Timm Faulwasser

Technische Universität Dortmund | TUD · Faculty of Electrical Engineering and Information Technology

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre- specified timing requirements. Such problems are commonly referred to as constrained output path-following problems. Specifically, we propose a predictive control approach to constrained path-following problems with...

This paper investigates the relations between three different properties, which are of importance in continuous-time optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady state, and the turnpike property. We show that dissipativity with respect to a steady state implie...

In recent years, Economic Model Predictive Control (empc) has received considerable attention of many research groups. The present tutorial survey summarizes state-of-the-art approaches in empc. In this context empc is to be understood as receding-horizon optimal control with a stage cost that does not simply penalize the distance to a desired equi...

For his work in the economics of climate change, Professor William Nordhaus was a co-recipient of the 2018 Nobel Memorial Prize for Economic Sciences. A core component of the work undertaken by Nordhaus is the Dynamic Integrated model of Climate and Economy, known as the DICE model. The DICE model is a discrete-time model with two control inputs an...

This paper presents an overview of the recent developments of modifier-adaptation schemes for real-time optimization of uncertain processes. These schemes have the ability to reach plant optimality upon convergence despite the presence of structural plant-model mismatch. Modifier Adaptation has its origins in the technique of Integrated System Opti...

We investigate the dynamics of a bicycle on an uneven mountain bike track split into straight sections with small jumps (kickers) and banked corners. A basic bike-rider model is proposed and used to derive equations of motion, which capture the possibilities to accelerate the bicycle without pedaling. Since this is a first approach to the problem,...

In this paper, we introduce and study different dissipativity notions and different turnpike properties for discrete-time stochastic nonlinear optimal control problems. The proposed stochastic dissipativity notions extend the classic notion of Jan C. Willems to $L^r$ random variables and to probability measures. Our stochastic turnpike properties r...

Many real-world applications require the joint optimization of a large number of flexible devices over some time horizon. The flexibility of multiple batteries, thermostatically controlled loads, or electric vehicles, e.g., can be used to support grid operations and to reduce operation costs. Using piecewise constant power values, the flexibility o...

Keynote given at the 6th IEEE Colombian Conference on Automatic Control. Motivated by ongoing research developments for control of multi-energy systems, we discuss recent progress of data-driven descriptions and control of stochastic LTI systems. Leveraging polynomial chaos expansions (PCE) of random variables, the origins of which date back to t...

We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. We show that from this time-varying di...

Data‐driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data‐driven stochastic control. In this paper, we propose a data‐driven stochastic predictive control scheme for LTI systems subject to possibly unbound...

We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on finite-time horizons. We analyze a class of optimal control problems, where the performance functional can be...

The safe and economical operation of large-scale networked systems is challenging. Optimization-based schemes are frequently employed, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. Hence, these schemes require solving large-scale optimization problems. Iterative techniques from distributed o...

This paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control Problem (OCP), which allows for forward prediction and optimization of statistical distributions of inputs an...

This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability measures or distributions. Typically, stochastic optimal control requires knowledge of underlying dynamics and is as...

We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy supply is intrinsic to the port-Hamiltonian structure, the necessary conditions of optimality resulting from Pontryagin's maximum principle may yield singular arcs. The underl...

We investigate pathwise turnpike behavior of discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. The analytical findings are illustrated by a numeric...

In this presentation we discuss the progress of data-driven descriptions for stochastic LTI systems. Leveraging polynomial chaos expansions (PCE) of random variables, the origins of which date back to Norbert Wiener, we answer the question of how to formulate the fundamental lemma of Jan C. Willems and co-authors for stochastic systems. We illustra...

Model predictive Path-Following Control (MPFC) is a viable option for motion systems in many application domains. However, despite considerable progress on tailored numerical methods for predictive control, the real-time implementation of predictive control and MPFC on small-scale autonomous platforms with low-cost embedded hardware remains challen...

Distributed model predictive control (DMPC) is a flexible and scalable feedback control method applicable to a wide range of systems. While stability analysis of DMPC is quite well understood, there exist only limited implementation results for realistic applications involving distributed computation and networked communication. This article approa...

Dimensionality reduction of decision variables is a practical and classic method to reduce the computational burden in linear and Nonlinear Model Predictive Control (NMPC). Available results range from early move-blocking ideas to singular-value decomposition. For schemes more complex than move-blocking it is seemingly not straightforward to guaran...

