Keywords: Optimization and Model Predictive Control
Abstract: We accelerate nonlinear model predictive control with an approach that successively detects and removes inactive constraints from the optimal control problem. In every time step and for every constraint, the cost function value is compared to a bound that can be calculated offline. If the current cost function value drops below one of these bounds, the corresponding constraint can be removed. We show how to extend this constraint removal method, which was originally developed for linear MPC, to the nonlinear case. While nonlinear MPC generally results in nonconvex optimal control problems that are much more difficult to solve than their convex linear counterparts, the added complexity of the nonlinear case only affects the offline part of the proposed method. Since the offline calculations only need to be carried out in a preparatory step, their complexity is not restrictive.

Keywords: Optimization and Model Predictive Control, Dedicated Optimization Solvers for Model Predictive Control
Abstract: The use of derivative-based solvers to compute solutions to optimal control problems with non-differentiable cost or dynamics often requires reformulations or relaxations that complicate the implementation or increase computational complexity. We present an initial framework for using the derivative-free Mesh Adaptive Direct Search (MADS) algorithm to solve Nonlinear Model Predictive Control problems with non-differentiable features without the need for reformulation. The MADS algorithm performs a structured search of the input space by simulating selected system trajectories and computing the subsequent cost value. We propose handling the path constraints and the Lagrange cost term by augmenting the system dynamics with additional states to compute the violation and cost value alongside the state trajectories, eliminating the need for reconstructing the state trajectories in a separate phase. We demonstrate the practicality of this framework by solving a robust rocket control problem, where the objective is to reach a target altitude as close as possible, given a system with uncertain parameters. This example uses a non-differentiable cost function and simulates two different system trajectories simultaneously, with each system having its own free final time.

Keywords: Optimization and Model Predictive Control, Explicit Model Predictive Control, Dedicated Optimization Solvers for Model Predictive Control
Abstract: We show that exact solutions to nonlinear MPC problems for a special class of bilinear systems can be obtained by solving a finite number of convex linear MPC problems. The underlying reformulation is realized through exact state linearization and supported by special biquadratic stage costs. While such stage costs are unusual, we show that they preserve beneficial properties such as positive definiteness and that they allow for meaningful tuning. We further show that the proposed reformulation reveals some interesting insights on the structure of the optimal control law and we illustrate our approach with a numerical example.

Keywords: Optimization and Model Predictive Control, IoT/IoE
Abstract: We use nonlinear model predictive control to procure a joint control of mobility and transmission to minimize total network communication energy use. The nonlinear optimization problem is solved numerically in a self-triggered framework, where the next control update time depends on the predicted state trajectory and the accuracy of the numerical solution. Solution accuracy must be accounted for in any circumstance where systems are run in open-loop for long stretches of time based on potentially inaccurate predictions. These triggering conditions allow us to place wireless nodes in low energy `idle' states for extended periods, saving over 70% of energy compared to a periodic policy where nodes consistently use energy to receive control updates.

Keywords: Real-Time Implementation of Model Predictive Control, Optimization and Model Predictive Control, Stability and Recursive Feasibility
Abstract: Nonlinear Model Predictive Control (NMPC) formulations through quasi-Linear Parameter Varying (qLPV) embeddings have been brought to focus in recent literature. The qLPV realisation of the nonlinear dynamics yields linear predictions at each sampling instant. Thereby, these strategies generate online programs with reduced numerical burden, much faster to solve than the Nonlinear Programs generated with “regular” NMPC. The general lines of these methods: (i) The qLPV embedding is formulated with state-dependent scheduling parameters; (ii) Recursive extrapolation procedures are used to estimate the values of these parameters along the prediction horizon; (iii) These estimates are used to compute linear predictions, which are incorporated by the constrained optimisation procedure. This paper details the overall concept of these novel NMPC techniques and reviews two different (efficient) implementation options. Realistic academic examples are provided to illustrate their performances.

