A parametric extension of mixed time/frequency robustidentification

A parametric extension to the time/frequency robust identification framework is presented. The results can be applied to stable linear time-invariant systems on which time and/or frequency experiments have been performed. The parametric portion of the model should be affine in the unknown parameters, which includes practical applications such as flexible structures. The consistency problem is cast as a constrained finite-dimensional convex optimization problem that can be formulated as a linear matrix inequality. The proposed procedure provides an interpolating identification algorithm, convergent and optimal up to a factor of two (with respect to central algorithms)     

Identification of block-oriented systems in the presence of nonparametric input nonlinearities of switch and backlash types

The problem of identifying Hammerstein-like systems containing dynamic nonlinearities, of the switch or backlash types, is considered. Interestingly, the nonlinearity borders are nonparametric borders (i.e. of unknown structure) and so are allowed to be noninvertible and cross each other. A semi-parametric identification approach is developed to estimate the linear subsystem parameters and m points on both nonlinearity borders. It relies on two main experiments designed so that during each one, the focus is on one lateral border exciting m specific points. Doing so, the initial nonparametric identification problem is decomposed into two simpler problems involving static parametric nonlinearities. The new problems are dealt with independently using least squares type estimators. It is formally shown that the experiments generate persistently exciting signals ensuring the consistency of all involved parameter estimators.     

Decoupling the linear and nonlinear parts in Hammerstein model identification

The main result of this paper is to show that the linear part can be made decoupled from the nonlinear part in Hammerstein model identification. Therefore, identification of the linear part for a Hammerstein model becomes a linear problem and accordingly enjoys the same convergence and consistency results as if the unknown nonlinearity is absent.     

Identification of Hammerstein systems in presence of hysteresis-backlash and hysteresis-relay nonlinearities

The problem of identifying Hammerstein systems (HamSys) is addressed in presence of hysteresis-backlash (HB) and hysteresis-relay (HR) nonlinearities. The memory feature makes it impossible to get a system parameterization involving linearly all unknown parameters. Therefore, the linear subsystem and the nonlinear element are estimated separately. The identification process involves appropriate system parameterizations and least-squares like parameter estimators. Specific input signals are designed to guarantee persistent excitation (PE) and estimator consistency.     

Problems of Adaptive Optimal Control of Discrete-Time Systems under Bounded Disturbance and Linear Performance Indexes

We present some problems of adaptive optimal robust control of linear discretetime systems under uncertainty and bounded external disturbance in which the optimal or guaranteed value of the performance index is a linear or linear-fractional function of unknown parameters of the system and set-membership estimation based on the method of recurrent objective inequalities reduces to recurrent updating of polyhedral estimates of unknown parameters. In such problems, computing current optimal estimates becomes a recurrent linear programming problem which is computationally tractable on modern computers for systems with a small number of estimated parameters.     

Improved estimation performance using known linear constraints

The additional information available in the form of linear or nonlinear constraints are often remain unexplored in the parameter identification problems related to linear dynamic systems. Our goal in this work is to explore the knowledge of the linear constraints to achieve significant improvement in the accuracy of the parameter estimates. In the class of problems being addressed here, the unknown boundary conditions appear as nuisance parameters. In practice, these nuisance parameters are eliminated from the loss function to get a variable projection optimization problem in the parameters of interest. In this work, we solve a constrained optimization problem instead, where the additional linear constraints are imposed in the form of partially known boundary conditions. In the process, we show how the accuracy of the estimates is improved by taking the constraints into account. The theoretical methodology is successfully applied also to numerical simulations as well as in real-world experiments.     

An approach to adaptive control using real time identification

An adaptive controller consisting of a real time identifier and a minimum variance regulator is discussed. The identification is done by augmenting the state with the unknown parameters of the process. This usually leads to a non-linear filtering problem. By choosing a model of special structure the problem can, however, be reduced to a linear problem. The control law is derived using stochastic optimal control theory. By choosing a special criterion, the stochastic control problem can be solved analytically. The behaviour of the adaptive controller is illustrated in two examples.     

