Control-oriented System Identification Research Articles

Robust System Identification for Anemia Management

Abstract Anemia is the condition in which patients suffer from the deficiency of the red blood cells to carry the oxygen in the body. One of the many causes of anemia is chronic kidney disease (CKD). CKD is a disease in which kidneys are partially or completely damaged, which results in a deficiency of the oxygen-carrying red blood cells. CKD is common in older people, and external human recombinant erythropoietin (EPO) is required to maintain healthy levels of hemoglobin (Hb). In order to effectively address the impact of inter and intra-individual variability in dose-response characteristics in CKD patients, individualized patient-specific models are required instead of traditional population-based models. In this research, individualized patient models are developed by using patient-specific time-domain data with robust system identification techniques. For control-oriented system identification, two robust identification techniques are investigated: (1) l1 robust identification considering zero initial conditions and (2) Semi-blind robust system identification considering non-zero initial conditions. The performance of these two techniques is compared and it is shown that the Semi-blind robust identification technique gives better results as compared to l1 robust identification.

Control Oriented System Identification for Performance Management in Virtualized Software System

Capability to manage the performance of a shared resources environment relies on the model estimation of all dynamics in the system. The main challenge is to capture the nonlinear characteristic which inherently exists in software system applications. Hammerstein-Wiener block structural model is widely regarded as a basis for description of nonlinear systems. This paper extends the existing work in system identification of software systems using Hammerstein-Wiener block structural model. As part of the estimation, the linear element is represented in terms of Frequency Sampling Filter model and the inverse static output non-linearity is estimated using B-Spline curve functions. Experimental studies show that the static nonlinearities estimated when using the B-Spline functions have less oscillations and the overall model has a better performance than the case when using polynomial functions.

Some System Identification Challenges and Approaches

The field of control-oriented system identification is mature. Nevertheless, it is still very active. This is because there are many important unsolved challenges. Of these, this paper considers a selection. This involves considering the estimation of general nonlinear model structures, together with accurate error bounds, using methods that scale well to models of high dimension. A particular strength of the system identification field is that it has always actively sought to understand, embrace and develop ideas from other fields, such as statistics, mathematics and econometrics. This paper proposes a continuation of this successful strategy by proposing and profiling the adoption of new ideas originating in statistics, signal processing and statistical mechanics.

Control-oriented system identification: an H/sub /spl infin// approach [Book Review

Control-oriented system identification: an H/sub /spl infin// approach [Book Review

Evolutionary L∞ identification and model reduction for robust control

An evolutionary approach for modern robust control oriented system identification and model reduction in the frequency domain is proposed. The technique provides both an optimized nominal model and a ‘worst-case’ additive or multiplicative uncertainty bounding function which is compatible with robust control design methodologies. In addition, the evolutionary approach is applicable to both continuous- and discrete-time systems without the need for linear parametrization or a confined problem domain for deterministic convex optimization. The proposed method is validated against a laboratory multiple-input multiple-output (MIMO) test rig and benchmark problems, which show a higher fitting accuracy and provides a tighter L∞ error bound than existing methods in the literature do.

On robust control-oriented identification of discrete and continuous-time systems

Robust control-oriented system identification is considered for discrete and continuous time systems. It is shown here how largely to eliminate the small noise-to- signal ratio and high computational cost issues which have been claimed to limit the usefulness of the new theory. This is achieved through a linear data preprocessing and compression step to obtain small nonlinear constrained optimization problems which are easy to solve even in real-time. In particular, a method based on sample correlation quantities and the Chebyshev criterion is considered. Furthermore, worst-case L1 identification is studied for BIBO stable linear continuous time systems. The existence of robustly convergent identification algorithms is established in the Banach space L1 in a constructive way. The topic of L1 identification of continuous time systems is nicely motivated by the recently developed robust sampled-data control theory of continuous-time systems.

