Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

100%

Freihold M., Hofer E.

International Journal of Applied Mathematics and Computer Science

2009

tom 19

nr 3

485-499

Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential to obtain the tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The use of these constraints in verified simulations of dynamical systems provides a computationally efficient procedure which restricts the state enclosures to regions that are physically meaningful. A branch and prune algorithm is modified to a consistency test, which is based on these constraints. Two application scenarios are studied in detail. First, the total energy is employed as a conservation property for the analysis of mechanical systems. It is shown that conservation properties, such as the energy, are applicable to any Hamiltonian system. The second scenario is based on constraints that are derived from decoupling properties, which are considered for a high-dimensional compartment model of granulopoiesis in human blood cell dynamics.

Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

81%

Rauh A., Minisini J., Hofer E.

International Journal of Applied Mathematics and Computer Science

2009

tom 19

nr 3

425-439

Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

2 Hofer E.

1 Freihold M.

1 Minisini J.

1 Rauh A.

2 2009

Wyniki wyszukiwania

Derivation of physically motivated constraints for efficient interval simulations applied to the analysis of uncertain dynamical systems

Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties