Moritz Diehl

University of Freiburg | Albert-Ludwigs-Universität Freiburg · Department of Microsystems Engineering (IMTEK)

We present a novel optimization-based method for parameter estimation of a time-varying dynamic linear system. This method optimizes the likelihood of the parameters given measured data using an optimization algorithm tailored to the structure of this maximum likelihood estimation problem. Some parameters of the covariance of process and measuremen...

Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct optimal control methods is rare. Indeed, the standard approach is to perform a state augmentation, adding the vel...

In many industrial applications a workpiece is continuously fed through a heating zone in order to reach a desired temperature to obtain specific material properties. Many examples of such distributed parameter systems exist in heavy industry and also in furniture production such processes can be found. In this paper, a real-time capable model for...

Efficient integrators with sensitivity propagation are an essential ingredient for the numerical solution of optimal control problems. This paper gives an overview on the acados integrators, their Python interface and presents a workflow that allows using them with their sensitivities within a nonlinear programming (NLP) solver interfaced by CasADi...

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we propose a self-supervised learning a...

This paper presents a modeling approach of an industrial heating process where a stripe-shaped workpiece is heated up to a specific temperature by applying hot air through a nozzle. The workpiece is moving through the heating zone and is considered to be of infinite length. The speed of the substrate is varying over time. The derived model is suppo...

In this paper we propose a formulation for approximate constrained nonlinear output-feedback stochastic model predictive control. Starting from the ideal but intractable stochastic optimal control problem (OCP), which involves the optimization over output-dependent policies, we use linearization with respect to the uncertainty to derive a tractable...

The future utility-scale deployment of airborne wind energy technologies requires the development of large-scale multi-megawatt systems. This study aims at quantifying the interaction between the atmospheric boundary layer (ABL) and large-scale airborne wind energy systems operating in a farm. To that end, we present a virtual flight simulator comb...

This paper introduces Finite Elements with Switch Detection (FESD), a numerical discretization method for nonsmooth differential equations. We regard the Filippov convexification of these systems and a transformation into dynamic complementarity systems introduced by Stewart. FESD is based on solving of nonlinear complementarity problems and able t...

In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to time-optimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear constraints which arise in motion planning of mechatronic systems. The algorithm applies a trust-region globaliz...

We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of oscillations, we only simulate a subset to approximate the slow change by constructing a semi-explicit differe...

We present a formulation for both implicit and explicit dual model predictive control with chance constraints. The formulation is applicable to systems that are affine in the state and disturbances, but possibly nonlinear in the controls. Awareness of uncertainty and dual control effect is achieved by including the covariance of a Kalman Filter sta...

This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk smoothness, and which is restricted by constraints. The algorithm predicts a trajectory by solving a parameter...

This letter introduces the open source software package for Nonsmooth Numerical Optimal Control (NOS-NOC). It is a modular tool based on CasADi [Andersson et al., 2019], IPOPT [W\"achter and Biegler, 2006] and MATLAB, for numerically solving Optimal Control Problems (OCP) with piecewise smooth systems (PSS). It relies on the recently introduced Fin...

This article regards numerical optimal control of a class of hybrid systems with hysteresis using solely techniques from nonlinear optimization, without any integer variables. Hysteresis is a rate independent memory effect which often results in severe nonsmoothness in the dynamics. These systems are not simply Piecewise Smooth Systems (PSS); they...

The tunnel-following nonlinear model predictive control (NMPC) scheme allows to exploit acceptable deviations around a path reference. This is done by using convex-over-nonlinear functions as objective and constraints in the underlying optimal control problem (OCP). The convex-over-nonlinear structure is exploited by algorithms such as the generali...

We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of oscillations, we only simulate a subset to approximate the slow change by constructing a semi-explicit differe...

This letter introduces the NOnSmooth Numerical Optimal Control (NOSNOC) open-source software package. It is a modular MATLAB tool based on CasADi and IPOPT for numerically solving Optimal Control Problems (OCP) with piecewise smooth systems (PSS). The tool supports: 1) automatic reformulation of systems with state jumps into PSS (via the time-freez...

This letter regards numerical optimal control of a class of hybrid systems with hysteresis using solely techniques from nonlinear optimization, without any integer variables. Hysteresis is a rate independent memory effect which often results in severe nonsmoothness in the dynamics. These systems are not simply Piecewise Smooth Systems (PSS); they a...

Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained mechanical systems, i.e., those whose state coordinates are subject to holonomic or nonholonomic constraints,...

This paper introduces the quadratically-constrained quadratic programming (QCQP) framework recently added in HPIPM alongside the original quadratic-programming (QP) framework. The aim of the new framework is unchanged, namely providing the building blocks to efficiently and reliably solve (more general classes of) optimal control problems (OCP). Th...

In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is derived for the setting where a limited number of iterations of the optimizer are carried out per sampling tim...

The future utility-scale deployment of airborne wind energy technologies requires the development of large-scale multi-megawatt systems. This study aims at quantifying the interaction between the atmospheric boundary layer (ABL) and large-scale airborne wind energy systems operating in a farm. To that end, we present a virtual flight simulator comb...

This paper introduces a novel reformulation and numerical methods for optimal control of complementarity Lagrangian systems with state jumps. The solutions of the reformulated system have jump discontinuities in the first time derivative instead of the trajectory itself, which is easier to handle theoretically and numerically. We cover not only the...

This paper presents the acados software package, a collection of solvers for fast embedded optimization intended for fast embedded applications. Its interfaces to higher-level languages make it useful for quickly designing an optimization-based control algorithm by putting together different algorithmic components that can be readily connected and...

We provide an overview of a class of iterative convex approximation methods for nonlinear optimization problems with convex-over-nonlinear substructure. These problems are characterized by outer convexities on the one hand, and nonlinear, generally nonconvex, but differentiable functions on the other hand. All methods from this class use only first...

Moving Horizon Estimation (MHE) is an optimization-based approach to nonlinear state estimation where the state estimate is obtained as the solution of a nonlinear optimization problem. Especially for large-scale nonlinear systems, the computational burden associated with the numerical solution of nonlinear optimization problems poses a major chall...

Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. This work focuses on the subclass of quadratic programs with linear complementarity constraints. A novel approach to solving a penalty reformulation using sequential conve...

This work presents the results of experimental operation of a solar‐driven climate system using mixed‐integer nonlinear model predictive control (MPC). The system is installed in a university building and consists of two solar thermal collector fields, an adsorption cooling machine with different operation modes, a stratified hot water storage with...

This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication protocol. In contrast to existing parallelizable optim...

Two complementary simulators aimed at the dynamic analysis of airborne wind energy systems based on multi-aircraft congurations are presented. The rst model considers a train of stacked aircraft linked among them by two inelastic and massless tethers with no aerodynamic drag. The architecture of the mechanical system in the second simulator is cong...

Airborne wind energy systems convert wind energy into electricity using tethered flying devices, typically flexible kites or aircraft. Replacing the tower and foundation of conventional wind turbines can substantially reduce the material use and, consequently, the cost of energy, while providing access to wind at higher altitudes. Because the fligh...

Solving the nonlinear optimal control problem (OCP) arising from Economic Nonlinear model predictive control (ENMPC) reliably in real time is still a challenge. In this chapter, we present an extended multi-level iteration scheme (MLI) and discuss the interplay of exact Hessian and Hessian approximations. We show the importance of proper use of reg...

Mathematical programs with complementarity constraints are notoriously difficult to solve due to their nonconvexity and lack of constraint qualifications in every feasible point. In this work we focus on the subclass of quadratic programs with linear complementarity constraints. We introduce a novel approach to solving a penalty reformulation using...

Trajectory planning with the consideration of obstacles is a classical task in autonomous driving and robotics applications. This paper introduces a novel solution approach for the subclass of autonomous racing problems which is additionally capable of dealing with reward objects. This special type of objects is representing particular regions in s...

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...

This paper describes the development of a control system for an industrial heating application. In this process a moving substrate is passing through a heating zone with variable speed. Heat is applied by hot air to the substrate with the air flow rate being the manipulated variable. The aim is to control the substrate’s temperature at a specific l...

In this paper, we propose an efficient zero-order algorithm that can be used to compute an approximate solution to robust optimal control problems (OCP) and robustified nonconvex programs in general. In particular, we focus on robustified OCPs that make use of ellipsoidal uncertainty sets and show that, with the proposed zero-order method, we can e...

First-order stochastic methods for solving large-scale non-convex optimization problems are widely used in many big-data applications, e.g. training deep neural networks as well as other complex and potentially non-convex machine learning models. Their inexpensive iterations generally come together with slow global convergence rate (mostly sublinea...

