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arXiv 2018年

作者： Tatarenko, Tatiana Control Methods and Robotics Lab Technical University Darmstadt Darmstadt Germany

Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function coincides with a global objective function to be maximized. In this approach, the agents correspond to the strategic decision makers and the optimization problem is equivalent to the problem of learning a potential function maximizer in the designed game. The paper deals with two different information settings in the system. Firstly, we consider systems, where agents have the access to the gradient of their utility functions. However, they do not possess the full information about the joint actions. Thus, to be able to move along the gradient toward a local optimum, they need to exchange the information with their neighbors by means of communication. The second setting refers to a payoff-based approach to learning potential function maximizers. Here, we assume that at each iteration agents can only observe their own played actions and experienced payoffs. In both cases, the paper studies unconstrained nonconvex optimization with a differentiable objective function. To develop the corresponding algorithms guaranteeing convergence to a local maximum of the potential function in the game, we utilize the idea of the well-known Robbins-Monro procedure based on the theory of stochastic approximation. Copyright © 2018, The Authors. All rights reserved.

关键词： Multi agent systems

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Time-Invariant control in LQ Optimal Tracking: An Alternative to Output Regulation

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IFAC-PapersOnLine 2017年第1期50卷 4912-4919页

作者： Bernhard S. Institute of Automatic Control Control Methods & Robotics Lab Technische Universität Darmstadt Darmstadt 64283 Germany

We propose a new time-invariant control for linear quadratic tracking problems with references and disturbances generated by linear exo-systems. The control consists of a static feedback and a static pre-filter similar as in output regulation theory (ORT). Instead of forcing the tracking error to converge to zero, a tolerated steady-state error is balanced against the necessary input-energy via a quadratic cost. For the first time in this context, we deduce a time-invariant control from algebraic equations such that necessary optimality conditions are satisfied on infinite horizons. Then, we prove strong optimality for bounded exo-system states. Hence, any other steady-state solution will lead to infinite additional cost. On finite horizons and for arbitrary exo-systems, we prove that our control is an agreeable plan as it approximates the computational expensive, time-varying optimal control of any suitably large horizon. Since our control applies for any initial conditions of the plant and the exo-system, it is well suited for a practical resource-efficient implementation. In this regard, a presented algorithm allows for an easy to carry out control design. Finally, an industrial application indicates the unified treatment of square, under- and over-actuated systems by our approach in contrast to ORT. © 2017

关键词： Agreeable Plans Disturbances Linear Quadratic Linear Systems Optimal Tracking Output Regulation Over-Actuated Time-Varying References Under-Actuated

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Optimal control of hybrid systems with sliding modes 14th

Optimal control of hybrid systems with sliding modes

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14th International Conference on Dynamical Systems: Theory and Applications, DSTA 2017

作者： Pytlak, Radoslaw Suski, Damian Tarnawski, Tomasz Faculty of Mathematics and Information Science Warsaw University of Technology Warsaw00-665 Poland Institute of Automatic Control and Robotics Warsaw University of Technology Warsaw02-525 Poland Department of Quantitative Methods and Information Technology Kozminski University Warsaw03-301 Poland

ISBN: (纸本)9783319965970

This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguish it from the other procedures for the problem. First of all a sliding mode is coped with differential–algebraic equations (DAEs) and that guarantees accurate tracking of the sliding motion surface. The second important feature is the calculation of cost and constraints functions gradients with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion. The third feature is the integration of the presented procedure with the Interactive Dynamic Optimization Server (IDOS) which is a computing environment dedicated to optimal control problems. IDOS user interface relies on Dynamic Optimization Modeling Language (DOML) which is an extension of Modelica language. In the paper we discuss the elements of DOML which help defining hybrid optimal control problems. The paper presents the application of the proposed procedure to an optimal control problem related to a mechanical system with dry friction. © Springer International Publishing AG, part of Springer Nature 2018.

关键词： Hybrid systems

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Optimal output regulation for square, over-actuated and under-actuated linear systems

arXiv

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arXiv 2018年

作者： Bernhard, Sebastian Adamy, Jürgen Institute of Automatic Control and Mechatronics Control Methods and Robotics Lab Technische Universität Darmstadt Landgraf-Georg Str. 4 Darmstadt64283 Germany

This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most accurately. These are typical challenges for over-actuated systems and for under-actuated systems, respectively. We formulate both goals as optimal output regulation problems. Then we contribute two new sets of regulator equations to output regulation theory that provide the desired solutions. A thorough study indicates solvability and uniqueness under weak assumptions. E.g., we can always determine the solution of the classical regulator equations that is most input energy efficient. This is of great value if there are infinitely many solutions. We derive our results by a linear quadratic tracking approach and establish a useful link to output regulation theory. Copyright © 2018, The Authors. All rights reserved.

关键词： Linear systems

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Efficient global localization using vision and digital offline map

Efficient global localization using vision and digital offli...

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International Conference on Intelligent Transportation

作者： Martin Buczko Volker Willert Control Methods & Robotics Lab TU Darmstadt Germany

ISBN: (纸本)9781538615270

We present an efficient method that combines visual odometry and offline map data for global localization. In contrast to other approaches, no further sensor as GPS or precise information on the initial pose is needed. Rough localization information like the current city or region can be used to speed up the initialization, but is not required. The proposed method uses the observation of street signs in a twofold manner: To roughly pre-localize the vehicle and to subsequently transform the three-dimensional vehicle-to-map-alignment-task into a one-dimensional search within a closed interval. This leads to a fast matching method, that finds the proper shift and rotation angle between the planar trajectory of the visual odometry and the offline map data. The method is evaluated on a real trajectory that is computed with a state-of-the-art visual odometry system to demonstrate its performance.

