Adaptive interconnection and damping assignment passivity-based control for linearly parameterized discrete-time port controlled Hamiltonian systems via I&I approach

In this paper, discrete-time adaptive control of linearly parameterized fully actuated Port-controlled Hamiltonian systems with parameter uncertainties in energy function is considered. A discrete-time adaptive interconnection and damping assignment passivity-based control (IDA-PBC) method, utilizing the immersion and invariance (I&I) approach, for the considered uncertain Hamiltonian system, is presented. A discrete-time parameter estimator based on the immersion and invariance approach is derived to obtain an automatic tuning mechanism for the IDA-PBC controller. The stability analysis for the estimator and the closed-loop system is done using the Lyapunov theory. The proposed method is applied to two fully actuated physical systems and its performance is tested by simulations. Simulation results show that the proposed I&I-based adaptive IDA-PBC controller successfully preserves the performance of the IDA-PBC controller designed with true parameters under a large amount of uncertainty.     

Asymptotic performance guarantees in adaptive control

In this paper we address the problem of improving the asymptotic performance guarantees of a class of model reference adaptive controllers under insufficient excitation and in the presence of perturbations such as non-parametric uncertainty and bounded disturbances. We show that for a class of perturbations whose normalized effect is bounded by an a priori known function of time an estimate of the parametric uncertainty set can be obtained on-line via a set membership estimator. Furthermore, by incorporating this estimate as an additional constraint in the adaptive law generating the controller parameters, we show that the resulting adaptive controller offers dead-zone-like performance guarantees in the lim-sup sense while preserving the desirable root-mean-square performance guarantees of gradient-based algorithms.     

A globally convergent direct adaptive pole‐placement controller for nonminimum phase systems with relaxed excitation assumptions

In this paper, we propose the first solution to the long‐standing problem of designing a globally convergent direct adaptive pole‐placement controller for linear, time‐invariant discrete‐time systems with arbitrary zeros that does not rely on persistency of excitation assumptions. As is well known, the main difficulty of this design is that it involves the estimation of parameters that enter nonlinearly in the regression model. This problem can be overcome introducing an overparameterized representation of the system, which imposes very strict persistency of excitation conditions to prove the parameter convergence. The latter is avoided here using a new version of the dynamic regressor extension and mixing parameter estimator recently proposed in the literature. The main feature of this estimator is that it generates, out of an m‐dimensional vector regression, m scalar regression models. This property allows us to estimate only the controller parameters of interest for the adaptive implementation, whose convergence is ensured under assumptions that are strictly weaker than the classical persistency of excitation requirement. Simulation results that illustrate the performance of the proposed scheme are also presented.     

Adaptive control of Burgers' equation with unknown viscosity

In this paper, we propose a fortified boundary control law and an adaptation law for Burgers' equation with unknown viscosity, where no a priori knowledge of a lower bound on viscosity is needed. This control law is decentralized, i.e., implementable without the need for central computer and wiring. Using the Lyapunov method, we prove that the closed‐loop system, including the parameter estimator as a dynamic component, is globally H¹ stable and well posed. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's Lemma which cannot be used in the present situation. Copyright © 2001 John Wiley & Sons, Ltd.     

Beta‐order minimum mean‐square error multichannel spectral amplitude estimation for speech enhancement

In this paper, the minimum mean‐square error (MMSE) β‐order estimator for multichannel speech enhancement is proposed. The estimator is an extension of the single‐channel MMSE β‐order and multichannel MMSE short‐time spectral amplitude estimators using Rayleigh and Gaussian distributions for the statistical models under the assumption of a diffuse noise field where the noise is estimated independently across each of the microphones. Experiments are performed to evaluate the new estimator against the baseline single‐channel and multichannel estimators using various values of the β parameter and number of microphones along with different levels of noises as a function of the input signal‐to‐noise ratio. By the utilization of additional microphones, the multichannel MMSE β‐order estimator achieves performance gains in noise reduction, speech distortion, and speech quality as measured by the segmental signal‐to‐noise ratio, log‐likelihood ratio, and perceptual evaluation of speech quality objective metrics. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite‐model adaptive control using an LS‐like algorithm

Adaptive control problem of a class of discrete‐time nonlinear uncertain systems, of which the internal uncertainty can be characterized by a finite set of functions, is formulated and studied by using an least squares (LS)‐like algorithm to design the feedback control law. For the finite‐model adaptive control problem, this algorithm is proposed as an extension of counterpart of traditional LS algorithm. Stability in sense of pth mean for the closed‐loop system is proved under a so‐called linear growth assumption, which is shown to be necessary in general by a counter‐example constructed in this paper. The main results have been also applied to parametric cases, which demonstrate how to bridge the non‐parametric case and parametric case. Copyright © 2006 John Wiley & Sons, Ltd.     