Identification of elastic materials using wavelet transform

This paper presents an identification method for material parameters using the observational boundary conditions and the wavelet analysis. The material parameter identification methods which belong to the deterministic approaches are classified into the inverse and direct approaches. The proposed method combines the inverse approach and the direct approach [Swoboda G, Ichikawa Y, Dong Q, Zaki M. Back analysis of large geotechnical models. Int J Numer Meth Geomech 1999;23:1455–72, Ichikawa Y, Ohkami T. A parameter identification procedure as a dual boundary control problem for linear elastic materials. Soils Foundat 1992;32(2):35–44], and by applying the discrete wavelet transform to the system matrix of the iteration equation, we estimate unknown material parameters for the case in which the number of unknown parameters exceeds the observed data. The validity of this method is examined for geotechnical engineering problems. This paper is a revised and extended version of reference [Ohkami T, Nagao J, Koyama S. Parameter identification method using wavelet transform. In: Topping B.H.V., editor, Proceedings of the ninth international conference on civil and structural engineering computing. Civil-Comp Press, Stirling (UK); 2003; Paper 116].     

利用工业大系统动态信息建立稳态模型及其强一致性分析

本文提出了一种在相当弱的条件下，仅仅利用优化过程中系统设定点例行阶跃变化作为激励信号，对各子系统并行使用简单最小二乘法和近似动态线性模型，充分运用大系统的动态信息，得到了大系统稳态模型的一致估计的理论证明，并利用数字仿真进一步验证了其方法的有效性。还给出了一种实用的，能强一致估计线性渐近定常大系统稳态模型的方法。     

Adaptive suboptimal robust control of the first-order plant

For a linear first-order plant, consideration was given to minimization of the deviation of its output from the specified value in an uncertain environment. Both the parameters of the plant itself and the upper bounds of the external disturbances and operator perturbations in output and control were assumed to be unknown. The suboptimal adaptive control was constructed on the basis of an approximate solution of the problem of optimal identification from the measurement data where the performance of the problem of control was used as an identification criterion.     

On the identifiability of parameters

A precise definition of identifiability of a parameter is given in terms of consistency in probability for the parameter estimate. Under some mild Uniformity assumptions on the conditional density parameterized by the unknown parameter, necessary and sufficient conditions for the unknown parameter to be identifiable are established. The assumptions and identifiability criteria are expressed in terms of the density of individual observations, conditioned upon all past observations. The results are applied to linear system identification problems.     

Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block

This note deals with identification of Hammerstein systems with discontinuous piecewise-linear memoryless block followed by a linear subsystem. Recursive algorithms are proposed for estimating coefficients of the linear subsystem and six unknown parameters contained in the nonlinear static block. By taking a sequence of iid random variables with uniform distribution to serve as the system input, strong consistency is proved for all estimates given in the note. The theoretical results are verified by computer simulation.     

A new algorithm for single-input single-output system identification via block-pulse functions

A new recursive algorithm via block-pulse functions is presented for estimating the unknown parameters of a linear continuous system from samples of input-output data. Compared with other methods via block-pulse functions, there are no integrals of input-output data to be computed and no initial states or values involved for the purpose of identification. This algorithm is therefore easy to implement and is especially applicable to those estimation problems in which the parameters vary slowly with time in an unknown way. The illustrative examples show that the new algorithm gives satisfactory results for identification problems.     

Identification of Wiener systems with binary-valued output observations

This work is concerned with identification of Wiener systems whose outputs are measured by binary-valued sensors. The system consists of a linear FIR (finite impulse response) subsystem of known order, followed by a nonlinear function with a known parametrization structure. The parameters of both linear and nonlinear parts are unknown. Input design, identification algorithms, and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible. It is shown that under scaled periodic inputs, identification of Wiener systems can be decomposed into a finite number of core identification problems. The concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the Wiener system can be identified with binary-valued observations. Under scaled full-rank conditions and joint identifiability, a strongly convergent algorithm is constructed. The algorithm is shown to be asymptotically efficient for the core identification problem, hence achieving asymptotic optimality in its convergence rate. For computational simplicity, recursive algorithms are also developed.     

