A systematic method for bandwidth parameter selection is desired for Thomson multitaper spectrum estimation. We give a method for determining the optimal bandwidth based on a mean squared error (MSE) criterion. When the true spectrum has a second-order Taylor series expansion, one can express quadratic local bias as a function of the curvature of the spectrum, that can be estimated by using a simple spline approximation. This is combined with a variance estimate, obtained by jackknifing over individual spectrum estimates, to produce an estimated MSE for the log spectrum estimate for each choice of time-bandwidth product. The bandwidth that minimizes the estimated MSE then gives the desired spectrum estimate. Additionally, the bandwidth obtained by using our method is also optimal for cepstrum estimates. We give an example of a damped oscillatory (Lorentzian) process in which the approximate optimal bandwidth can be written as a function of the damping parameter. The true optimal bandwidth agrees well with that given by minimizing estimated the MSE in these examples.

We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious computational difficulties as the number of scenarios becomes large and the complexity of the system and planning horizons increase, necessitating the use of parallel computing. Our novel hybrid parallel implementation PIPS is based on interior-point methods and uses a Schur complement technique to obtain a scenario-based decomposition of the linear algebra. PIPS is applied to a stochastic economic dispatch problem that uses hourly wind forecasts and a detailed physical power flow model. Solving this problem is necessary for efficient integration of wind power with the Illinois power grid and real-time energy market. Strong scaling efficiency of 96% is obtained on 32 racks (131,072 cores) of the "Intrepid" Blue Gene/P system at Argonne National Laboratory.

This paper studies optimal control of multiple robot systems with frictional contact. The task is to move the robots into goal regions with specified velocities using external control forces. The robots have nonlinear dynamics, which may arise from the robot body dynamics, friction between robot and environment, and friction between robot and robot. Nonpenetration constraints between robots are imposed, and the robots are assumed rigid. The problem is modeled as a mathematical program with complementarity constraints (MPCC). The MPCC model is solved by using its elastic mode, which is a well-behaved nonlinear programming problem. Preliminary results with this approach are illustrated on example problems. The main contributions of this paper are a novel optimal control model that can deal with friction in the multiple robot system, and application of a new mathematical programming algorithm to solve the MPCC formulation. This optimal control model has potential applications in robot systems with friction, such as multifinger manipulation, manipulation with ropes, and multirobot pushing coordination.

We present a fixed time-step algorithm for the simulation of multi-rigid-body dynamics with joints, contact, collision, and friction. The method solves a linear complementarity problem (LCP) at each step. We show that the algorithm can be obtained as the stiff limit of fixed time-step schemes applied to regularized contact models. We do not perform collision detection. Instead, a noninterpenetration constraint is replaced by its linearization, which, together with a judicious choice of the active constraints, guarantees geometrical constraint stabilization without the need to perform a reduction of the time step to detect new collision or stick-slip transition events. Partially elastic collisions are accommodated by a suitable modification of the free term of the LCP.

The design of a M-band FIR paraunitary filter bank adapted to input signal statistics is considered. The adaptation criterion is energy compaction. A simple, efficient technique for computing globally optimal filter banks of arbitrary, finite degree is presented.