Nonlinear Approximative Explicit Model Predictive Control Through Neural Networks : Characterizing Architectures and Training Behavior
Sammanfattning: Model predictive control (MPC) is a paradigm within automatic control notable for its ability to handle constraints. This ability come at the cost of high computational demand, which until recently has limited use of MPC to slow systems. Recent advances have however enabled MPC to be used in embedded applications, where its ability to handle constraints can be leveraged to reduce wear, increase efficiency and improve overall performance in everything from cars to wind turbines. MPC controllers can be made even faster by precomputing the resulting policy and storing it in a lookup table. A method known as explicit MPC. An alternative way of leveraging precomputation is to train a neural network to approximate the policy. This is an attractive proposal both due to neural networks ability to imitate policies for nonlinear systems, and results that indicate that neural networks can efficiently represent explicit MPC policies. Limited work has been done in this area. How the networks are setup and trained therefore tends to reflect recent trends in other application areas rather than being based on what is known to work well for approximating MPC policies. This thesis attempts to alleviate this situation by evaluating how some common neural network architectures and training methods performs when used for this purpose. The evaluations are carried out through a literature study and by training several networks with different architectures to replicate the policy of a nonlinear MPC controller tasked with stabilizing an inverted pendulum. The results suggest that ReLU activation functions give better performance than hyperbolic tangent and SELU functions; and that dropout and batch normalization degrades the ability to approximate policies; and that depth significantly increases the performance. However, the neural network controllers do occasionally exhibit problematic behaviors, such as steady state errors and oscillating control signals close to constraints.
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