On autoregressive models, the parsimony principle, and their use in control-oriented system identification

A perspective is given on the use and limitations of autoregressive type models and the parsimony principle in the context of control-oriented system identification. It is demonstrated that the non-systematic application of the parsimony principle tends to favour low-order autoregressive type models that can be detrimental in subsequent control design especially for unstable or poorly damped systems. Furthermore, an existence condition for smooth coprime factorizations and system stabilizability is given.

Worst case system identification in H/sub ∞/: validation of a priori information, essentially optimal algorithms, and error bounds

Resolves several important open issues pertaining to a worst-case control-oriented system identification problem known as identification in H/sub /spl infin//. First, a method is presented for developing confidence that certain a priori information available for identification is not invalid. This method requires the solution of a certain nondifferentiable convex program. Second, an essentially optimal identification algorithm is constructed. This algorithm is (worst-case strongly) optimal to within a factor of two. Finally, new upper and lower bounds on the optimal identification error are derived and used to estimate the identification error associated with the given algorithm. Interestingly, the development of each of these results draws heavily upon the classical Nevanlinna-Pick interpolation theory. As such, the authors' results establish a clear link between the areas of system identification and optimal interpolation theory. Both the formulation and techniques in this paper are applicable to problems where the frequency data available for identification may essentially be arbitrarily distributed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An algorithm for identification of smooth nonlinear systems based on parametrized linearization families

This paper presents results concerning the identification of a class of nonlinear systems. The main result of the paper gives the approximation power of a parametrized linearization family constructed from a given nonlinear system. The identification procedure derived from this approximation theory consists of constructing a parametrized linearization family from a set of input-output measurements of a given nonlinear system along a given trajectory. This paper utilizes related work on control-oriented system identification. Simulation results are included to support the theoretical development.

Comments on "Least squares methods for H/spl infin/ control oriented system identification"

In the above paper by Helmicki-Jacobson (ibid. vol.38, no.5, p.819-26 (1993)), the authors present two sets of convergent least squares algorithms for identification in H/spl infin/. In this paper we: (1) point out an error in the proof of convergence for the first set; (2) show that the first set of optimization problems is really equivalent to a special case of the second set; and (3) provide a small correction to the derivation of the error bounds for the second set of algorithms. >

Least squares methods for H/sub infinity / control-oriented system identification

A series of system identification algorithms that yield identified models which are compatible with current robust controller design methodologies is presented. These algorithms are applicable to a broad class of stable, distributed, linear, shift-invariant plants. The a priori information necessary for their application consists of a lower bound on the relative stability of the unknown plant, an upper bound on a certain gain associated with the unknown plant, and an upper bound on the noise level. The a posteriori data information consists of a finite number of corrugated point frequency response estimates of the unknown plant. The extent to which certain standard Hilbert-space or least-squares method are applicable to the H/sub infinity / system identification problem considered is examined. Results are established that connect the H/sub 2/ error of the least-squares methods to the H/sub infinity / error needed for control-oriented system identification. >

Time domain identification for robust control

In this paper, we are concerned with a problem of robust control-oriented system identification in the time domain. Based on the well-known Schur-Takagi-AAK Theorem, we propose a linear algorithm to obtain the nominal model of the plant to be identified and the minimal bound of the uncertainty of the nominal model error which is measured by H ∞ -norm. It is also shown that, in the model set defined by the nominal model and the uncertainty bound, there exists at least one model which matches the prescribed input-output data given in the time domain.

Control oriented system identification: a worst-case/deterministic approach in H/sub infinity /

The authors formulate and solve two related control-oriented system identification problems for stable linear shift-invariant distributed parameter plants. In each of these problems the assumed a priori information is minimal, consisting only of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, and an upper bound on the noise level. The first of these problems involves identification of a point sample of the plant frequency response from a noisy, finite, output time series obtained in response to an applied sinusoidal input with frequency corresponding to the frequency point of interest. This problem leads naturally to the second problem, which involves identification of the plant transfer function in H/sub infinity / from a finite number of noisy point samples of the plant frequency response. Concrete plans for identification algorithms are provided for each of these two problems. >