971 research outputs found
Fast Optimal Energy Management with Engine On/Off Decisions for Plug-in Hybrid Electric Vehicles
In this paper we demonstrate a novel alternating direction method of
multipliers (ADMM) algorithm for the solution of the hybrid vehicle energy
management problem considering both power split and engine on/off decisions.
The solution of a convex relaxation of the problem is used to initialize the
optimization, which is necessarily nonconvex, and whilst only local convergence
can be guaranteed, it is demonstrated that the algorithm will terminate with
the optimal power split for the given engine switching sequence. The algorithm
is compared in simulation against a charge-depleting/charge-sustaining (CDCS)
strategy and dynamic programming (DP) using real world driver behaviour data,
and it is demonstrated that the algorithm achieves 90\% of the fuel savings
obtained using DP with a 3000-fold reduction in computational time
Strong Stationarity Conditions for Optimal Control of Hybrid Systems
We present necessary and sufficient optimality conditions for finite time
optimal control problems for a class of hybrid systems described by linear
complementarity models. Although these optimal control problems are difficult
in general due to the presence of complementarity constraints, we provide a set
of structural assumptions ensuring that the tangent cone of the constraints
possesses geometric regularity properties. These imply that the classical
Karush-Kuhn-Tucker conditions of nonlinear programming theory are both
necessary and sufficient for local optimality, which is not the case for
general mathematical programs with complementarity constraints. We also present
sufficient conditions for global optimality.
We proceed to show that the dynamics of every continuous piecewise affine
system can be written as the optimizer of a mathematical program which results
in a linear complementarity model satisfying our structural assumptions. Hence,
our stationarity results apply to a large class of hybrid systems with
piecewise affine dynamics. We present simulation results showing the
substantial benefits possible from using a nonlinear programming approach to
the optimal control problem with complementarity constraints instead of a more
traditional mixed-integer formulation.Comment: 30 pages, 4 figure
Global optimization for low-dimensional switching linear regression and bounded-error estimation
The paper provides global optimization algorithms for two particularly
difficult nonconvex problems raised by hybrid system identification: switching
linear regression and bounded-error estimation. While most works focus on local
optimization heuristics without global optimality guarantees or with guarantees
valid only under restrictive conditions, the proposed approach always yields a
solution with a certificate of global optimality. This approach relies on a
branch-and-bound strategy for which we devise lower bounds that can be
efficiently computed. In order to obtain scalable algorithms with respect to
the number of data, we directly optimize the model parameters in a continuous
optimization setting without involving integer variables. Numerical experiments
show that the proposed algorithms offer a higher accuracy than convex
relaxations with a reasonable computational burden for hybrid system
identification. In addition, we discuss how bounded-error estimation is related
to robust estimation in the presence of outliers and exact recovery under
sparse noise, for which we also obtain promising numerical results
Shortest Paths in Graphs of Convex Sets
Given a graph, the shortest-path problem requires finding a sequence of edges
with minimum cumulative length that connects a source to a target vertex. We
consider a generalization of this classical problem in which the position of
each vertex in the graph is a continuous decision variable, constrained to lie
in a corresponding convex set. The length of an edge is then defined as a
convex function of the positions of the vertices it connects. Problems of this
form arise naturally in road networks, robot navigation, and even optimal
control of hybrid dynamical systems. The price for such a wide applicability is
the complexity of this problem, which is easily seen to be NP-hard. Our main
contribution is a strong mixed-integer convex formulation based on perspective
functions. This formulation has a very tight convex relaxation and allows to
efficiently find globally-optimal paths in large graphs and in high-dimensional
spaces
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