211,884 research outputs found
Numerical Verification of Affine Systems with up to a Billion Dimensions
Affine systems reachability is the basis of many verification methods. With
further computation, methods exist to reason about richer models with inputs,
nonlinear differential equations, and hybrid dynamics. As such, the scalability
of affine systems verification is a prerequisite to scalable analysis for more
complex systems. In this paper, we improve the scalability of affine systems
verification, in terms of the number of dimensions (variables) in the system.
The reachable states of affine systems can be written in terms of the matrix
exponential, and safety checking can be performed at specific time steps with
linear programming. Unfortunately, for large systems with many state variables,
this direct approach requires an intractable amount of memory while using an
intractable amount of computation time. We overcome these challenges by
combining several methods that leverage common problem structure. Memory is
reduced by exploiting initial states that are not full-dimensional and safety
properties (outputs) over a few linear projections of the state variables.
Computation time is saved by using numerical simulations to compute only
projections of the matrix exponential relevant for the verification problem.
Since large systems often have sparse dynamics, we use Krylov-subspace
simulation approaches based on the Arnoldi or Lanczos iterations. Our method
produces accurate counter-examples when properties are violated and, in the
extreme case with sufficient problem structure, can analyze a system with one
billion real-valued state variables
Fast Non-Parametric Learning to Accelerate Mixed-Integer Programming for Online Hybrid Model Predictive Control
Today's fast linear algebra and numerical optimization tools have pushed the
frontier of model predictive control (MPC) forward, to the efficient control of
highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated
that exact optimal control law can be computed, e.g., by mixed-integer
programming (MIP) under piecewise-affine (PWA) system models. Despite the
elegant theory, online solving hybrid MPC is still out of reach for many
applications. We aim to speed up MIP by combining geometric insights from
hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start
techniques. Following a line of work in approximate explicit MPC, the proposed
learning-control algorithm, LNMS, gains computational advantage over MIP at
little cost and is straightforward for practitioners to implement
Continuous-time Proportional-Integral Distributed Optimization for Networked Systems
In this paper we explore the relationship between dual decomposition and the
consensus-based method for distributed optimization. The relationship is
developed by examining the similarities between the two approaches and their
relationship to gradient-based constrained optimization. By formulating each
algorithm in continuous-time, it is seen that both approaches use a gradient
method for optimization with one using a proportional control term and the
other using an integral control term to drive the system to the constraint set.
Therefore, a significant contribution of this paper is to combine these methods
to develop a continuous-time proportional-integral distributed optimization
method. Furthermore, we establish convergence using Lyapunov stability
techniques and utilizing properties from the network structure of the
multi-agent system.Comment: 23 Pages, submission to Journal of Control and Decision, under
review. Takes comments from previous review process into account. Reasons for
a continuous approach are given and minor technical details are remedied.
Largest revision is reformatting for the Journal of Control and Decisio
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