Mathematical models play a crucial role in systems and control theory. They can take various forms, including ordinary or partial differential equations, difference equations, transfer matrices, and their combinations with logic elements. There are several ways to obtain a mathematical model for a physical system. The most common approach is to app...

This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability measures or distributions. Typically, stochastic optimal control requires knowledge of underlying dynamics and is as...

Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect the dynamics. In this paper, we leverage Polynomial Chaos Expansions (PCE) to extend the deterministic fundam...

Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this paper, we propose a data-driven stochastic predictive control scheme for LTI systems subject to possibly unbound...

The paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control Problem (OCP), which allows for forward prediction and optimization of statistical distributions of inputs and...

Recently, the fundamental lemma by Willems et al. has seen frequent use for the design of data-driven output-feedback predictive control. However, the majority of existing results considers deterministic Linear Time-Invariant (LTI) systems with or without measurement noise. In this paper, we analyze data-driven output-feedback predictive control of...

We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions exhibit the manifold turnpike phenomenon with respect to the manifold of thermodynamic equilibria. We illustr...

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we...

Jan Willems introduced the system-theoretic notion of dissipativity in his foundational two-part paper which appeared in the Archive of Rational Mechanics and Analysis in 1972. Even earlier, in a likewise pivotal 1971 IEEE Transactions on Automatic Control paper, he investigated infinite-horizon least-squares optimal control and the algebraic Ricca...

Im Projekt 5hine werden 5G Kommunikationslösungen für Steuerung, Monitoring und Wartung verteilter industrieller Anlagen mit sehr hoher Anzahl und Dichte an Teilsystemen am Beispiel eines solarthermischen Kraftwerks entwickelt.

The necessity to obtain, to parametrize, and to maintain models of the underlying dynamics impedes predictive control of energy systems in many real-world applications. To alleviate the need for explicit model knowledge this paper proposes a framework for the operation of distributed multi-energy systems via data-driven predictive control with stoc...

Dimensionality reduction of decision variables is a practical and classic method to reduce the computational burden in linear and Nonlinear Model Predictive Control (NMPC). Available results range from early move-blocking ideas to singular-value decomposition. For schemes more complex than move-blocking it is seemingly not straightforward to guaran...

The fundamental lemma by Jan C. Willems and co-workers has become one of the supporting pillars of the recent progress on data-driven control and system analysis. The lemma is deeply rooted in behavioral systems theory, which so far has been focused on finite-dimensional deterministic systems. This tutorial combines recent insights into stochastic...

Classical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those...

Non-convex optimization problems arise in many problems of practical relevance-for example in distributed nonlinear MPC or distributed optimal power flow. Only few existing decentralized optimization methods have local convergence guarantees for general nonconvex problems. We present novel convergence results for non-convex problems for a bi-level...

Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time,...

This paper is about computationally tractable methods for power system parameter estimation and Optimal Experiment Design (OED). Here, the main motivation is that OED has the potential to significantly increase the accuracy of power system parameter estimates, for example, if only a few batches of data are available. The problem is, however, that s...

Model Predictive Control (MPC) for {networked, cyber-physical, multi-agent} systems requires numerical methods to solve optimal control problems while meeting communication and real-time requirements. This paper presents an introduction on six distributed optimization algorithms and compares their properties in the context of distributed MPC for li...

Acoustic levitation has recently demonstrated the ability to create volumetric content by trapping and quickly moving particles along reference paths to reveal shapes in mid-air. However, the problem of specifying physically feasible trap trajectories to display desired shapes remains unsolved. Even if only the final shape is of interest to the con...

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we...

Acoustic levitation has recently demonstrated the ability to create volumetric content by trapping and quickly moving particles along reference paths to reveal shapes in mid-air. However, the problem of specifying physically feasible trap trajectories to display desired shapes remains unsolved. Even if only the final shape is of interest to the con...

We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions exhibit the manifold turnpike phenomenon with respect to the manifold of thermodynamic equilibria. We illustr...

In this paper we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modelling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constr...

The turnpike property refers to the phenomenon that in many optimal control problems, the solutions for different initial conditions and varying horizons approach a neighborhood of a specific steady state, then stay in this neighborhood for the major part of the time horizon, until they may finally depart. While early observations of the phenomenon...

