# A unified parameter identification method for nonlinear time-delay systems

@article{Chai2013AUP, title={A unified parameter identification method for nonlinear time-delay systems}, author={Qinqin Chai and R. Loxton and K. Teo and C. Yang}, journal={Journal of Industrial and Management Optimization}, year={2013}, volume={9}, pages={471-486} }

This paper deals with the problem of identifying unknown time-delays and model parameters in a general nonlinear time-delay system. We propose a unified computational approach that involves solving a dynamic optimization problem, whose cost function measures the discrepancy between predicted and observed system output, to determine optimal values for the unknown quantities. Our main contribution is to show that the partial derivatives of this cost function can be computed by solving a set of… Expand

#### 42 Citations

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#### References

SHOWING 1-10 OF 27 REFERENCES

An Optimization Approach to State-Delay Identification $ $

- Mathematics, Computer Science
- IEEE Transactions on Automatic Control
- 2010

A dynamic optimization problem in which the state-delays are decision variables and the cost function measures the discrepancy between predicted and observed system output is formulated and the gradient of this problem's cost function can be computed by solving an auxiliary delay-differential system. Expand

Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications

- Computer Science
- 2009

It is shown that this type of problem can be approximated by a sequence of time delayed optimal control problems subject to inequality constraints in canonical form and with multiple characteristic time points appearing in the cost and constraint functions. Expand

Robust suboptimal control of nonlinear systems

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2011

It is shown that the system sensitivity can be computed by solving an auxiliary initial value problem and this result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. Expand

Optimal control problems with multiple characteristic time points in the objective and constraints

- Mathematics, Computer Science
- Autom.
- 2008

This paper develops a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points that is approximated by a sequence of approximate optimal parameter selection problems. Expand

A New Computational Method for a Class of Free Terminal Time Optimal Control Problems

- Mathematics
- 2011

We develop a numerical method for solving an optimal control problem whose terminal time is not fixed, but is instead determined by a state-dependent stopping criterion. The main idea of this method… Expand

Parameters estimation of systems with delayed and structured entries

- Mathematics, Computer Science
- Autom.
- 2009

The proposed cancellation method allows to obtain non asymptotic estimators for the unknown coefficients of continuous-time systems with structured entries and application to delayed and switching hybrid systems. Expand

A New Computational Method for Optimizing Nonlinear Impulsive Systems

- Mathematics
- 2011

In this paper, we consider a system that evolves by switching between several subsystems of ordinary differential equations. The switching mechanism in this system induces an instantaneous change in… Expand

An identification method of time-varying delay based on genetic algorithm

- Computer Science
- Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693)
- 2003

Simulation results show that the identification precision is satisfied, and GA (genetic algorithm) is used to track the time-varying delay, which can simultaneously evaluate many points in the parameter space, and increase the likelihood of finding the global optimum solution. Expand

Identifiability of a nonlinear delayed-differential aerospace model

- Computer Science, Mathematics
- IEEE Transactions on Automatic Control
- 2006

This technical note shows the identifiability of a nonlinear delayed-differential model describing aircraft dynamics, which requires initial conditions corresponding to an equilibrium state, which is implemented during the experimentation. Expand

Delay identification in time-delay systems using variable structure observers

- Mathematics, Computer Science
- Annu. Rev. Control.
- 2006

Several algorithms for the delay identification based on variable structure observers are proposed and some of them are based on existing estimation techniques as well as identifiability studies. Expand