439 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
Low-Complexity Quantized Switching Controllers using Approximate Bisimulation
In this paper, we consider the problem of synthesizing low-complexity
controllers for incrementally stable switched systems. For that purpose, we
establish a new approximation result for the computation of symbolic models
that are approximately bisimilar to a given switched system. The main advantage
over existing results is that it allows us to design naturally quantized
switching controllers for safety or reachability specifications; these can be
pre-computed offline and therefore the online execution time is reduced. Then,
we present a technique to reduce the memory needed to store the control law by
borrowing ideas from algebraic decision diagrams for compact function
representation and by exploiting the non-determinism of the synthesized
controllers. We show the merits of our approach by applying it to a simple
model of temperature regulation in a building
Symbolic models for nonlinear control systems without stability assumptions
Finite-state models of control systems were proposed by several researchers
as a convenient mechanism to synthesize controllers enforcing complex
specifications. Most techniques for the construction of such symbolic models
have two main drawbacks: either they can only be applied to restrictive classes
of systems, or they require the exact computation of reachable sets. In this
paper, we propose a new abstraction technique that is applicable to any smooth
control system as long as we are only interested in its behavior in a compact
set. Moreover, the exact computation of reachable sets is not required. The
effectiveness of the proposed results is illustrated by synthesizing a
controller to steer a vehicle.Comment: 11 pages, 2 figures, journa
A Control-Oriented Notion of Finite State Approximation
We consider the problem of approximating discrete-time plants with
finite-valued sensors and actu- ators by deterministic finite memory systems
for the purpose of certified-by-design controller synthesis. Building on ideas
from robust control, we propose a control-oriented notion of finite state
approximation for these systems, demonstrate its relevance to the control
synthesis problem, and discuss its key features.Comment: IEEE Transactions on Automatic Control, to appea
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