Open AccessAn optimal PID controller design for nonlinear constrained optimal control problems
Author(s) -
Bin Li,
Kok Lay Teo,
ChengChew Lim,
Guang Ren Duan
Publication year - 2011
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2011.16.1101
Subject(s) - optimal control , pid controller , mathematical optimization , smoothing , constraint (computer aided design) , control theory (sociology) , nonlinear system , penalty method , mathematics , sequence (biology) , terminal (telecommunication) , computer science , control (management) , engineering , control engineering , temperature control , statistics , physics , quantum mechanics , artificial intelligence , biology , telecommunications , geometry , genetics
In this paper, we consider a class of optimal PID control problems subject to continuous inequality constraints and terminal equality constraint. By applying the constraint transcription method and a local smoothing technique to these continuous inequality constraint functions, we construct the corresponding smooth approximate functions. We use the concept of the penalty function to append these smooth approximate functions to the cost function, forming a new cost function. Then, the constrained optimal PID control problem is approximated by a sequence of optimal parameter selection problems subject to only terminal equality constraint. Each of these optimal parameter selection problems can be viewed and hence solved as a nonlinear optimization problem. The gradient formulas of the new appended cost function and the terminal equality constraint function are derived, and a reliable computation algorithm is given. The method proposed is used to solve a ship steering control problem.Bin Li, Kok Lay Teo, Cheng-Chew Lim and Guang Ren Dua