120,134 research outputs found
Accuracy of Numerical Solution to Dynamic Programming Models
Dynamic programming models with continuous state and control variables are solved approximately using numerical methods in most applications. We develop a method for measuring the accuracy of numerical solution of stochastic dynamic programming models. Using this method, we compare the accuracy of various interpolation schemes. As expected, the results show that the accuracy improves as number of nodes is increased. Comparison of Chebyshev and linear spline indicates that the linear spline may give higher maximum absolute error than Chebyshev, however, the overall performance of spline interpolation is better than Chebyshev interpolation for non-smooth functions. Two-stage grid search method of optimization is developed and examined with accuracy analysis. The results show that this method is more efficient and accurate. Accuracy is also examined by allocating a different number of nodes for each dimension. The results show that a change in node configuration may yield a more efficient and accurate solution.Research Methods/ Statistical Methods,
Approximate Dynamic Programming via Sum of Squares Programming
We describe an approximate dynamic programming method for stochastic control
problems on infinite state and input spaces. The optimal value function is
approximated by a linear combination of basis functions with coefficients as
decision variables. By relaxing the Bellman equation to an inequality, one
obtains a linear program in the basis coefficients with an infinite set of
constraints. We show that a recently introduced method, which obtains convex
quadratic value function approximations, can be extended to higher order
polynomial approximations via sum of squares programming techniques. An
approximate value function can then be computed offline by solving a
semidefinite program, without having to sample the infinite constraint. The
policy is evaluated online by solving a polynomial optimization problem, which
also turns out to be convex in some cases. We experimentally validate the
method on an autonomous helicopter testbed using a 10-dimensional helicopter
model.Comment: 7 pages, 5 figures. Submitted to the 2013 European Control
Conference, Zurich, Switzerlan
Model predictive control techniques for hybrid systems
This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581
An Efficient Policy Iteration Algorithm for Dynamic Programming Equations
We present an accelerated algorithm for the solution of static
Hamilton-Jacobi-Bellman equations related to optimal control problems. Our
scheme is based on a classic policy iteration procedure, which is known to have
superlinear convergence in many relevant cases provided the initial guess is
sufficiently close to the solution. In many cases, this limitation degenerates
into a behavior similar to a value iteration method, with an increased
computation time. The new scheme circumvents this problem by combining the
advantages of both algorithms with an efficient coupling. The method starts
with a value iteration phase and then switches to a policy iteration procedure
when a certain error threshold is reached. A delicate point is to determine
this threshold in order to avoid cumbersome computation with the value
iteration and, at the same time, to be reasonably sure that the policy
iteration method will finally converge to the optimal solution. We analyze the
methods and efficient coupling in a number of examples in dimension two, three
and four illustrating its properties
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