Identification of Constant Parameters of Dynamic Systems by a Time-Frequency Method

A time-frequency method for identifying linear dynamic systems of a general form with constant parameters and delays in their observable variables is considered. The identification problem is found to be decomposable into the problem of estimating unknown parameters and the problem of estimating the initial conditions. Applying the time-frequency method to identify the differential equation of the Van der Pol oscillator, which is nonlinear by both its state and parameters, is considered. Examples are used to show that the time-frequency method solves the identification problem both for stable and unstable dynamic systems.     

Hammerstein Systems Identification in Presence of Hard Nonlinearities of Preload and Dead-Zone Type

Hammerstein system identification is considered in presence of preload and dead zone nonlinearities. The discontinuous feature of these nonlinearities makes it difficult to get a single system parameterization involving linearly all unknown parameters (those of the linear subsystem and those of the nonlinearity). Therefore, system identification has generally been dealt with using multiple stage schemes including different parametrizations and several data acquisition experiences. However, the consistency issue has only been solved under restrictive assumptions regarding the identified system. In this paper, a new identification scheme is designed and shown to be consistent under mild assumptions.     

On-line identification and nonlinear control of an industrial pH process

The control of pH for industrial processes is a highly nonlinear and challenging problem, especially when the nonlinearity is unknown and time-varying. In this work, a controller is developed and implemented for an industrial pH process with unknown chemical composition. The method used is an application of a general algorithm for pH processes, which is based on a representation of the nonlinearity that leads to on-line identification of a small number of parameters. The results show good performance of the pH control algorithm under normal operating conditions and satisfactory performance during several unusual hardware or process problems.     

Estimation of Time-Varying Parameters in Statistical Models: An Optimization Approach

We propose a convex optimization approach to solving the nonparametric regression estimation problem when the underlying regression function is Lipschitz continuous. This approach is based on the minimization of the sum of empirical squared errors, subject to the constraints implied by Lipschitz continuity. The resulting optimization problem has a convex objective function and linear constraints, and as a result, is efficiently solvable. The estimated function computed by this technique, is proven to convergeto the underlying regression function uniformly and almost surely, when the sample size grows to infinity, thus providing a very strong form of consistency. Wealso propose a convex optimization approach to the maximum likelihood estimation of unknown parameters in statistical models, where the parameters depend continuously on some observable input variables. For a number of classical distributional forms, the objective function in the underlying optimization problem is convex and the constraints are linear. These problems are, therefore, also efficiently solvable.     

Reinforcement learning based computational adaptive optimal control and system identification for linear systems

The duality of estimation and control problems is a well known fact in control theory literature. Simultaneous parameter estimation while maintaining closed loop stability is a very difficult proposition and more so for unstable systems, even for linear systems. This typically motivates system identification to be performed only in offline experiments. Clearly, there is a need for a higher level abstraction for a control and identification scheme which acts in stages and prioritizes various aspects of the problem at each of these stages. The stage abstraction for the controller design in this paper is inspired by human intuition towards dealing with control and identification simultaneously and hence named “Intuitive Control Framework”. The first phase prioritizes stabilization of the system only. The controller moves onto the next phase after the unknown system is stabilized. The subsequent stages during this phase involve optimization with different performance metrics through adaptive learning. After enough information for identification is acquired, the control schemes developed for various optimal metrics are used to estimate the unknown parameters in the final phase. This narrative for selective prioritization of objectives and a higher level abstraction for control schemes is illustrated for a continuous linear time invariant state space realization with state feedback. Numerous real-world applications can benefit from this online system identification routine inspired by the human cognitive process. This offers a seamless integration of control and identification with a higher level of priorities. Such a framework is presented with explicit formulations for certain classes of dynamic systems, and evaluated with computer simulations as well as experimental results. An unstable multi-input multi-output linear system is used as an example to illustrate the approach.     

带饱和执行器的不确定时滞系统的 鲁棒控制

研究了一类具有饱和执行器约束的不确定时滞系统时滞依赖型无记忆鲁棒控制问题 .所考虑的时滞系统包括时变未知但有界的不确定参数以及状态和控制的时滞项 .文中应用了 Lyapunov定理以及线性矩阵不等式 ( LMI)方法来研究该系统的分析和综合问题 ,导出了一个新的鲁棒可镇定判据和相应的无记忆鲁棒镇定控制律设计方法 .所得的基于一组LMIs的结果是与时滞相关的