53,657 research outputs found
Investigation on energetic optimization problems of stochastic thermodynamics with iterative dynamic programming
The energetic optimization problem, e.g., searching for the optimal switch-
ing protocol of certain system parameters to minimize the input work, has been
extensively studied by stochastic thermodynamics. In current work, we study
this problem numerically with iterative dynamic programming. The model systems
under investigation are toy actuators consisting of spring-linked beads with
loading force imposed on both ending beads. For the simplest case, i.e., a
one-spring actuator driven by tuning the stiffness of the spring, we compare
the optimal control protocol of the stiffness for both the overdamped and the
underdamped situations, and discuss how inertial effects alter the
irreversibility of the driven process and thus modify the optimal protocol.
Then, we study the systems with multiple degrees of freedom by constructing
oligomer actuators, in which the harmonic interaction between the two ending
beads is tuned externally. With the same rated output work, actuators of
different constructions demand different minimal input work, reflecting the
influence of the internal degrees of freedom on the performance of the
actuators.Comment: 14 pages, 7 figures, communications in computational physics, in
pres
Optimal transport over a linear dynamical system
We consider the problem of steering an initial probability density for the state vector of a linear system
to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator () this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schroedinger bridge. As the white noise intensity tends to zero, the flow of densities converges to that of the deterministic dynamics and can serve as a way to compute the solution of its deterministic counterpart. The solution can be expressed in closed-form for Gaussian initial and final state densities in both cases
Inverse stochastic optimal controls
We study an inverse problem of the stochastic optimal control of general
diffusions with performance index having the quadratic penalty term of the
control process. Under mild conditions on the drift, the volatility, the cost
functions of the state, and under the assumption that the optimal control
belongs to the interior of the control set, we show that our inverse problem is
well-posed using a stochastic maximum principle. Then, with the well-posedness,
we reduce the inverse problem to some root finding problem of the expectation
of a random variable involved with the value function, which has a unique
solution. Based on this result, we propose a numerical method for our inverse
problem by replacing the expectation above with arithmetic mean of observed
optimal control processes and the corresponding state processes. The recent
progress of numerical analyses of Hamilton-Jacobi-Bellman equations enables the
proposed method to be implementable for multi-dimensional cases. In particular,
with the help of the kernel-based collocation method for
Hamilton-Jacobi-Bellman equations, our method for the inverse problems still
works well even when an explicit form of the value function is unavailable.
Several numerical experiments show that the numerical method recover the
unknown weight parameter with high accuracy
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