A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme

A Natural Value Unit - Econophysics as Arbiter between Finance and Economics

Foreign exchange markets show that currency units (= accounting or nominal price units) are variables. Technical and economic progress evidence that the consumer baskets (= purchasing power units or real price units) are also variables. In contrast, all physical measurement units are constants and either defined in the SI (= metric) convention or based upon natural constants (= "natural" or Planck units). Econophysics can identify a constant natural value scale or vaue unit (natural numaraire) based upon Planck energy. In honour of the economist L. Walras, this "Planck value" could be called walras (Wal), thereby using the SI naming convention. One Wal can be shown to have a physiological and an economic interpretation in that it is equal to the annual minimal real cost of physiological life of a reference person at minimal activity. The price of one Wal in terms of any currency can be estimated by hedonic regression techniques used in inflation measurement (axiometry). This pilot research uses official disaggregated Swiss Producer and Consumer Price Index data and estimates the hedonic walras price (HWP), quoted in Swiss francs in 2003, and its inverse, the physical purchasing power (PhPP) of the Swiss franc in 2003.Comment: 19 pages, 1 table, Appendix with 2 tables, RevTex4, APFA5 200

Achieving an optimal trade-off between revenue and energy peak within a smart grid environment

We consider an energy provider whose goal is to simultaneously set revenue-maximizing prices and meet a peak load constraint. In our bilevel setting, the provider acts as a leader (upper level) that takes into account a smart grid (lower level) that minimizes the sum of users' disutilities. The latter bases its decisions on the hourly prices set by the leader, as well as the schedule preferences set by the users for each task. Considering both the monopolistic and competitive situations, we illustrate numerically the validity of the approach, which achieves an 'optimal' trade-off between three objectives: revenue, user cost, and peak demand