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p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at thenumerical solution of optimal control (OC) problems with an infinite timehorizon for parabolic systems of PDE over 1D or 2D spatial domains. The basicidea is to treat the OC problem via the associated canonical system in twosteps. First we use pde2path to find branches of stationary solutions of thecanonical system, also called canonical steady states (CSS). In a second stepwe use the results and the spatial discretization of the first step tocalculate the objective values of time-dependent canonical paths ending at aCSS with the so called saddle point property. This is a (typically very highdimensional) boundary value problem (BVP) in time, which we solve by combininga modification of the BVP solver TOM with a continuation algorithm in theinitial states. We explain the design and usage of the package via two exampleproblems, namely the optimal management of a distributed shallow lake model,and of a semi-arid grazing system. Both show interesting bifurcations of socalled patterned CSS, and in particular the latter also a variety of patternedoptimal steady states. The package (library and demos) can be downloaded atwww.staff.uni-oldenburg.de/hannes.uecker/pde2path.

The pde2path add-on toolbox p2pOC for solving infinite time-horizon spatially distributed optimal control problems - Quickstart Guide -