# Optimal Control

Monday, June 4, 2018 - 10:00am - 10:50am

Suzanne Lenhart (University of Tennessee)

Two examples with different optimal control techniques to choose management actions will be presented. One model is a PDE system representing Zika spreading across a state in Brazil; the control varying in space and time is a vaccination rate. Data from Brazil were used to estimate parameters. The second model represents a large scale forest fire. We incorporate the stochasticity of the time of a fire into our model and explore the trade-offs between prevention management spending and suppression spending.

Friday, May 11, 2018 - 10:00am - 10:50am

Bozenna Pasik-Duncan (University of Kansas)

Some control problems are explicitly solved for bilinear evolution equations where the noise is a Gauss-Volterra process. The Gauss-Volterra noise processes are obtained from the integral of a Brownian motion with a suitable kernel function. These noise processes include fractional Brownian motions with Hurst parameter from (1/2, 1), Liouville fractional Brownian motions with H from (1/2, 1(, and some multi fractional Brownian motions. The controls are chosen from the family of linear feedback gains.

Monday, March 14, 2016 - 11:30am - 12:00pm

Tyrone Duncan (University of Kansas)

Fractional Brownian motions (FBMs) denote a family of Gaussian processes indexed by the Hurst parameter H ∈ (0, 1) that can be empirically justified as models for noise in many physical systems. While this family includes Brownian motion (H = 1/2), the other Gaussian processes in this family are neither Markov nor semimartingales. Thus many of the traditional stochastic methods for the solution of control problems are not available.

Friday, March 18, 2016 - 9:00am - 9:30am

Ekkehard Sachs (Universität Trier)

In this talk we consider modern developments of the neoclassical growth model developed by Ramsey almost 90 years ago. One example is the extension to peer-to-peer banking, which leads to a vector optimization problem. Another aspect we consider is the extension of the model with a finite number of households which leads to an optimal control problem with partial differential equations including nonlocal effects. We give theoretical results obtained from optimal control and compare it to their economical interpretation supported by numerical results.

Wednesday, March 16, 2016 - 3:00pm - 3:30pm

Suzanne Lenhart (University of Tennessee)

We discuss an important ecological issue of population movement and its distribution in reaction to resources and to competition. We present the choices of directed movement through controlling the advective coefficients in a system of parabolic partial differential equations, modeling two competing species. We seek to maximize population levels while minimizing the cost of controls. In addition to presenting the optimal control analysis, different resource functions and corresponding directed movement choices are shown numerically.

Wednesday, March 16, 2016 - 11:00am - 11:30am

Mark Opmeer (University of Bath)

For discretizations of partial differential equations, the standard methods for numerically solving Lyapunov and Riccati equations (as for example implemented in matlab) are usually not suitable since the computational effort and storage requirements are too high. Analysis of the underlying partial differential equation shows that often good low rank approximations to the exact solution of the Lyapunov or Riccati equation exist. Such low rank approximations are cheap to store and can often be efficiently computed.

Monday, March 14, 2016 - 4:30pm - 5:00pm

Omar Ghattas (The University of Texas at Austin)

We present methods for the optimal control of systems governed by partial differential equations with an infinite-dimensional uncertain parameter field. We consider an objective function that involves the mean

Monday, March 14, 2016 - 3:00pm - 4:00pm

Matthias Heinkenschloss (Rice University)

Many science and engineering problems lead to optimization problems governed by partial differential equations (PDEs), and in many of these problems some of the problem data are not known exactly. I focus on a class of such optimization problems where the uncertain data are modeled by random variables or random fields, and where decision variables (controls/designs) are deterministic and have to be computed before the uncertainty is observed. It is important that the uncertainty in problem data is adequately incorporated into the formulation of the optimization problem.

Thursday, June 13, 2013 - 11:00am - 11:50am

Eugene Cliff (Virginia Polytechnic Institute and State University)

In most cases mathematical models for building thermal control assume that the state of the zone-air can be represented as a single temperature - the well-mixed hypothesis. In cases such as non-uniform solar loads, or buoyancy-driven cooling such models are problematic. In recent work we have developed data-driven approaches wherein results from CFD simulations are used to develop linear-time-invariant reduced-order models (ROM).

Wednesday, June 12, 2013 - 9:30am - 10:20am

Jim Braun (Purdue University)

Compared to other energy sectors (e.g., transportation, industrial), there are significant challenges in realizing energy efficiency improvements in buildings due to the structure of the marketplace and the fact that buildings are not mass produced. In particular, intelligent control and diagnostic strategies that can optimize operations have not been widely implemented in buildings because each system tends to be unique and the costs associated with developing and updating specialized software can be prohibitive.