Abstract
Optimal control problems for nonlinear systems are generally difficult to study. Closed-form solutions are often limited to linear systems and quadratic performance indices. This paper proposes a numerical approach to solve nonlinear optimal control problems using Bellman's principle of optimality in discrete time and space. The approach is based on Simple Cell Mapping (SCM), a numerical procedure to approximately describe nonlinear state-space dynamics. The paper discusses the construction of a general control database and performance index database along with a backward search algorithm to formulate optimal control policy. The cell space dynamic programming methodology is investigated on a nonlinear CSTR model. Numerical studies dealing with the influence of space and time discretization on computational feasibility are presented
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