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In this work we illustrate how approximate dynamic programing can be utilized to address problems of stochastic reachability in infinite state and control spaces. In particular we focus on the reach-avoid problem and approximate the value function on a linear combination of radial basis functions. In this way we get significant computational advantages with which we obtain tractable solutions to problems...
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...
A model predictive control law is given by the solution to a parametric optimization problem that can be pre-computed offline and provides an explicit map from state to control input. In this paper, an algorithm is introduced based on wavelet multiresolution analysis that returns a low complexity explicit model predictive control law built on a hierarchy of second-order interpolets. The resulting...
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