1,195 research outputs found
Successive Convexification of Non-Convex Optimal Control Problems and Its Convergence Properties
This paper presents an algorithm to solve non-convex optimal control
problems, where non-convexity can arise from nonlinear dynamics, and non-convex
state and control constraints. This paper assumes that the state and control
constraints are already convex or convexified, the proposed algorithm
convexifies the nonlinear dynamics, via a linearization, in a successive
manner. Thus at each succession, a convex optimal control subproblem is solved.
Since the dynamics are linearized and other constraints are convex, after a
discretization, the subproblem can be expressed as a finite dimensional convex
programming subproblem. Since convex optimization problems can be solved very
efficiently, especially with custom solvers, this subproblem can be solved in
time-critical applications, such as real-time path planning for autonomous
vehicles. Several safe-guarding techniques are incorporated into the algorithm,
namely virtual control and trust regions, which add another layer of
algorithmic robustness. A convergence analysis is presented in continuous- time
setting. By doing so, our convergence results will be independent from any
numerical schemes used for discretization. Numerical simulations are performed
for an illustrative trajectory optimization example.Comment: Updates: corrected wordings for LICQ. This is the full version. A
brief version of this paper is published in 2016 IEEE 55th Conference on
Decision and Control (CDC). http://ieeexplore.ieee.org/document/7798816
Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Coupled problems with various combinations of multiple physics, scales, and
domains are found in numerous areas of science and engineering. A key challenge
in the formulation and implementation of corresponding coupled numerical models
is to facilitate the communication of information across physics, scale, and
domain interfaces, as well as between the iterations of solvers used for
response computations. In a probabilistic context, any information that is to
be communicated between subproblems or iterations should be characterized by an
appropriate probabilistic representation. Although the number of sources of
uncertainty can be expected to be large in most coupled problems, our
contention is that exchanged probabilistic information often resides in a
considerably lower dimensional space than the sources themselves. In this work,
we thus use a dimension-reduction technique for obtaining the representation of
the exchanged information. The main subject of this work is the investigation
of a measure-transformation technique that allows implementations to exploit
this dimension reduction to achieve computational gains. The effectiveness of
the proposed dimension-reduction and measure-transformation methodology is
demonstrated through a multiphysics problem relevant to nuclear engineering
Graphical Models for Optimal Power Flow
Optimal power flow (OPF) is the central optimization problem in electric
power grids. Although solved routinely in the course of power grid operations,
it is known to be strongly NP-hard in general, and weakly NP-hard over tree
networks. In this paper, we formulate the optimal power flow problem over tree
networks as an inference problem over a tree-structured graphical model where
the nodal variables are low-dimensional vectors. We adapt the standard dynamic
programming algorithm for inference over a tree-structured graphical model to
the OPF problem. Combining this with an interval discretization of the nodal
variables, we develop an approximation algorithm for the OPF problem. Further,
we use techniques from constraint programming (CP) to perform interval
computations and adaptive bound propagation to obtain practically efficient
algorithms. Compared to previous algorithms that solve OPF with optimality
guarantees using convex relaxations, our approach is able to work for arbitrary
distribution networks and handle mixed-integer optimization problems. Further,
it can be implemented in a distributed message-passing fashion that is scalable
and is suitable for "smart grid" applications like control of distributed
energy resources. We evaluate our technique numerically on several benchmark
networks and show that practical OPF problems can be solved effectively using
this approach.Comment: To appear in Proceedings of the 22nd International Conference on
Principles and Practice of Constraint Programming (CP 2016
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