Optimal state-delay control in nonlinear dynamic systems

This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameteri...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 135; p. 109981
Main Authors: Liu, Chongyang, Loxton, Ryan, Teo, Kok Lay, Wang, Song
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.01.2022
Subjects:
Control parameterization
Delay systems
Numerical optimization
Optimal control
Delay systems
Numerical optimization
Control parameterization
Optimal control
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:This paper considers a class of nonlinear systems in which the control function is a time-varying state-delay. The optimal control problem is to optimize the time-varying delay and a set of time-invariant system parameters subject to lower and upper bounds. To solve this problem, we first parameterize the delay in terms of piecewise-quadratic basis functions, thus yielding a finite-dimensional approximate problem with continuous-time inequality constraints induced by the delay bounds. We then exploit the quadratic structure of the delay to convert these continuous-time constraints into a finite set of canonical point constraints. We also develop an efficient numerical method for computing the gradients of the system cost function. This method, which involves integrating an auxiliary impulsive system with time-varying advance backwards in time, can be combined with any existing gradient-based optimization algorithm to generate approximate solutions for the optimal control problem.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2021.109981