Canonical Form of Datatic Description in Control Systems
arxiv(2024)
摘要
The design of feedback controllers is undergoing a paradigm shift from
modelic (i.e., model-driven) control to datatic (i.e., data-driven) control.
Canonical form of state space model is an important concept in modelic control
systems, exemplified by Jordan form, controllable form and observable form,
whose purpose is to facilitate system analysis and controller synthesis. In the
realm of datatic control, there is a notable absence in the standardization of
data-based system representation. This paper for the first time introduces the
concept of canonical data form for the purpose of achieving more effective
design of datatic controllers. In a control system, the data sample in
canonical form consists of a transition component and an attribute component.
The former encapsulates the plant dynamics at the sampling time independently,
which is a tuple containing three elements: a state, an action and their
corresponding next state. The latter describes one or some artificial
characteristics of the current sample, whose calculation must be performed in
an online manner. The attribute of each sample must adhere to two requirements:
(1) causality, ensuring independence from any future samples; and (2) locality,
allowing dependence on historical samples but constrained to a finite
neighboring set. The purpose of adding attribute is to offer some kinds of
benefits for controller design in terms of effectiveness and efficiency. To
provide a more close-up illustration, we present two canonical data forms:
temporal form and spatial form, and demonstrate their advantages in reducing
instability and enhancing training efficiency in two datatic control systems.
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