Open-loop regulation and tracking control based on a genealogical decision tree

Abstract

The goal of this paper is to design a new control algorithm for open-loop control of complex systems. This control approach is based on a genealogical decision tree for both regulation and tracking control problems. The idea behind this control strategy consists of associating Gaussian distributions to both the norms of the control actions and the tracking errors. This stochastic search model can be interpreted as a simple genetic particle evolution model with a natural birth and death interpretation. It converges on probability. A numerical example dealing with the control of a fluidized bed combustion power plant illustrates the feasibility and the performance of this control algorithm.

Process regulation via genealogical decision trees

“…124 E. IKONEN, E. GOMEZ-RAMIREZ AND K. NAJIM Convergence in probability can be shown, see [12] and references there for more details. The main idea is to translate the cost function as the likelihood of a conditional probability, which gives a duality between optimal regulation and optimal filtering.…”

“…given the initial state and the desired trajectory, a sequence of optimal control actions is computed so as to minimize the quadratic cost in the horizon of length T . Analysis of the scheme and a number of applications in chemical engineering and robotics have been reported [11][12][13]. Results indicate good performance of the optimization scheme.…”

“…A set of examples is reported in [13], including studies on a single link manipulator, a two-joint robot arm, and a three component batch CSTR plant, among others. A multi-input multi-output FBC plant was considered in [12], and GDT-based control of an FBC plant with additional SISO-PI feedback controls was considered in [14].…”

“…Recent results allow us to quantify with precision their ability to also solve any optimal control problems that can be interpreted in terms of a nonlinear filtering problem. Lately, GDTs have been introduced for solving open-loop regulation and tracking control problems [11,12].The GDT-based control approach is a random search technique for solving a sequential optimization problem. The algorithm is simple to implement, the number of design parameters is limited and the values of the parameters are easy to choose.…”

“…Recent results allow us to quantify with precision their ability to also solve any optimal control problems that can be interpreted in terms of a nonlinear filtering problem. Lately, GDTs have been introduced for solving open-loop regulation and tracking control problems [11,12].…”