2 research outputs found
Synthesis of separable controlled invariant sets for modular local control design
Many correct-by-construction control synthesis methods suffer from the curse
of dimensionality. Motivated by this challenge, we seek to reduce a
correct-by-construction control synthesis problem to subproblems of more modest
dimension. As a step towards this goal, in this paper we consider the problem
of synthesizing decoupled robustly controlled invariant sets for dynamically
coupled linear subsystems with state and input constraints. Our approach, which
gives sufficient conditions for decoupled invariance, is based on optimization
over linear matrix inequalities which are obtained using slack variable
identities. We illustrate the applicability of our method on several examples,
including one where we solve local control synthesis problems in a
compositional manner
Compositional Analysis of Hybrid Systems Defined Over Finite Alphabets
We consider the stability and the input-output analysis problems of a class
of large-scale hybrid systems composed of continuous dynamics coupled with
discrete dynamics defined over finite alphabets, e.g., deterministic finite
state machines (DFSMs). This class of hybrid systems can be used to model
physical systems controlled by software. For such classes of systems, we use a
method based on dissipativity theory for compositional analysis that allows us
to study stability, passivity and input-output norms. We show that the
certificates of the method based on dissipativity theory can be computed by
solving a set of semi-definite programs. Nonetheless, the formulation based on
semi-definite programs become computationally intractable for relatively large
number of discrete and continuous states. We demonstrate that, for systems with
large number of states consisting of an interconnection of smaller hybrid
systems, accelerated alternating method of multipliers can be used to carry out
the computations in a scalable and distributed manner. The proposed methodology
is illustrated by an example of a system with 60 continuous states and 18
discrete states.Comment: 8 pages, to appear in ADHS 201