AN OPTIMAL PID CONTROLLER DESIGN FOR NONLINEAR CONSTRAINED OPTIMAL CONTROL PROBLEMS

作者：Li Bin^*; Teo Kok Lay; Lim Cheng Chew; Duan Guang Ren

来源：Discrete and Continuous Dynamical Systems-Series B, 2011, 16(4): 1101-1117.

DOI：10.3934/dcdsb.2011.16.1101

• Nonlinear optimal control
• continuous inequality constraints
• constraint transcription
• local smoothing
• penalty function
• PID controller
• computational algorithm
• ship steering control

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.

• 出版日期2011-11
• 单位哈尔滨工业大学