Towards parallelizable sampling-based Nonlinear Model Predictive Control

This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use the sequence of predicted inputs from the previous time step as a warm start, and to iteratively update this sequence by changing its elements one by one, starting from the last predicted input and ending with the first predicted input. This strategy, which resembles the dynamic programming principle, allows for parallelization up to a certain level and yields a suboptimal nonlinear MPC algorithm with guaranteed recursive feasibility, stability and improved cost function at every iteration, which is suitable for real-time implementation. The complexity of the algorithm per each time step in the prediction horizon depends only on the horizon, the number of samples and parallel threads, and it is independent of the measured system state. Comparisons with the fmincon nonlinear optimization solver on benchmark examples indicate that as the simulation time progresses, the proposed algorithm converges rapidly to the "optimal" solution, even when using a small number of samples.Comment: 9 pages, 9 pictures, submitted to IFAC World Congress 201

Direct data-driven control of constrained linear parameter-varying systems: A hierarchical approach

In many nonlinear control problems, the plant can be accurately described by a linear model whose operating point depends on some measurable variables, called scheduling signals. When such a linear parameter-varying (LPV) model of the open-loop plant needs to be derived from a set of data, several issues arise in terms of parameterization, estimation, and validation of the model before designing the controller. Moreover, the way modeling errors affect the closed-loop performance is still largely unknown in the LPV context. In this paper, a direct data-driven control method is proposed to design LPV controllers directly from data without deriving a model of the plant. The main idea of the approach is to use a hierarchical control architecture, where the inner controller is designed to match a simple and a-priori specified closed-loop behavior. Then, an outer model predictive controller is synthesized to handle input/output constraints and to enhance the performance of the inner loop. The effectiveness of the approach is illustrated by means of a simulation and an experimental example. Practical implementation issues are also discussed.Comment: Preliminary version of the paper "Direct data-driven control of constrained systems" published in the IEEE Transactions on Control Systems Technolog

Sensitivity-based multistep MPC for embedded systems

In model predictive control (MPC), an optimization problem is solved every sampling instant to determine an optimal control for a physical system. We aim to accelerate this procedure for fast systems applications and address the challenge of implementing the resulting MPC scheme on an embedded system with limited computing power. We present the sensitivity-based multistep MPC, a strategy which considerably reduces the computing requirements in terms of floating point operations (FLOPs), compared to a standard MPC formulation, while fulfilling closed- loop performance expectations. We illustrate by applying the method to a DC-DC converter model and show how a designer can optimally trade off closed-loop performance considerations with computing requirements in order to fit the controller into a resource-constrained embedded system

A Real-time Nonlinear Model Predictive Controller for Yaw Motion Optimization of Distributed Drive Electric Vehicles

This paper proposes a real-time nonlinear model predictive control (NMPC) strategy for direct yaw moment control (DYC) of distributed drive electric vehicles (DDEVs). The NMPC strategy is based on a control-oriented model built by integrating a single track vehicle model with the Magic Formula (MF) tire model. To mitigate the NMPC computational cost, the continuation/generalized minimal residual (C/GMRES) algorithm is employed and modified for real-time optimization. Since the traditional C/GMRES algorithm cannot directly solve the inequality constraint problem, the external penalty method is introduced to transform inequality constraints into an equivalently unconstrained optimization problem. Based on the Pontryagin’s minimum principle (PMP), the existence and uniqueness for solution of the proposed C/GMRES algorithm are proven. Additionally, to achieve fast initialization in C/GMRES algorithm, the varying predictive duration is adopted so that the analytic expressions of optimally initial solutions in C/GMRES algorithm can be derived and gained. A Karush-Kuhn-Tucker (KKT) condition based control allocation method distributes the desired traction and yaw moment among four independent motors. Numerical simulations are carried out by combining CarSim and Matlab/Simulink to evaluate the effectiveness of the proposed strategy. Results demonstrate that the real-time NMPC strategy can achieve superior vehicle stability performance, guarantee the given safety constraints, and significantly reduce the computational efforts

Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For discrete time nonlinear systems satisfying an exponential or finite time controllability assumption, we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints. Based on our formula, we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

Integrated Dynamic Facade Control with an Agent-based Architecture for Commercial Buildings

Dynamic façades have significant technical potential to minimize heating, cooling, and lighting energy use and peak electric demand in the perimeter zone of commercial buildings, but the performance of these systems is reliant on being able to balance complex trade-offs between solar control, daylight admission, comfort, and view over the life of the installation. As the context for controllable energy-efficiency technologies grows more complex with the increased use of intermittent renewable energy resources on the grid, it has become increasingly important to look ahead towards more advanced approaches to integrated systems control in order to achieve optimum life-cycle performance at a lower cost. This study examines the feasibility of a model predictive control system for low-cost autonomous dynamic façades. A system architecture designed around lightweight, simple agents is proposed. The architecture accommodates whole building and grid level demands through its modular, hierarchical approach. Automatically-generated models for computing window heat gains, daylight illuminance, and discomfort glare are described. The open source Modelica and JModelica software tools were used to determine the optimum state of control given inputs of window heat gains and lighting loads for a 24-hour optimization horizon. Penalty functions for glare and view/ daylight quality were implemented as constraints. The control system was tested on a low-power controller (1.4 GHz single core with 2 GB of RAM) to evaluate feasibility. The target platform is a low-cost ($35/unit) embedded controller with 1.2 GHz dual-core cpu and 1 GB of RAM. Configuration and commissioning of the curtainwall unit was designed to be largely plug and play with minimal inputs required by the manufacturer through a web-based user interface. An example application was used to demonstrate optimal control of a three-zone electrochromic window for a south-facing zone. The overall approach was deemed to be promising. Further engineering is required to enable scalable, turnkey solutions