Keywords: Economic Predictive Control, Learning and Predictive Control
Abstract: In the Economic Nonlinear Model Predictive (ENMPC) context, closed-loop stability relates to the existence of a storage function satisfying a dissipation inequality. Finding the storage function is in general-- for nonlinear dynamics and cost-- challenging, and has attracted attentions recently. Q-Learning is a well-known Reinforcement Learning (RL) techniques that attempts to capture action-value functions based on the state-input transitions and stage cost of the system. In this paper, we present the use of the Q-Learning approach to obtain the storage function and verify the dissipativity for discrete-time systems subject to state-input constraints. We show that undiscounted Q-learning is able to capture the storage function for dissipative problems when the parameterization is rich enough. The efficiency of the proposed method will be illustrated in the different case studies.

Keywords: Learning and Predictive Control
Abstract: Model predictive control (MPC) is a powerful trajectory optimization control technique capable of controlling complex nonlinear systems while respecting system constraints and ensuring safe operation. The MPC’s capabilities come at the cost of a high online computational complexity, the requirement of an accurate model of the system dynamics, and the necessity of tuning its parameters to the specific control application. The main tunable parameter affecting the computational complexity is the prediction horizon length, controlling how far into the future the MPC predicts the system response and thus evaluates the optimality of its computed trajectory. A longer horizon generally increases the control performance, but requires an increasingly powerful computing platform, excluding certain control applications.The performance sensitivity to the prediction horizon length varies over the state space, and this motivated adaptive horizon model predictive control (AHMPC), which adapts the prediction horizon according to some criteria. In this paper we propose to learn the optimal prediction horizon as a function of the state using reinforcement learning (RL). We show how the RL learning problem can be formulated and test our method on two control tasks — showing clear improvements over the fixed horizon MPC scheme — while requiring only minutes of learning.

Keywords: Learning and Predictive Control, Biological Systems, Optimization and Model Predictive Control
Abstract: Many processes operate repetitively, for example batch processes in biotechnologyor chemical engineering. We propose a method for risk-aware run-to-run optimization andmodel predictive control of repetitive processes with uncertain models. The goal is to increasethe performance as the number of runs increases by improving the model despite limitedmeasurements while considering model uncertainty and avoiding uncertain areas. The methoduses a gray-box model, i.e. a model formed by a first principle and a machine learning component,in this case an artificial neural network. The model uncertainty might be large, particularlyin the first runs, where only a few measurements are available. We propose to quantify thisuncertainty using Bayesian inference. This is in turn reflected by a risk measure entering anopen-loop optimal control problem and a shrinking-horizon Model Predictive Controller as aconstraint to limit control and exploitation in high risk areas. We show that using this riskmeasure we are able to efficiently reach high process performance. The proposed method istested in simulations on two biotechnological fed-batch processes.

Keywords: Tracking and Path Following Predictive Control, Learning and Predictive Control, Motion Control
Abstract: Often, systems need to adapt their behavior to other systems in their surroundings while obeying constraints to achieve good performance or due to safety reasons. We consider repetitive applications, where the reference for the controller stems from noisy sensor data. Including preview information of the reference, e.g. extrapolating from previous cycles or similar instances, can significantly improve the overall tracking performance and ensure constraint satisfaction. We propose a learning-supported predictive controller that uses Gaussian processes as reference generators for its control task. A Gaussian process is used to learn, filter, and predict the references. It learns references tailored to model predictive control, taking into account continuous-time system dynamics and constraints via constrained hyperparameter optimization. We illustrate the benefits concerning approximation and control performance of the informed Gaussian-process training by a cooperative, mobile robot example.

Keywords: Automotive, Optimization and Model Predictive Control, Robust Model Predictive Control
Abstract: This paper proposes a Model Predictive Control (MPC) design method for the intake manifold pressure of an internal combustion engine. This controller uses a nominal nonlinear model of the physical system to optimize a cost function. The noise sensibility of MPC is reduced and the robustness of the state estimation is achieved by using an Extended Kalman Filter (EKF). The proposed approach is evaluated using the Matlab Simulink model of the intake manifold of a spark ignition combustion engine in which parametric uncertainties and saturation are added. Different settings for EKF and MPC are tested for comparison purposes.

