works effectively as a wide‐range variable inductor. The advantageous characteristics of the antiresonant tank provide overcurrent protection in the case of the short‐circuited load condition as well as in the startup interval. Thus, the technical challenges of a conventional LLC DC‐DC converter can be overcome, and the reliability of the relevant switch‐mode power supplies can be improved. The operating principle of the LLCLC DC‐DC converter is described, after which its performance is evaluated in an experimental setup based on the 2.5 kW prototype. Finally, the feasibility of the proposed DC‐DC converter is discussed from a practical point of view.     

Modified Z‐transform‐based FDTD algorithm for the anisotropic perfectly matched layer

A modified Z‐transform‐based algorithm for implementing the D‐H anisotropic perfectly matched layer (APML) is presented for truncating the finite‐difference time‐domain (FDTD) lattices. The main advantage is that, as compared with the previous Z‐transform‐based implementation for the D‐H APML, the proposed algorithm requires less auxiliary variables in the PML regions, and thus the memory requirement and the computational time are saved. These formulations are simple and independent of the material properties of the FDTD computational domain. Two numerical tests have been carried out to validate these formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

Prescribed performance bound‐based adaptive path‐following control of uncertain nonholonomic mobile robots

In this paper, we consider the transient performance of path‐following control of nonholonomic mobile robots with parametric uncertainties. By incorporating prescribed performance bound (PPB) technique, the transient performances on position and orientational tracking errors will be guaranteed with convergence rates no less than certain pre‐specified values and sufficiently small maximum overshoots. We also extend the proposed scheme to solve the formation control problem for a group of N unicycle‐type mobile robots without inter‐robot communications. It is ensured that all the robots can track their references with arbitrarily small errors and no collision will occur between any two robots. Simulation studies verify the established theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.