Data-Driven Control of Linear Time-Varying Systems

In this paper, we propose an adaptive data-driven control approach for linear time varying systems, affected by bounded measurement noise. The plant to be controlled is assumed to be unknown, and no information in regard to its time varying behaviour is exploited. First, using set-membership identification techniques, we formulate the controller design problem through a model-matching scheme, i.e., designing a controller such that the closed-loop behaviour matches that of a given reference model. The problem is then reformulated as to derive a controller that corresponds to the minimum variation bounding its parameters. Finally, a convex relaxation approach is proposed to solve the formulated controller design problem by means of linear programming. The effectiveness of the proposed scheme is demonstrated by means of two simulation examples.

Download Full-text

Data-Driven Networked Optimal Iterative Learning Control for Discrete Linear Time-Varying Systems with One-Operation Bernoulli-Type Communication Delays

Discrete Dynamics in Nature and Society ◽

10.1155/2017/9846846 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Yan Geng ◽

Xiaoe Ruan ◽

Hyo-Sung Ahn

Keyword(s):

Iterative Learning Control ◽

Linear Time ◽

Tracking Error ◽

Learning Control ◽

Iterative Learning ◽

Data Driven ◽

Time Varying ◽

Communication Delays ◽

System Matrix ◽

Time Varying Systems

This paper develops a type of data-driven networked optimal iterative learning control strategy for a class of discrete linear time-varying systems with one-operation Bernoulli-type communication delays. In terms of the stochastic Bernoulli-type one-operation communication delayed inputs and outputs, the previous-iteration synchronous compensations are adopted. By means of deriving gradients of two types of objective functions that express the optimal approximation of the system matrix and the minimal tracking error, the strategy approximates the system matrix and upgrades the control inputs in an interact mode as the iteration evolves. By taking advantage of matrix theory and statistical technique, it is derived that the approximation discrepancy of the system matrix is bounded and the mathematical expectation of the tracking error vanishes as the iteration goes on. Numerical simulations manifest the validity and effectiveness.

Download Full-text

Controllability of Linear Time Varying Systems: New Algebraic Criteria

1993 American Control Conference ◽

10.23919/acc.1993.4793155 ◽

1993 ◽

Author(s):

Hngo Leiva ◽

Brad Lehman

Keyword(s):

Linear Time ◽

Time Varying ◽

Time Varying Systems

Download Full-text

The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽

10.3390/eng2010008 ◽

2021 ◽

Vol 2 (1) ◽

pp. 99-125

Author(s):

Edward W. Kamen

Keyword(s):

Discrete Time ◽

Initial Conditions ◽

Linear Time ◽

Order Term ◽

Initial Time ◽

Time Varying ◽

Varying Coefficients ◽

Time Signals ◽

Time Varying Systems ◽

Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

Download Full-text