Parameter Identification for Dynamical Systems Using Optimal Control Techniques

In this work, we apply transcription methods known from optimal control to nonlinear dynamic parameter identification problems. We analyze and compare the methods with the help of an application example from robotics. More specifically, we investigate their robustness against varying initial parameters and show numerically, that an increasing number of variables leads to a more robust optimization behavior and qualitatively better solutions.

“…The aim is to identify parameters p with which the model approximates simulated data θ d best. For a more detailed model and problem description we refer to [4].…”

Section: General Problem Formulation and Methodsmentioning

confidence: 99%

A Numerical Study of the Robustness of Transcription Methods for Parameter Identification Problems

Schäfer

Flaßkamp

Büskens

2018

“…The model's state derivative values depend on the optimization parameters p ∈ R np , current state values, and on the controls applied (usually supplied in the measurement data), which have to be approximated to the time point of model evaluation as u app (t) ∈ R nu . Solving this problem is possible in a number of ways, in the following the approach of full discretization [7] as implemented in the software tool Topas Model Fitting [8] will be used, relying on the nonlinear solver WORHP [9]. With the correct parameters found, the model function can be applied to generate a forecast of the respective propertyfor a dynamical system, that means integrating the ODE (here using the odeint-function of Python Library SciPy).…”

Section: Theoretical Background 21 Data-based Modelling and Parameter...mentioning

confidence: 99%

Towards modelling of energy storages for use in an intelligent energy management system

Kappertz

Büskens

2023

With the transition towards renewable energy underway, demand‐side management together with the local generation of renewable energy is receiving growing attention. Optimizing the self‐consumption of locally produced renewable energy can not only have financial benefits for the respective household or business (and improve their autarky from increasingly unstable energy markets), but also help improve grid stability against the volatility of some sources of renewable energy. In order to optimize the self‐consumption of a given household or enterprise with an energy management system, the energy demand and generation, as well as the behaviour of all controlled devices have to be forecast. There are many different methods of mathematically modelling these different properties, but the task becomes especially challenging for dynamic systems like energy storage systems. Here, the state of charge at a specific time point depends on both external influences and the previous time point's state of charge, thus modelling errors quickly accumulate. In the context of small and medium agricultural enterprises, examples of such dynamic systems can be electrical storages, like a battery, or thermal storages like a milk cooling tank or a heat pump. In this work, a common way for the modelling of these systems is explored, namely parameter identification. Here, the parameters of an ordinary differential equation representing the assumed physical behaviour of the system are identified from measured data of states and controls in an optimization problem. The success of this approach, and with it the performance of the derived model depends on how well the physical equations actually describe the system, but also on the quality, quantity and content of the measurement data used. In the case of a household battery storage already a simple physical model with parameters identified from measurement data of state of charge and battery power provides useful results. The example of a milk cooling tank provides a situation where external forcing has an important influence on the system's state of charge, its temperature. The cleaning of the tank generates a large heat influx, and raises the temperature, while the filling and emptying of milk influences the heat capacity. While these influences are shown to also be representable by equations based on the physical processes, parameter identification becomes difficult when they are not included in the measurement data. Thus, different approaches to derive these external forcings from the available data are outlined.

“…M and F represent the mass matrix and forcing terms (a more detailed formulation can be found in [4]). In the corresponding Euler-Lagrange equations M (θ, p)θ = F (θ,θ, p, I), the joint angles θ serve as generalized coordinates, while I describes an input that controls the robot externally.…”

Section: Combined Homotopy-optimization For Parameter Identificationmentioning

confidence: 99%

“…In the corresponding Euler-Lagrange equations M (θ, p)θ = F (θ,θ, p, I), the joint angles θ serve as generalized coordinates, while I describes an input that controls the robot externally. M and F represent the mass matrix and forcing terms (a more detailed formulation can be found in [4]). Given measurementsθ and an input I on the time interval [0, 5], the aim is to identify a single parameter p representing the moment of inertia of the second link.…”

Section: Combined Homotopy-optimization For Parameter Identificationmentioning

confidence: 99%

A Combined Homotopy‐Optimization Approach to Parameter Identification for Dynamical Systems

Schäfer

Flaßkamp

Fliege

et al. 2019

When applying the single shooting approach to solve nonlinear dynamic parameter identification problems, difficulties like undesired minima can occur. To circumvent this, we apply a homotopy continuation to find global minima. In contrast to the literature, we reduce the resulting series of optimization problems to a single one which leads us to the opportunity to compute homotopy paths in a more efficient way. We demonstrate our method with the help of a numerical example.