Min–max MPC using a tractable QP problem

Min–max model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min–max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min–max problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper

Neural Networks for Fast Optimisation in Model Predictive Control: A Review

Model Predictive Control (MPC) is an optimal control algorithm with strong stability and robustness guarantees. Despite its popularity in robotics and industrial applications, the main challenge in deploying MPC is its high computation cost, stemming from the need to solve an optimisation problem at each control interval. There are several methods to reduce this cost. This survey focusses on approaches where a neural network is used to approximate an existing controller. Herein, relevant and unique neural approximation methods for linear, nonlinear, and robust MPC are presented and compared. Comparisons are based on the theoretical guarantees that are preserved, the factor by which the original controller is sped up, and the size of problem that a framework is applicable to. Research contributions include: a taxonomy that organises existing knowledge, a summary of literary gaps, discussion on promising research directions, and simple guidelines for choosing an approximation framework. The main conclusions are that (1) new benchmarking tools are needed to help prove the generalisability and scalability of approximation frameworks, (2) future breakthroughs most likely lie in the development of ties between control and learning, and (3) the potential and applicability of recently developed neural architectures and tools remains unexplored in this field.Comment: 34 pages, 6 figures 3 tables. Submitted to ACM Computing Survey

The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control

We introduce the Control Toolbox (CT), an open-source C++ library for efficient modeling, control, estimation, trajectory optimization and Model Predictive Control. The CT is applicable to a broad class of dynamic systems but features interfaces to modeling tools specifically designed for robotic applications. This paper outlines the general concept of the toolbox, its main building blocks, and highlights selected application examples. The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems. The CT was designed for intuitive modeling of systems governed by ordinary differential or difference equations. It supports rapid prototyping of cost functions and constraints and provides standard interfaces for different optimal control solvers. To date, we support Single Shooting, the iterative Linear-Quadratic Regulator, Gauss-Newton Multiple Shooting and classical Direct Multiple Shooting. We provide interfaces to general purpose NLP solvers and Riccati-based linear-quadratic optimal control solvers. The CT was designed to solve large-scale optimal control and estimation problems efficiently and allows for online control of dynamic systems. Some of the key features to enable fast run-time performance are full compatibility with Automatic Differentiation, derivative code generation, and multi-threading. Still, the CT is designed as a modular framework whose building blocks can also be used for other control and estimation applications such as inverse dynamics control, extended Kalman filters or kinematic planning

Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance

Fixed-point implementation of a proximal Newton method for embedded model predictive control (I)

Extending the success of model predictive control (MPC) technologies in embedded applications heavily depends on the capability of improving quadratic programming (QP) solvers. Improvements can be done in two directions: better algorithms that reduce the number of arithmetic operations required to compute a solution, and more efficient architectures in terms of speed, power consumption, memory occupancy and cost. This paper proposes a fixed point implementation of a proximal Newton method to solve optimization problems arising in input-constrained MPC. The main advantages of the algorithm are its fast asymptotic convergence rate and its relatively low computational cost per iteration since it the solution of a small linear system is required. A detailed analysis on the effects of quantization errors is presented, showing the robustness of the algorithm with respect to finite-precision computations. A hardware implementation with specific optimizations to minimize computation times and memory footprint is also described, demonstrating the viability of low-cost, low-power controllers for high-bandwidth MPC applications. The algorithm is shown to be very effective for embedded MPC applications through a number of simulation experiments

Integration of CasADi and JModelica.org

This paper presents the integration of two open source softwares: CasADi, which is a framework for efficient evaluation of expressions and their derivatives, and the Modelica-based platform JModelica.org. The integration of the tools is based on an XML format for exchange of DAE models. The JModelica.org platform supports export of model in this XML format, whereas CasADi supports import of models expressed in this format. Furthermore, we have carried out comparisons with ACADO, which is a multiple shooting package for solving optimal control problems. CasADi, in turn, has been interfaced with ACADO Toolkit, enabling users to define optimal control problems using Modelica and Optimica specifications, and use solve using direct multiple shooting. In addition, a collocation algorithm targeted at solving large- scale DAE constrained dynamic optimization problems has been implemented. This implementation explores CasADi’s Python and IPOPT interfaces, which offers a convenient, yet highly efficient environment for development of optimization algorithms. The algorithms are evaluated using industrially relevant benchmark problems