关键词： Trajectory Visual odometry Optical character recognition software Global Positioning System Image reconstruction Conferences

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All stabilizing PID controllers for interval systems and systems with affine parametric uncertainties

All stabilizing PID controllers for interval systems and sys...

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Asian control Conference

作者： Dinu Mihailescu-Stoica Frank Schrödel Jürgen Adamy Control Methods and Robotics Lab Technische Universität Darmstadt Darmstadt Germany IAV GmbH Chemnitz Germany

ISBN: (纸本)9781509015740;9781509015733

Robust PID controller synthesis for plants with unknown or slowly varying parameters is still an open topic. A novel method is presented allowing to exactly determine all stabilizing controller gains for systems with interval and affine parametric uncertainties. This leads to far less conservative stability areas, compared to existing methods which are based on over-bounding by interval polynomials. As a consequence, iterative searches containing robust synthesis and analysis are omitted, which greatly reduces the time and effort to find potential controller parameters as robust stability is already guaranteed. Additionally, due to the inherent decoupling at singular frequencies, no frequency grinding is needed. The proposed method is based on a combination of a modified Parameter Space Approach with results from robust test set theory.

关键词： Aerospace electronics Stability analysis Robustness Uncertainty Mathematical model Transfer functions control systems

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Optimal stationary synchronization of heterogeneous linear multi-agent systems

arXiv

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arXiv 2017年

作者： Bernhard, Sebastian Khodaverdian, Saman Adamy, Jürgen Institute of Automatic Control and Mechatronics Control Methods and Robotics Lab Technische Universität Darmstadt Landgraf-Georg Str. 4 Darmstadt64283 Germany

In this paper, we address the output synchronization of heterogeneous linear networks. In the literature, all agents are typically required to synchronize exactly to a common trajectory. Here, we introduce optimal stationary synchronization (OSS) instead which permits non-zero steadystate synchronization errors. As a benefit, we are able to relax standard requirements. E.g., agents are allowed to participate in the network even when they usually cannot synchronize exactly. In addition, OSS enables agents to save input-energy by synchronizing within tolerable error-bounds. Our new method combines the synchronization of bounded exosystems with local infinite-time linear quadratic tracking (LQT). This results in an optimal balance of each agent's synchronization error versus its consumed input-energy. Moreover, we extend recent results in LQT such that the derived time-invariant optimal control guarantees that the synchronization error satisfies given strict bounds. All these aspects are demonstrated by an illustrative simulation example with a detailed analysis.93C05, 93C15, 93C35, 49K15 Copyright © 2017, The Authors. All rights reserved.

关键词： Synchronization

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Asymptotic stabilization of nonlinear systems using passivity indices

Asymptotic stabilization of nonlinear systems using passivit...

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2016 American control Conference, ACC 2016

作者： De Madeira, Diego S. Adamy, Jürgen Control Methods and Robotics Lab Technische Universität Darmstadt Darmstadt64283 Germany

ISBN: (纸本)9781467386821

This work presents a new controller design technique for asymptotic stabilization of nonlinear systems using passivity indices. The aforementioned indices measure the level of passivity of a system and we address the question of how to use this information to design a dynamic output feedback controller that stabilizes the closed-loop at a given equilibrium. As full state information is not always available for feedback, a measurable output has to be used. The main contribution of this paper consists of a systematic way of determining a stabilizing controller based on the passivity indices of the plant and on sum of squares (SOS) relaxations. A new method for determining the passivity indices of a nonlinear system in a domain of its state is presented as well. An example is provided in order to demonstrate the applicability of our strategy. Polynomial input-affine systems are considered. © 2016 American Automatic control Council (AACC).

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Output feedback control of rational nonlinear systems: A new approach based on passivity indices 55

Output feedback control of rational nonlinear systems: A new...

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55th IEEE Conference on Decision and control, CDC 2016

作者： De Madeira, Diego S. Adamy, Jurgen Control Methods and Robotics Lab Technische Universität Darmstadt Darmstadt64283 Germany

ISBN: (纸本)9781509018376

Recently, a new strategy for local analysis of passivity indices and its application for output feedback asymptotic stabilization of nonlinear systems was proposed [2]. Polynomial input-affine systems were considered and sum of squares (SOS) techniques were employed for estimating a domain in which the passivity indices are valid and stability is guaranteed. Though simple and useful, the method still demands improvements, as the estimates obtained can be quite conservative. In this context, this work applies the Finsler's Lemma and the notion of linear annihilators for enlarging the estimates of the aforementioned regions of attraction by reformulating the estimation problem as a polytopic LMI condition. In addition, we extended the results of [2] for the class of the rational nonlinear systems with possibly rational Lyapunov functions. Numerical examples are also provided in order to demonstrate the applicability of the method. © 2016 IEEE.

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Static output feedback: An LMI condition for stabilizability based on passivity indices

Static output feedback: An LMI condition for stabilizability...

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2016 IEEE Conference on control Applications, CCA 2016

作者： De Madeira, Diego S. Adamy, Jurgen Control Methods and Robotics Lab Technische Universität Darmstadt Darmstadt64283 Germany

ISBN: (纸本)9781509007554

This note deals with the static output feedback stabilization problem of linear time-invariant (LTI) systems, one of the most relevant open problems in the field of control theory. We present a new sufficient linear matrix inequality (LMI) condition to test stabilizability by static output feedback. The notion of passivity indices, as a measure of the level of passivity of a system, is employed. Unlike the methods currently available in the literature, our LMI condition is non iterative and does not rely on similarity transformations, allowing for a straightforward determination of a constant feedback gain that asymptotically stabilizes the closed-loop. We also provide numerical examples of our strategy in order to demonstrate its applicability in different scenarios. © 2016 IEEE.

关键词： Linear matrix inequalities

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