Accelerating genetic optimization of nonlinear model predictive control by learning optimal search space size

TL;DR

This paper proposes accelerating the genetic optimization of NMPC by learning optimal search space size by trains a multivariate regression model to adaptively predict the best smallest size of the search space in every control cycle.

Abstract

Genetic algorithm (GA) is typically used to solve nonlinear model predictive control's optimization problem. However, the size of the search space in which the GA searches for the optimal control inputs is crucial for its applicability to fast-response systems. This paper proposes accelerating the genetic optimization of NMPC by learning optimal search space size. The approach trains a multivariate regression model to adaptively predict the best smallest size of the search space in every control cycle. The proposed approach reduces the GA's computational time, improves the chance of convergence to better control inputs, and provides a stable and feasible solution. The proposed approach was evaluated on three nonlinear systems and compared to four other evolutionary algorithms implemented in a processor-in-the-loop fashion. The results show that the proposed approach provides a 17-45\% reduction in computational time and increases the convergence rate by 35-47\%. The source code is available on GitHub.

Figures (13)

• Figure 1: Nonlinear model predictive control (NMPC) overall architecture. At each control cycle, NMPC estimates the optimal vector of system inputs $[\mathbf{u}^{T}_{c}, \dots, \mathbf{u}^{T}_{c + h - 1}]^{T}$ that satisfies a given set of constraints for a fixed horizon length of $h$ time steps. Only the first control input ($\mathbf{u}_{c}$) is applied to the system, and new system states ($\mathbf{\bar{x}}_{c+1}$) are produced, and this process is repeated in the next control cycle of NMPC.
• Figure 2: Illustration of using the genetic algorithm to solve the NMPC optimization problem. GA begins by initializing a population of candidate solutions, which are evaluated, and the best are selected. These selected solutions then undergo crossover and mutation to produce a new generation. The process repeats until a termination condition or convergence is reached.
• Figure 3: A Graphical representation of the search spaces of GA. In (a), we show a contour (A) that represents the search space that comes from the physical constraints of the system, and another contour (B) marked with dashed red lines represents the BSM. In (b), we show how the candidate control inputs solutions at the current cycle are obtained by time-shifting the previous cycle control inputs by one-time step and searching around it in the BSM region marked by dashed red lines.
• Figure 5: A box plot shows the relation between the values of $\{\mathcal{E}_{c}^{\max}\}$ sorted in 10 percentiles and their corresponding $\Delta_{c}^{\max}$ values. The $\Delta_{c}^{\max}$ increases as $\mathcal{E}_{c}^{\max}$ increases.
• Figure 6: Workflow of the proposed approach. The process begins with offline simulation, where a dataset is generated. Regression models are then trained on this dataset. In the runtime, the trained models predict the Best Smallest Margin (BSM), which is used for genetic algorithm optimization in NMPC.