Direct optimization of dynamic systems described by differential-algebraic equations

2008 ◽  
Vol 29 (6) ◽  
pp. 445-466 ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Dynamic Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Direct Optimization

A Technique for the Direct Optimization of Dynamic Systems Described by Differential-Algebraic Equations

2007 ◽  
Author(s):  
Brian C. Fabien
Keyword(s):  
Optimal Control ◽  
Dynamic Systems ◽  
Differential Algebraic Equations ◽  
Time Interval ◽  
Algebraic Equations ◽  
Direct Optimization ◽  
Programming Technique ◽  
Piecewise Constant ◽  
Infinite Dimensional ◽  
Parameter Identification Problems

This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the differential-algebraic equations are approximated using a Rosenbrock-Wanner (ROW) method. In this way the infinite dimensional optimal control problem is transformed into a finite dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming technique. The paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem, and (ii) an efficient technique for evaluation the function, constraints and gradients associated with the NLP problem. The paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method.

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

Differential–Algebraic Equations and Dynamic Systems on Manifolds

2016 ◽  
Vol 52 (3) ◽  
pp. 408-418 ◽  
Author(s):  
Iu. G. Kryvonos ◽  
V. P. Kharchenko ◽  
N. M. Glazunov
Keyword(s):  
Dynamic Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations

STEADY-STATE METHODS OF DIFFERENTIAL-ALGEBRAIC EQUATIONS IN CIRCUIT SIMULATION

2005 ◽  
Vol 14 (02) ◽  
pp. 383-393
Author(s):  
YAO-LIN JIANG
Keyword(s):  
Steady State ◽  
Dynamic Systems ◽  
Krylov Subspace ◽  
Circuit Simulation ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Linear Dynamic Systems ◽  
Autonomous Case ◽  
Newton Iterations ◽  
Pseudo Inverse

In the paper, we study the steady-state methods of large dynamic systems. For a nonlinear system of differential-algebraic equations with a known period T, we decouple it, in function space, into linear subsystems by quasilinearization. The resulting linear dynamic systems can be solved by a waveform Krylov subspace method. For the autonomous case, that is, the period T is unknown, the well-known shooting process can be applied where Newton iterations are computed with pseudo-inverse.

scholarly journals A Direct Optimization Algorithm for Problems with Differential-Algebraic Constraints: Application to Heat and Mass Transfer

2020 ◽  
Vol 10 (24) ◽  
pp. 9027
Author(s):  
Paweł Drąg
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Control Function ◽  
Differential Algebraic Equations ◽  
Sequential Optimization ◽  
Multiple Shooting ◽  
Optimization Approach ◽  
Algebraic Equations ◽  
Direct Optimization ◽  
Optimization Task

In this article, an optimization task with nonlinear differential-algebraic equations (DAEs) is considered. As a main result, a new solution procedure is designed. The computational procedure represents the sequential optimization approach. The proposed algorithm is based on a multiple shooting parametrization method. Two main aspects of a generalized parametrization approach are analyzed in detail: a control function and DAE model parametrization. A comparison between the original and modified DAEs is made. The new algorithm is applied to solve an optimization task in heat and mass transfer engineering.

Subset Selection Methods for Design Sensitivity Analysis of Constrained Dynamic Systems

1990 ◽  
Author(s):  
Jun-Tien Twu ◽  
Prakash Krishnaswami ◽  
Rajiv Rampalli
Keyword(s):  
Dynamic Systems ◽  
Correct Choice ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Selection Methods ◽  
Constrained Motion ◽  
Differentiation Formula ◽  
Backward Differentiation Formula ◽  
Solution Methods

Abstract In the Lagrangian formulation of the constrained motion of mechanical systems, a system of Differential-Algebraic Equations is generally encountered. The popular Backward Differentiation Formula for the numerical solution of such problems leads to an over-determined system of equations. The correct choice of a proper exactly determined subset can greatly enhance the performance of a solution algorithm. In this paper, we discuss four solution methods with different choices of subsets. Three numerical examples are solved to compare the accuracy and efficiency of these methods.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

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