arXiv subjects

Carsten W. Scherer

Publications and source records attributed to Carsten W. Scherer.

29 records · Page 2Linked to original sources

arXiv2022

Combining Prior Knowledge and Data for Robust Controller Design

We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter a novel and unifying disturbance description is employed. While large parts of the paper focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.

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arXiv2022

Dissipativity, Convexity and Tight O'Shea-Zames-Falb Multipliers for Safety Guarantees

We develop a novel convex parametrization of integral quadratic constraints with a terminal cost for subdifferentials of convex functions, involving general O'Shea-Zames-Falb multipliers. We show the benefit of our results for the reduction of conservatism of existing techniques, and sketch applications to the analysis of optimization algorithms or the stability analysis of neural network controllers. The development is prepared by providing a novel link between the convex integrability of a multivariable mapping and dissipativity theory.

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arXiv2022

Revisiting and Generalizing the Dual Iteration for Static and Robust Output-Feedback Synthesis

The dual iteration was introduced in a conference paper in 1997 by Iwasaki as an iterative and heuristic procedure for the challenging and non-convex design of static output-feedback controllers. We recall in detail its essential ingredients and go beyond the work of Iwasaki by demonstrating that the framework of linear fractional representations allows for a seamless extension of the dual iteration to output-feedback designs of practical relevance, such as the design of robust or robust gain-scheduled controllers. In the paper of Iwasaki, the dual iteration is solely based on, and motivated by algebraic manipulations resulting from the elimination lemma. We provide a novel control theoretic interpretation of the individual steps, which paves the way for further generalizations of the powerful scheme to situations where the elimination lemma is not applicable. As an illustration, we extend the dual iteration to a design of static output-feedback controllers with multiple objectives. We demonstrate the approach with numerous numerical examples inspired from the literature.

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arXiv2022

Robust Differential Dynamic Programming

Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input constraints. In this contribution, we develop a robust version of Differential Dynamic Programming that uses generalized plants and multiplier relaxations for uncertainties. To this end, we study a version of the Bellman principle and use convex relaxations to account for uncertainties in the dynamic program. The resulting algorithm can be seen as a robust trajectory generation tool for nonlinear systems.

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arXiv2022

Output-Feedback Synthesis for a Class of Aperiodic Impulsive Systems

We derive novel criteria for designing stabilizing dynamic output-feedback controllers for a class of aperiodic impulsive systems subject to a range dwell-time condition. Our synthesis conditions are formulated as clock-dependent linear matrix inequalities (LMIs) which can be solved numerically, e.g., by using matrix sum-of-squares relaxation methods. We show that our results allow us to design dynamic output-feedback controllers for aperiodic sample-data systems and illustrate the proposed approach by means of a numerical example.

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arXiv2021

Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guarantees

The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and control-theoretic guarantees is of utmost importance, yet difficult to achieve for learning-based control schemes. We present a general framework for learning-enhanced robust control that allows for systematic integration of prior engineering knowledge, is fully compatible with modern robust control and still comes with rigorous and practically meaningful guarantees. Building on the established Linear Fractional Representation and Integral Quadratic Constraints framework, we integrate Gaussian Process Regression as a learning component and state-of-the-art robust controller synthesis. In a concrete robust control example, our approach is demonstrated to yield improved performance with more data, while guarantees are maintained throughout.

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arXiv2020

Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions

This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains strongly convex functions with Lipschitz gradients but also non-convex functions, which allows not only to address optimization problems but also saddle-point problems. The proposed design procedure relies on a suitable class of Lyapunov functions and on convex semi-definite programming. The proposed synthesis allows the design of algorithms that reach the performance of state-of-the-art accelerated gradient methods and beyond.

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arXiv2020

Robust data-driven state-feedback design

We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the $\mathcal{H}_\infty$-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.

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arXiv2020

Controller Design via Experimental Exploration with Robustness Guarantees

For a partially unknown linear systems, we present a systematic control design approach based on generated data from measurements of closed-loop experiments with suitable test controllers. These experiments are used to improve the achieved performance and to reduce the uncertainty about the unknown parts of the system. This is achieved through a parametrization of auspicious controllers with convex relaxation techniques from robust control, which guarantees that their implementation on the unknown plant is safe. This approach permits to systematically incorporate available prior knowledge about the system by employing the framework of linear fractional representations.

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arXiv2018

Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions

In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections based on the notion of finite-horizon integral quadratic constraints with a terminal cost. As the main benefit, this opens up opportunities for guaranteeing constraints on the transient responses of trajectories in feedback loops within absolute stability theory. For parametric robustness, we show how to generate tight robustly invariant ellipsoids on the basis of a classical frequency-domain stability test, with illustrations by a numerical example.

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arXiv2013

Structured $H_\infty$-Optimal Control for Nested Interconnections: A State-Space Solution

If imposing general structural constraints on controllers, it is unknown how to design $H_\infty$-controllers by convex optimization. Under a so-called quadratic invariance structure of the generalized plant, the Youla parametrization allows to translate the structured synthesis problem into an infinite-dimensional convex program. Nested interconnections that are characterized by a standard plant with a block-triangular structure fall into this class. Recently it has been shown how to design optimal $H_2$-controllers for such nested structures in the state-space by solving algebraic Riccati equations. In the present paper we provide a state-space solution of the corresponding output-feedback $H_\infty$ synthesis problem without any counterpart in the literature. We argue that a solution based on Riccati equations is - even for state-feedback problems - not feasible and we illustrate our results by means of a simple numerical example.

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