57,625 research outputs found
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
Algorithmic design of self-assembling structures
We study inverse statistical mechanics: how can one design a potential
function so as to produce a specified ground state? In this paper, we show that
unexpectedly simple potential functions suffice for certain symmetrical
configurations, and we apply techniques from coding and information theory to
provide mathematical proof that the ground state has been achieved. These
potential functions are required to be decreasing and convex, which rules out
the use of potential wells. Furthermore, we give an algorithm for constructing
a potential function with a desired ground state.Comment: 8 pages, 5 figure
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