A.J. Helmicki

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. >

Worst-case/deterministic identification in H/sub infinity /: the continuous-time case

Results obtained by the authors (1991) worst-case/deterministic H/sub infinity / identification of discrete-time plants are extended to continuous-time plants. The problem involves identification of the transfer function of a stable strictly proper continuous-time plant from a finite number of noisy point samples of the plant frequency response. The assumed information consists of a lower bound on the relative stability of the plant, an upper bound on a certain gain associated with the plant, an upper bound on the roll-off rate of the plant, and an upper bound on the noise level. Concrete plans of identification algorithms are provided for this problem. Explicit worst-case/deterministic error bounds for each algorithm establish that they are robustly convergent and (essentially) asymptotically optimal. Additionally, these bounds provide an a priori computable H/sub infinity / uncertainty specification, corresponding to the resulting identified plant transfer function, as an explicit function of the plant and noise prior information and the data cardinality. >

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. >

Ill-posed distributed parameter systems: a control viewpoint

The use of linear time-invariant distributed parameter systems (LTIDPSs) as models of physical processes is considered from a control viewpoint. Specifically, classes of LTIDPSs exhibiting properties which potentially limit their usefulness in feedback design are defined and termed ill-posed. The structure of these classes is investigated within a general mathematical framework which encompasses many distributed parameter systems of engineering interest. Within this framework necessary and sufficient conditions are derived which completely characterize these classes and establish their equivalence. >

On zero-order hold equivalents of distributed parameter systems

In this paper various connections are established between linear, time-invariant, distributed parameter, continuous-time systems and their zero-order hold discrete-time equivalents. These connections are established in both the time and frequency-domains. The time-domain connections relate various growth constants and norm bounds of the continuous-time systems considered to those of their zero-order hold discrete-time equivalents. The frequency-domain connection provides an upper bound on the difference between the frequency response of a continuous-time system and that of its zero-order hold discrete-time equivalent.