Optimal-tuning of proportional-integral-derivative-like controller for constrained nonlinear systems and application to ship steering control

In this paper, we consider an optimal-tuning problem of proportional-integral-derivative-like (PID-like) controller for constrained nonlinear systems with continuous-time inequality constraints and a terminal state constraint. Due to the complexity of such constraints, it is difficult to solve this problem by using conventional optimization methods. To overcome this difficulty, a constraint transcription approach and a smoothing function are applied to these continuous-time inequality constraints. An augmented cost functional is obtained by appending these continuous-time inequality constraints to the cost functional. Then, this optimal-tuning problem can be converted into an approximate optimal parameter selection problem. The gradient formulae of the augmented cost function and the terminal constraint function are derived, and a gradient-based numerical algorithm is developed for solving this approximate problem. Convergence results show that there only exist a finite number of iterates such that the sequence obtained by using the algorithm is infeasible, and any optimal solution of the approximate problem is also an optimal solution of the original problem. Finally, a ship steering control problem is solved to illustrate the effectiveness of the approach proposed by us.