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

Error estimates for a tree structure algorithm solving finite horizon control problems

In the Dynamic Programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this approach suffers of the "curse of dimensionality" and this limitation has reduced its practical in real world applications. Here we analyze a dynamic programming algorithm based on a tree structure. The tree is built by the time discrete dynamics avoiding in this way the use of a fixed space grid which is the bottleneck for high-dimensional problems, this also drops the projection on the grid in the approximation of the value function. We present some error estimates for a first order approximation based on the tree-structure algorithm. Moreover, we analyze a pruning technique for the tree to reduce the complexity and minimize the computational effort. Finally, we present some numerical tests

Flux tubes in the SU(3) vacuum

We analyze the distribution of the chromoelectric field generated by a static quark-antiquark pair in the SU(3) vacuum. We find that the transverse profile of the flux tube resembles the dual version of the Abrikosov vortex field distribution and give an estimate of the London penetration length in the confined vacuum.Comment: 7 pages, 3 figures, poster contribution to the XXIX International Symposium on Lattice Field Theory, LATTICE 201

Reply to: "The Possible Role of Anti-methicillin-resistant Staphylococus Aureus Antimicrobial Agents in Spontaneous Bacterial Peritonitis"

Letter answering to a comment about an articl

Optimal scheduling and control for constrained multi-agent networked control systems

In this paper, we study optimal control and communication schedule co-design for multi-agent networked control systems, with assuming shared parallel communication channels and uncertain constrained linear time-invariant discrete-time systems. To that end, we specify the communication demand for each system using an associated robust control invariant set and reachability analysis. We use these communication demands and invariant sets to formulate tube-based model predictive control and offline/online communication schedule co-design problems. Since the scheduling part includes an infinite dimension integer problem, we propose heuristics to find suboptimal solutions that guarantee robust constraints satisfaction and recursive feasibility. The effectiveness of our approach is illustrated through numerical simulations

An Experimental Study on Developing a Cognitive Model for Human Reliability Analysis

Serious incidents that occur inside or caused by industrial plants represent a very critical issue. In this context, the human reliability analysis (HRA) is an important tool to assess human factors that influence human behaviour in disasters scenario. In fact, the reliability assessment of interaction between human-machine systems is an important factor that affects the overall performance and safety in industrial plants. However, even though HRA techniques have been available for decades, there is not a universal method/procedure to reduce human errors that affect human performance. This study aims to design a novel approach to investigate the relationship between human reliability and operator performance considering the dependence on the available time to make decisions