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This paper proposes a Genetic Programming based algorithm that can be used to design optimal controllers. The proposed algorithm will be named a Multiple Basis Function Genetic Programming (MBFGP). Herein, the main ideas concerning the initial population, the tree structure, genetic operations, and other proposed non-genetic operations are discussed in details. An optimization algorithm called numeric constant mutation is embedded to strengthen the search for the optimal solutions. The results of solving the optimal control for linear as well as nonlinear systems show the feasibility and effectiveness of the proposed MBFGP as compared to the optimal solutions which are based on numerical methods. Furthermore, this algorithm enriches the set of suboptimal state feedback controllers to include controllers that have product time-state terms.
In this work, a nonlinear model predictive
controller is developed for a batch polymerization process. The physical model
of the process is parameterized along a desired trajectory resulting in a
trajectory linearized piecewise model (a multiple linear model bank) and the
parameters are identified for an experimental polymerization reactor. Then, a multiple
model adaptive predictive controller is designed for thermal trajectory
tracking of the MMA polymerization. The input control signal to the process is
constrained by the maximum thermal power provided by the heaters. The
constrained optimization in the model predictive controller is solved via genetic
algorithms to minimize a DMC cost function in each sampling interval.