Stochastic bioeconomic model of a lake system invasion and its optimal control

Bioeconomic problems inherit complexities of ecological, economic, and optimization problems. Stochasticity is an important component of ecological models, such as biological invasions or survival in small populations. The problem of optimal invasion management adds cost-benefit analysis of ecological processes, mechanisms of control, and optimal allocation of management resources in space and time. A common tool for such problems is stochastic dynamic programming (SDP). However, SDP has strong limitations on complexity of the problem.  We consider a stochastic model for the spread of an aquatic invader in a lake system.  We assume that the invader transport between the lakes can be controlled. Standard SDP approach allows us to solve the problem for at most 10-12 lakes.  We have developed a new technique, which is based upon neurodynamic programming.  It allows us to reformulate the optimal control task as a problem of data fitting and to obtain approximate but reasonable control policy for essentially bigger lake systems.  One of the advantages of this approach is that it can be considered as a model for a manager decision making on the basis of limited information.  The proposed method may be applicable in other complex problems of optimal management and control.