Precision analysis of kinetic modelling estimates in dynamic contrast enhanced MRI

Object  

Dynamic contrast enhanced MRI and pharmacokinetic modelling provide a powerful tool for tumour diagnosis and treatment evaluation. However, several studies show low reproducibility of the technique and poor precision of the transendothelial transfer constant K ^trans. This work proposes a theoretical framework describing how finite signal-noise-ratio (SNR) in the MR images is propagated throughout the measurement protocol to uncertainty on the kinetic parameter estimates.     

Stability of the equilibria of adaptive systems with leakage estimator

We study the stability of the equilibria of the differential equations that describe an adaptive controller in closed loop with a linear time-invariant (LTI) undermodelled plant when the parameter update law is a leaky gradient, i.e. a s?-modified estimator. Hsu and Costa studied the full-order case and showed that under certain limiting conditions the resulting dynamic system has three, possibly unstable, equilibrium points. Here we provide a modest extension to that work by further characterizing the class of undermodelled LTI plants for which the equilibria exist and are (un)stable Interestingly enough, it is shown that the equilibria are stable iff a given compensator stabilizes the plant. This compensator is, up to the plant ‘steady state gain’, known to the designer.     

可再生能源接入下考虑短路电流限制的发输电鲁棒规划方法

随着用电负荷密度增大、电网结构紧密程度提高及可再生能源接入带来的不确定性,短路电流越限问题突出.文中提出了一种可再生能源接入下满足短路电流限制的发输电系统鲁棒规划方法.首先,改进了计及网络拓扑结构和电源接入的短路电流计算方法,并内嵌网络结构优化和机组开停机操作优化短路电流水平.其次,采用自适应多面体不确定集合,考虑可再生能源出力不确定性和N-1随机故障,建立发输电系统三层鲁棒规划模型.上层为短路电流限制下的规划决策问题,以输电网扩展、电源建设年投资成本以及最差场景下的年运行成本之和最小为目标;中层寻找包含可再生能源出力与N-1随机故障的最差组合场景;下层为满足不确定场景运行约束的最优潮流问题.然后,利用对偶变换将三层问题转化为经典双层模型,采用列与约束生成算法进行有效求解.最后,IEEE 24节点系统的结果表明,规划方案在可再生能源出力不确定性下均能满足短路电流要求.     

A new paradigm for parameter estimation in system modeling

In this paper, we consider a basic problem in system identification, that of estimating the unknown parameters of a given model by using input/output data. Available methods (extended Kalman filtering, unscented Kalman filtering, particle filtering, maximum likelihood, prediction error method, etc.) have been extensively studied in the literature, especially in relation to consistency analysis. Yet, other important aspects, such as computational complexity, have been somewhat overlooked so that, when such methods are used in practical problems, remarkable drawbacks may arise. This is why parameter estimation is often performed using empirical procedures. This paper aims to revisit the issue of setting up an estimator that is able to provide reliable estimates at low computational cost. In contrast to other paradigms, the main idea in the new introduced two‐stage estimation method is to retrieve the estimator through simulation experiments in a training phase. Once training is terminated, the user is provided with an explicitly given estimator that can be used over and over basically with no computational effort. The advantages and drawbacks of the two‐stage approach as well as other traditional paradigms are identified with an illustrative example. A more concrete example of tire parameter estimation is also provided. Copyright © 2012 John Wiley & Sons, Ltd.     

Guaranteed recursive non‐linear state bounding using interval analysis

The problem considered here is state estimation in the presence of unknown but bounded state perturbations and measurement noise. In this context, most available results are for linear models, and the purpose of the present paper is to deal with the non‐linear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the perturbation and noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first estimator for which this claim can be made. The precision of the set estimate can be improved, at the cost of more computation. Theoretical properties of the estimator are studied, and computer implementation receives special attention. A simple illustrative example is treated. Copyright © 2002 John Wiley & Sons, Ltd.     

On the almost sure central limit theorem for ARX processes in adaptive tracking

The goal of this paper is to highlight the almost sure central limit theorem (ASCLT) for martingales to the control community. We shall establish the ASCLT for the least squares estimator of the unknown parameter of a controllable ARX(p,q) process in adaptive tracking. The usual notion of controllability for ARX(p,q) processes allows us to avoid the use of a persistent excitation in the adaptive tracking control. We shall also provide strongly consistent estimators of the even moments of the driven noise as well as two quadratic strong laws for the average costs and the estimation errors sequences. Our theoretical results are illustrated by numerical experiments.     

