Abstract
Model Predictive Control (MPC) algorithms typically use the classical L cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function; (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L norm even gives better performance than the classical L one in terms of the classical control performance indicator that measures squared control errors.
Highlights
In order to obtain a quadratic optimisation Model Predictive Control (MPC)-L1 optimisation problem, we take into account the general nonlinear MPC-L1 optimisation task defined by Equation (5) in which the first part of the minimised cost function is approximated by Equation (22)
Comparing the MPC algorithms with the norm L1, in which one trajectory linearisation and quadratic optimisation are executed at each sampling instant, the best results are obtained in the MPC-NPLT3-L1 scheme, in which the trajectory linearisation is performed using an inverse static model of the process
Thanks to using a neural differentiable approximator of the non-differentiable absolute value function and on-line advanced trajectory linearisation, computationally simple quadratic optimisation is used in place of demanding nonlinear optimisation
Summary
In Model Predictive Control (MPC), a dynamical model of the process is used online to repeatedly make predictions of the future values of the controlled variables and to optimise the current and future control policy [1,2]. In the presented approach, the classical MPC-L1 cost function is replaced by its differentiable representation Such a representation is obtained by means of the neural approximator. Quasi-linear neural models [48,49] In this approach, the dynamical model has the classical linear form, but its parameters depend on the operating point of the process and their values are determined on-line by neural networks. Neural networks may be utilised to accelerate and simplify on-line calculations in MPC: Neural inverse static models are used to try to cancel process nonlinearity. Such a method is frequently used when Wiener cascade models are considered [47,57].
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