308 research outputs found
Approximately bisimilar symbolic models for nonlinear control systems
Control systems are usually modeled by differential equations describing how
physical phenomena can be influenced by certain control parameters or inputs.
Although these models are very powerful when dealing with physical phenomena,
they are less suitable to describe software and hardware interfacing the
physical world. For this reason there is a growing interest in describing
control systems through symbolic models that are abstract descriptions of the
continuous dynamics, where each "symbol" corresponds to an "aggregate" of
states in the continuous model. Since these symbolic models are of the same
nature of the models used in computer science to describe software and
hardware, they provide a unified language to study problems of control in which
software and hardware interact with the physical world. Furthermore the use of
symbolic models enables one to leverage techniques from supervisory control and
algorithms from game theory for controller synthesis purposes. In this paper we
show that every incrementally globally asymptotically stable nonlinear control
system is approximately equivalent (bisimilar) to a symbolic model. The
approximation error is a design parameter in the construction of the symbolic
model and can be rendered as small as desired. Furthermore if the state space
of the control system is bounded the obtained symbolic model is finite. For
digital control systems, and under the stronger assumption of incremental
input-to-state stability, symbolic models can be constructed through a suitable
quantization of the inputs.Comment: Corrected typo
Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach
In this paper, we present some preliminary results for compositional analysis
of heterogeneous systems containing both discrete state models and continuous
systems using consistent notions of dissipativity and passivity. We study the
following problem: given a physical plant model and a continuous feedback
controller designed using traditional control techniques, how is the
closed-loop passivity affected when the continuous controller is replaced by a
discrete (i.e., symbolic) implementation within this framework? Specifically,
we give quantitative results on performance degradation when the discrete
control implementation is approximately bisimilar to the continuous controller,
and based on them, we provide conditions that guarantee the boundedness
property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in
Japa
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