Kavli Affiliate: Biao Huang
| First 5 Authors: Yitao Yan, Jie Bao, Biao Huang, ,
| Summary:
In the data-based setting, analysis and control design of dynamical systems
using measured data are typically based on overlapping trajectory segments of
the input and output variables. This could lead to complex designs because the
system internal dynamics, which is typically reflected by the system state
variable, is unavailable. In this paper, we will show that the coefficient
vector in a modified version of Willems’ fundamental lemma is an intrinsic and
observable state variable for the system behavior. This argument evolves from
the behavioral framework without the requirement of prior knowledge on the
causality among system variables or any predefined representation structure
(e.g., a state space representation). Such a view allows for the construction
of a state map based on the fundamental lemma, bridging the trajectory space
and the state space. The state property of the coefficient vector allows for a
simple stability design approach using memoryless quadratic functions of it as
Lyapunov functions, from which the control action for each step can be
explicitly constructed. Using the coefficient vector as a state variable could
see wide applications in the analysis and control design of dynamical systems
including directions beyond the discussions in this paper.
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