This article discusses how to use optimization-based methods to efficiently operate microgrids with a large share of renewables. We discuss how to apply a frequency-based method to tune the droop parameters in order to stabilize the grid and improve oscillation damping after disturbances. Moreover, we propose a centralized real-time feasible nonlin...

In this article, we describe the design and implementation of a current controller for a reluctance synchronous machine (RSM) based on continuous control set nonlinear model predictive control (NMPC). A computationally efficient gray box model of the flux linkage map, the Gaussian-linear-arctangent (GLA) model, is proposed and employed in a trackin...

The advances in computer processor technology have enabled the application of nonlinear model predictive control (NMPC) to agile systems, such as quadrotors. These systems are characterized by their underactuation, nonlinearities, bounded inputs, and time-delays. Classical control solutions fall short in overcoming these difficulties and fully expl...

This paper proposes a Nonlinear Model Predictive Controller (NMPC) for pitch control of Horizontal-Axis Wind Turbines (HAWTs) in Region 3 to avoid flutter aero-elastic instability. First, an aero-elastic HAWT rotor model was derived based on extended Hamilton's principle using the coupled flap-wise and torsional motions of each blade. As for the ae...

We present a real-time feasible Nonlinear Model Predictive Control (NMPC) scheme to control a microgrid described by a detailed Differential Algebraic Equation (DAE). Our NMPC formulation allows to consider secondary voltage and frequency control, steady-state equal load sharing, economic goals and all relevant operational constraints in a single o...

We present a novel reformulation of nonsmooth differential equations with state jumps enabling their easier simulation and use in optimal control problems without the need for integer variables. The main idea is to introduce an auxiliary differential equation to mimic the state jump map. Thereby, a clock state is introduced which does not evolve du...

Robust and accurate pose estimation of moving systems is a challenging task that is often tackled by combining information from different sensor subsystems in a multi-sensor fusion setup. To obtain robust and accurate estimates, it is crucial to respect the exact time of each measurement. Data fusion is additionally challenged when the sensors are...

This paper is an in-depth investigation of using kernel methods to immunize optimization solutions against distributional ambiguity. We propose kernel distributionally robust optimization (K-DRO) using insights from the robust optimization theory and functional analysis. Our method uses reproducing kernel Hilbert spaces (RKHS) to construct ambiguit...

Following early work on Hessian-free methods for deep learning, we study a stochastic generalized Gauss-Newton method (SGN) for training DNNs. SGN is a second-order optimization method, with efficient iterations, that we demonstrate to often require substantially fewer iterations than standard SGD to converge. As the name suggests, SGN uses a Gauss...

This article discusses how to use optimization-based methods to efficiently operate microgrids with a large share of renewables. We discuss how to apply a frequency-based method to tune the droop parameters in order to stabilize the grid and improve oscilation damping after disturbances. Moreover, we propose a centralized real-time feasible nonline...

Economic nonlinear model predictive control (NMPC) is a variant of NMPC that directly optimizes an economic performance index instead of a tracking error. Although economic NMPC can achieve excellent closed-loop performance, the associated computational effort as well as the difficulty of guaranteeing stability in practice are its main drawbacks. M...

Basic Linear Algebra Subroutines For Embedded Optimization (BLASFEO) is a dense linear algebra library providing high-performance implementations of BLAS- and LAPACK-like routines for use in embedded optimization and other applications targeting relatively small matrices. BLASFEO defines an application programming interface (API) which uses a packe...

Economic nonlinear model predictive control (NMPC) is a variant of NMPC that directly optimizes an economic performance index instead of a tracking error. Although economic NMPC can achieve excellent closed-loop performance, the associated computational effort as well as the difficulty of guaranteeing stability in practice are its main drawbacks. M...

In this paper, an asymptotic stability proof for a class of real-time methods for nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and stability results are derived for the setting where a single iteration of the optimizer is carried out per sampling time. To this end, a Lyapu...

We present a novel reformulation of nonsmooth differential equations with state jumps which enables their easier simulation and use in optimal control problems without the need of using integer variables. The main idea is to introduce an auxiliary differential equation to mimic the state jump map. Thereby, also a clock state is introduced which doe...

This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and provides interior point method (IPM) solvers as well (partial) condensing routines. In particular, the IPM for...