Sampling based control of a combustion process using a neural network model

An important application of neural networks is the identification of the dynamics of a nonlinear system with no known closed-form model, especially a system whose dynamic behavior may change with time. When this is done quickly and robustly, the model may be used for closed-loop Nonlinear Model Predictive Control (NMPC). NMPC methods that rely on linearization about an equilibrium point or excessive parameter tuning require a priori information that limits the robustness of those methods for a system with changing dynamic behavior. This paper presents a novel method for adaptive NMPC of multiple input, multiple output (MIMO) systems, called Sampling Based Model Predictive Control (SBMPC) that, like most MPC approaches, has the ability to enforce hard constraints on the system inputs and states. However, unlike other NMPC methods, it does not rely on linearizing the system or gradient based optimization. Instead, it discretizes the input space to the model via pseudo-random sampling and feeds the sampled inputs through the nonlinear plant, hence producing a graph for which an optimal path can be found using an efficient graph search method such as A* optimization. Although SBMPC can be applied to any form of a nonlinear model, here a radial basis function neural network is used to model the nonlinear system due to its ability to represent a very general class of nonlinear systems. Using the Minimal Resource Allocation Network (MRAN) learning algorithm, the neural network size and parameter values may be adjusted even while the controller is active. After presenting the general methodology, Adaptive SBMPC is used in simulation to control the chemical concentrations of flue gas exiting a steam boiler´s combustion chamber, represented by a 3-state time-varying nonlinear model with two inputs and three outputs.