An optimal PID controller design for nonlinear optimal control problems with continuous state inequality constraints

In this paper, we consider an optimal PID control problem subject to continuous state inequality constraints. By applying the constraint transcription method, a local smoothing technique to these continuous state inequality constraint functions, we construct the corresponding smooth approximate functions. Then, by using the concept of the penalty function, these smooth approximate functions are appended to the cost function, forming a new cost function. Then, the constrained optimal PID control problem is approximated by a sequence of unconstrained optimal control problems. Each of which can be viewed and hence solved as an unconstrained nonlinear optimization problem. The gradient formula of the new appended cost function is derived, and a reliable computation algorithm is given.