In this letter we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems’ fundamental lemma, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constr...

The implementation of data-driven predictive control schemes based on Willems’ fundamental lemma often relies on a single-shooting approach, i.e., it uses one large Hankel matrix to cover the entire optimization horizon. However, the numerical solution is fostered by the use of multiple segmented horizons which require less data in smaller Hankel m...

Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect the dynamics. In this paper, we leverage Polynomial Chaos Expansions (PCE) to extend the deterministic fundam...

This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems with non-convex constraints. Moreover, our method exhibits a small communication footprint and it achieves a...

This paper analyzes the interplay between dissipativity and stability properties in continuous-time infinite-horizon Optimal Control Problems (OCPs). We establish several relations between these properties, which culminate in a set of equivalence conditions. Moreover, we investigate convergence and stability of the infinite-horizon optimal adjoint...

This note discusses the interplay between dissipativity and the asymptotics of continuous-time infinite-horizon optimal control problems. We focus on the results on convergence of optimal primal solutions derived in [6]. Moreover, we present a result on the attractivity of the infinite-horizon optimal adjoint trajectories, which is closely related...

The uncertainty associated with renewable energies creates challenges in the operation of distribution grids. One way for Distribution System Operators to deal with this is the computation of probabilistic forecasts of the full state of the grid. Recently, probabilistic forecasts have seen increased interest for quantifying the uncertainty of renew...

Due to their large power draws and increasing adoption rates, electric vehicles (EVs) will become a significant challenge for electric distribution grids. However, with proper charging control strategies, the challenge can be mitigated without the need for expensive grid reinforcements. This article presents and analyzes new distributed charging co...

This article introduces an open‐source software for distributed and decentralized non‐convex optimization named ALADIN‐. ALADIN‐ is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. It is user interface is convenient for rapid prototyping of non‐convex distributed optim...

Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this...

Distributed and decentralized optimization are key for the control of network systems -- for example in distributed model predictive control, and in distributed sensing or estimation. Non-linear systems, however, lead to problems with non-convex constraints for which classical decentralized optimization algorithms lack convergence guarantees. Moreo...

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. W...

We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems. We study the reachability properties of the system and prove that optimal states exhibit a turnpike behavior with respect to the conservative subspace. Further, we derive a input-state turnpike towards a subspa...

Since the earliest conceptualizations by Lee and Markus, and Propoi in the 1960s, Model Predictive Control (MPC) has become a major success story of systems and control with respect to industrial impact and with respect to continued and wide-spread research interest. The field has evolved from conceptually simple linear-quadratic (convex) settings...

We consider the problem of minimizing the supplied energy of infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit the turnpike phenomenon towards certain subspaces induced by the dissipation of the dynamics.

We consider model predictive path-following control (MPFC) without stabilizing terminal constraints or costs. We investigate sufficient stability conditions in the framework of cost controllability. Then, we analyze cost controllability for path-following problems of differentially flat systems. Using this result, we establish that under suitable a...

This chapter compares different formulations for economic nonlinear model predictive control (EMPC) which are all based on an established dissipativity assumption on the underlying optimal control problem (OCP). This includes schemes with and without stabilizing terminal constraints, respectively, or with stabilizing terminal costs. We recall that...

This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, af...

Classical turnpikes correspond to optimal steady states which are attractors of optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions on a symmetry-induced manifold coincide with those of a reduced-order problem un...

Scheduling the power exchange between a population of heterogeneous distributed energy resources and the corresponding upper-level grid is an important control problem in power systems. A key challenge is the large number of (partially uncertain) variables that increase the computational burden and that complicate the structured consideration of un...

This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An advantage of the proposed method compared to existing distributed model predictive algorithms is the primal f...

Virtual Power Plants (VPPs) comprising renewables and hydrogen production through power-to-gas technologies can help to increase renewable penetration and to improve operational flexibility and economic performance. However, the uncertainty inherent to forecasts of renewable generation and energy prices renders cost effective operation difficult. T...

The decentralized solution of linear systems of equations arises as a subproblem in optimization over networks. Typical examples include the KKT system corresponding to equality constrained quadratic programs in distributed optimization algorithms or in active set methods. This note presents a tailored structure-exploiting decentralized variant of...