This paper is a sequel to the one in this same session which surveys recent results on the role of convexity in Hamilton-Jacobi theory. We describe here how value functions in optimal control can be represented as upper and lower envelopes involving so-called kernel functions. Particularly noteworthy is a lower envelope formula given in terms of the dualizing kernel, which is a value function i...

Example 6.2 For the second example, we consider the stabilized parameters μ = δ = 0.5. Table 2 shows that a first-order convergence is obtained for the control, which is well matched with the theoretical analysis. Figures 4, 5, and 6 show the approximate profiles of the control, the state, and the flux state, respectively, when the lowest order RT element is adopted for the approximation of the...

A survey of numerical methods for optimal control is given. The objective of the article is to describe the major methods that have been developed over the years for solving general optimal control problems. In particular, the two broad classes of indirect and direct methods are discussed, the main approaches that are used in each class are described, and an extensive list is provided to releva...

In this paper, we present a recovery type a posteriori error estimate and the superconvergence analysis for the finite element approximation of the distributed convex optimal control problems governed by integraldifferential equations. We provide the recovery type a posteriori error estimates for both the control and the state approximation, which is equivalent to the exact error generally. Und...

This paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices Yi of the form Yi ≤ Y i, where Y i is given. The contributions of this paper are a set of conditions that characterize global optimality, and an iterative algorithm for finding a solution to the optimality conditions. This iterative algorithm is...

We formulated a discrete time model in order to study optimal control strategies for single influenza outbreak. In our model, we divided the population into four classes: susceptible, infectious, treated, and recovered individuals. The total population was divided into subgroups according to activity or susceptibility levels. The goal was to determine how treatment doses should be distributed i...