Towards a performance theory of robust adaptive control

We consider standard robust adaptive control designs based on the dead‐zone and projection modifications, and compare their performance w.r.t. a worst case transient cost functional penalizing the ??^∞ norm of the output, control and control derivative. If a bound on the ??^∞ norm of the disturbance is known, it is shown that the dead‐zone controller outperforms the projection controller if the a priori information on the uncertainty level is sufficiently conservative. The second result shows that the projection controller is superior to the dead‐zone controller when the a priori information on the disturbance level is sufficiently conservative. For conceptual clarity the results are presented on a non‐linear scalar system with a single uncertain parameter and generalizations are briefly discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors

In this paper, we are interested in the problem of adaptive control of non‐linearly parametrized systems. We investigate the viability of defining a stabilizing parameter update law for the case when the plant model is convex on the uncertain parameters. We show that, when the only prior knowledge is convexity, there does not exist an adaptation law—derivable from the standard separable Lyapunov function technique of Parks—applicable for all the state space. Therefore, we propose a semi‐adaptive state feedback controller where adaptation takes place only in the region of the state space where convexity can be used to reduce parameter uncertainty. In the remaining part of the state space we freeze the adaptation and switch to a robust controller. This scheme ensures semi‐global stability for convexly parametrized non‐linear systems with matched uncertainty. The proposed controller is then applied to the problem of temperature regulation of continuous stirred exothermic chemical reactors where reaction heat is convex in the uncertain parameters. Copyright © 2001 John Wiley & Sons, Ltd.     

Linear-like properties arise naturally in the adaptive control setting

Classical discrete-time adaptive controllers typically provide asymptotic stabilization and tracking; usually the affect of the noise is at best bounded-input bounded-output. Recently we have shown that if you design a discrete-time adaptive controller in just the right way, then in a variety of situations you not only obtain exponential stability, but also a bounded gain on the noise in every p−norm, as well as a never-before-seen linear-like convolution bound on the input–output behavior. Quite surprisingly, the approach is very natural, and relies on the use of the unmodified, original projection algorithm to carry out parameter estimation; if the set of plant uncertainty is not convex, then a multi-estimator and switching are used. The goal of this paper is to provide an overview of the approach, discuss the results-to-date, and list some of the open problems.     

Convergence analysis of the quasi‐OBE algorithm and related performance issues

‘Quasi‐OBE’ (QOBE) is an adaptive set identification and filtering algorithm which is based on the principles of optimal bounding ellipsoid processing, but which has other geometric and classic least‐squares interpretations which greatly enhance its application potential. In particular, because of its unusual optimization criterion, the ellipsoidal membership set associated with QOBE is more likely to retain (i.e. to move in the parameter space with) the system model's ‘true parameters, ’ say θ _*, when those parameters are time varying. Moreover, in the unlikely event that θ _* moves outside the set, the integrity of the point‐set estimation remains intact, and the estimator provably converges under known conditions. The consistency of the set estimation can be restored at any time using typical ‘rescue procedures’ if desired. Understanding convergence performance is very critical to successful QOBE application. Convergence analysis of both the central point estimate and measures of the hyperellipsoidal membership set is presented. The main results give conditions for point estimate convergence, and show that set convergence to a point is not possible. Implications of these convergence results for practical application are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Power System State Estimation with Equality Constraints

ABSTRACT

In this paper, a new technique for constrained power system state estimation is presented. The new technique is based on a recently developed least absolute value (LAV) state estimation procedure. Unlike least squares state estimation, least absolute value state estimation is well suited to constrained estimation problems.

Most power systems contain zero injection buses at which there is no load or generation. These buses impose constraints on a state estimator, since the real and reactive power injected at these buses is fixed at zero.

The least absolute value state estimator, which is presented in this paper, will initially treat all constaints as measurements. This increases the redundancy ratio of the measurement set without adding any additional metering costs.

After a preliminary (least squares) estimate is calculated, all of the constraints are placed in the interpolated measurement set. The interpolated measurement set is then completed with the addition of some of the actual measurements. The LAV state estimate is then computed using the interpolated measurement set.     

改进U-I法异步电机转子磁链估计器

在磁场定向控制的异步电机驱动系统中，精确的磁链估计是提高系统性能的关键。然而，参数摄动和量测噪声会导致估计器性能的下降。为了减小估计误差，必须抑制这些不确定因素对估计器的影响。在基于跟踪-微分器的电流定向的坐标系中，提出了定子电阻辨识和稳态磁链估计的新方法，该方法本身完全独立于电阻和转速。利用其结果，提出了改进U—I法磁链估计器。该估计器在适应定子电阻和抑止噪声积累方面优于U—I法。仿真表明该估计器具有很高的精度和良好的抗扰性。     

Parameter identification of linear time‐invariant systems using dynamic regressor extension and mixing

Dynamic regressor extension and mixing (DREM) is a new technique for parameter estimation that has proven instrumental in the solution of several open problems in system identification and adaptive control. A key property of the estimator is that, by generation of scalar regression models, it guarantees monotonicity of each element of the parameter error vector that is a much stronger property than monotonicity of the vector norm , as ensured with classical gradient or least‐squares estimators. On the other hand, the overall performance improvement of the estimator is strongly dependent on the suitable choice of certain operators that enter in the design. In this paper, we investigate the impact of these operators on the convergence properties of the estimator in the context of identification of linear single‐input single‐output time‐invariant systems with periodic excitation. The most important contribution is that the DREM (almost surely) converges under the same persistence of excitation (PE) conditions as the gradient estimator while providing improved transient performance. In particular, we give some guidelines how to select the DREM operators to ensure convergence under the same PE conditions as standard identification schemes.