Grüne, Lars
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Grüne, Lars
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Grüne, Lars
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Item-typ:Veröffentlichung, Monotone dynamical systems, graphs, and stability of large-scale interconnected systems(2007-09-19); ; ; For a class of monotone operators T on the positive orthant of n-dimensional Euclidean space we introduce the concept of decay sets. These consist of points x satisfying T(x)<x. Considering the induced dynamical system x(k 1)=T(x(k)), we establish results relating stability properties of the origin, order conditions on T, and topological properties of decay sets. In particular, we construct paths in the decay sets and derive a quasi-invertibility result of the operator (Id-T).These results are applied to derive generalized small-gain type conditions for the input-to-state stability(ISS) of large-scale interconnections of (individually input-to-state stable) control systems: The interconnection topology together with the ISS gains yields a monotone operator with an inherent graph structure. We provide trajectory estimate based small-gain theorems and also construct ISS Lyapunov functions for the composite system. It is also shown how an algorithm due to Eaves can be used to numerically verify the small-gain condition.Dissertation808 397 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Optimalitätsbedingungen, parametrische Sensitivitätsanalyse und Echtzeitanpassung optimaler Regel- und Schätzverfahren(2012-09-11); ; ; This dissertation covers the derivation of necessary and sufficient optimality condition for linear quadratic regulator (LQR) problems. Based on this, parametric sensitivity methods and real time adaption techniques from nonlinear optimization theory are applied to LQR problems. In addition to that, through dual theory, these methods are extended to linear quadratic estimator problems as well as combined regulator-estimator problems. All derived adaption techniques are numerically tested for two examples.Dissertation587 334 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Stability, observer design and control of networks using Lyapunov methods(2012-05-23); ; ; We investigate different aspects of the analysis and control of interconnected systems. Different tools, based on Lyapunov methods, are provided to analyze such systems in view of stability, to design observers and to control systems subject to stabilization. All the different tools presented in this work can be used for many applications and extend the analysis toolbox of networks. Considering systems with inputs, the stability property input-to-state dynamical stability (ISDS) has some advantages over input-to-state stability (ISS). We introduce the ISDS property for interconnected systems and provide an ISDS small-gain theorem with a construction of an ISDS-Lyapunov function and the rate and the gains of the ISDS estimation for the whole system. This result is applied to observer design for single and interconnected systems. Observers are used in many applications where the measurement of the state is not possible or disturbed due to physical reasons or the measurement is uneconomical. By the help of error Lyapunov functions we design observers, which have a so-called quasi ISS or quasi-ISDS property to guarantee that the dynamics of the estimation error of the systems state has the ISS or ISDS property, respectively. This is applied to quantized feedback stabilization. In many applications, there occur time-delays and/or instantaneous "jumps" of the systems state. At first, we provide tools to check whether a network of time-delay systems has the ISS property using ISS-Lyapunov-Razumikhin functions and ISS-Lyapunov-Krasovskii functionals. Then, these approaches are also used for interconnected impulsive systems with time-delays using exponential Lyapunov-Razumikhin functions and exponential Lyapunov-Krasovskii functionals. We derive conditions to assure ISS of an impulsive network with time-delays. Controlling a system in a desired and optimal way under given constraints is a challenging task. One approach to handle such problems is model predictive control (MPC). In this thesis, we introduce the ISDS property for MPC of single and interconnected systems. We provide conditions to assure the ISDS property of systems using MPC, where the previous result of this thesis, the ISDS small-gain theorem, is applied. Furthermore, we investigate the ISS property for MPC of time-delay systems using the Lyapunov-Krasovskii approach. We prove theorems, which guarantee ISS for single and interconnected systems using MPC.Dissertation312 128