Keywords: Automotive, Optimization and Model Predictive Control, Tracking and Path Following Predictive Control
Abstract: This paper deals with the analysis and design of motion cueing algorithms which can be formulated in terms of constrained control problems. Automotive manufacturers using driving simulation for ADAS development need to design their controllers, called Motion Cueing Algorithms (MCA), in order to render the expected feelings to the subjects. Ultimately, the goal is to bring the virtual driving environment to the realism of the driving scenes. Our contribution in the present work is focused on the development of two nonlinear MPC schemes that include the inherent physical constraints but consider also the real-time requirements. The first one privileges the lateral linear movement of the platform while the other focuses on the nonlinear rotational part. The paper summarizes this line of development with a horizon-based design of MCA using the trade-off between computational effort and tracking performance.

Keywords: Learning and Predictive Control, Robust Model Predictive Control, Stability and Recursive Feasibility
Abstract: Model predictive control requires the real-time solution of an optimal control problem, which can be challenging on computationally limited systems. Approximating the solution such as by neural networks or series expansions, or deriving an explicit solution, can overcome this challenge. Using neural networks for approximation, a question arises as to how to guarantee closed-loop safety and stability. We use robust control theoretic tools to provide stability guarantees using a neural network trained to approximate a model predictive controller. Notably, the model predictive controller, which might offer desirable closed-loop performance, is not required to provide provable stability properties. To provide stability guarantees for the neural network approximated controller, the closed-loop system is reformulated as a diagonal nonlinear differential form, exploiting that the neural network activation functions are sector bounded and that their slopes are globally bounded. Based on this representation, we establish sufficient closed-loop stability conditions in form of linear matrix inequalities for the nominal and the disturbed system using the neural network approximated model predictive controller.

Keywords: Optimization and Model Predictive Control, Hybrid Model Predictive Control, Automotive
Abstract: Cells within the same battery pack age unequally fast due to the non-uniform manufacturing process, and inhomogeneous operating conditions, and environment. This paper proposes a nonlinear Model Predictive Control approach for optimal pack balancing while taking pack and cell limitations into account. The control is designed for a sophisticated battery pack, which is a pack augmented by semiconductor switches to vary the number of cells connected in series. This pack is usually composed of more cells than a conventional battery pack. Each serial cell in the pack can be activated or deactivated while keeping the serial connection. Simulation results based on a realistic mission profile illustrate the effectiveness of the proposed approach by optimizing the overall performance and degradation of the battery architecture.

Keywords: Real-Time Implementation of Model Predictive Control, Automotive, Tracking and Path Following Predictive Control
Abstract: This paper presents a real-time capable nonlinear model predictive control (NMPC) strategy to effectively control the driving performance of an electric vehicle (EV) while optimizing thermal utilization. The prediction model is based on an experimentally validated two-node lumped parameter thermal network (LPTN) and one-dimensional driving dynamics. An efficient solver for the trajectory tracking problem is exported using acados and deployed on a dSPACE SCALEXIO embedded system. The lap time of a high-load driving cycle compared to a state-of-the-art derating strategy improved by 2.56% with an energy consumption reduction of 2.43% while respecting the temperature constraints of the electric drive.

Keywords: Optimization and Model Predictive Control

Keywords: Optimization and Model Predictive Control

Keywords: Learning and Predictive Control, Stability and Recursive Feasibility
Abstract: We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered class of systems, we show how to use historical trajectory data collected during iterative tasks to construct a convex value function approximation along with a convex safe set in a lifted space of virtual outputs. These constructions are iteratively updated with historical data and used to synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on the kinematic unicycle.

Keywords: Automotive, Optimization and Model Predictive Control