11 research outputs found
Compositional Synthesis via a Convex Parameterization of Assume-Guarantee Contracts
We develop an assume-guarantee framework for control of large scale linear
(time-varying) systems from finite-time reach and avoid or infinite-time
invariance specifications. The contracts describe the admissible set of states
and controls for individual subsystems. A set of contracts compose correctly if
mutual assumptions and guarantees match in a way that we formalize. We propose
a rich parameterization of contracts such that the set of parameters that
compose correctly is convex. Moreover, we design a potential function of
parameters that describes the distance of contracts from a correct composition.
Thus, the verification and synthesis for the aggregate system are broken to
solving small convex programs for individual subsystems, where correctness is
ultimately achieved in a compositional way. Illustrative examples demonstrate
the scalability of our method
Practical Volume Estimation by a New Annealing Schedule for Cooling Convex Bodies
We study the problem of estimating the volume of convex polytopes, focusing
on H- and V-polytopes, as well as zonotopes. Although a lot of effort is
devoted to practical algorithms for H-polytopes there is no such method for the
latter two representations. We propose a new, practical algorithm for all
representations, which is faster than existing methods. It relies on
Hit-and-Run sampling, and combines a new simulated annealing method with the
Multiphase Monte Carlo (MMC) approach. Our method introduces the following key
features to make it adaptive: (a) It defines a sequence of convex bodies in MMC
by introducing a new annealing schedule, whose length is shorter than in
previous methods with high probability, and the need of computing an enclosing
and an inscribed ball is removed; (b) It exploits statistical properties in
rejection-sampling and proposes a better empirical convergence criterion for
specifying each step; (c) For zonotopes, it may use a sequence of convex bodies
for MMC different than balls, where the chosen body adapts to the input. We
offer an open-source, optimized C++ implementation, and analyze its performance
to show that it outperforms state-of-the-art software for H-polytopes by
Cousins-Vempala (2016) and Emiris-Fisikopoulos (2018), while it undertakes
volume computations that were intractable until now, as it is the first
polynomial-time, practical method for V-polytopes and zonotopes that scales to
high dimensions (currently 100). We further focus on zonotopes, and
characterize them by their order (number of generators over dimension), because
this largely determines sampling complexity. We analyze a related application,
where we evaluate methods of zonotope approximation in engineering.Comment: 20 pages, 12 figures, 3 table
Adaptive Parameter Tuning for Reachability Analysis of Linear Systems
Despite the possibility to quickly compute reachable sets of large-scale
linear systems, current methods are not yet widely applied by practitioners.
The main reason for this is probably that current approaches are not
push-button-capable and still require to manually set crucial parameters, such
as time step sizes and the accuracy of the used set representation---these
settings require expert knowledge. We present a generic framework to
automatically find near-optimal parameters for reachability analysis of linear
systems given a user-defined accuracy. To limit the computational overhead as
much as possible, our methods tune all relevant parameters during runtime. We
evaluate our approach on benchmarks from the ARCH competition as well as on
random examples. Our results show that our new framework verifies the selected
benchmarks faster than manually-tuned parameters and is an order of magnitude
faster compared to genetic algorithms
Robust explicit model predictive control for hybrid linear systems with parameter uncertainties
Explicit model-predictive control (MPC) is a widely used control design
method that employs optimization tools to find control policies offline;
commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP
in the case of hybrid systems. However, mixed-integer SDPs are computationally
expensive, motivating alternative formulations, such as zonotope-based MPC
(zonotopes are a special type of symmetric polytopes). In this paper, we
propose a robust explicit MPC method applicable to hybrid systems. More
precisely, we extend existing zonotope-based MPC methods to account for
multiplicative parametric uncertainty. Additionally, we propose a convex
zonotope order reduction method that takes advantage of the iterative structure
of the zonotope propagation problem to promote diagonal blocks in the zonotope
generators and lower the number of decision variables. Finally, we developed a
quasi-time-free policy choice algorithm, allowing the system to start from any
point on the trajectory and avoid chattering associated with discrete switching
of linear control policies based on the current state's membership in
state-space regions. Last but not least, we verify the validity of the proposed
methods on two experimental setups, varying physical parameters between
experiments
Compositional Synthesis for Linear Systems via Convex Optimization of Assume-Guarantee Contracts
We take a divide and conquer approach to design controllers for reachability
problems given large-scale linear systems with polyhedral constraints on
states, controls, and disturbances. Such systems are made of small subsystems
with coupled dynamics. We treat the couplings as additional disturbances and
use assume-guarantee (AG) contracts to characterize these disturbance sets. For
each subsystem, we design and implement a robust controller locally, subject to
its own constraints and contracts. The main contribution of this paper is a
method to derive the contracts via a novel parameterization and a corresponding
potential function that characterizes the distance to the correct composition
of controllers and contracts, where all contracts are held. We show that the
potential function is convex in the contract parameters. This enables the
subsystems to negotiate the contracts with the gradient information from the
dual of their local synthesis optimization problems in a distributed way,
facilitating compositional control synthesis that scales to large systems. We
present numerical examples, including a scalability study on a system with tens
of thousands of dimensions, and a case study on applying our method to a
distributed Model Predictive Control (MPC) problem in a power system