Numerical solution of constrained optimal control problems with parameters (Q1354307)

The following optimal control problem with state, control and parameter inequality constraints is considered \[ J= \Phi \bigl(x(t_f), w\bigr)+ \int^{t_f}_{t_0} L\bigl(x(t), u(t),w\bigr) dt\to \min \] subject to \(\dot x=f(x,u,w)\), \(0=c(x,u,w)\), \(0\leq d(x,u,w)\), \(0= \psi_0 (x(t_0),w)\), \(0= \psi_j (x(t_f),w)\). The author uses a penalty function technique to transform the inequality constrained problem into a problem without inequality constraints. Applying a multiple shooting (continuation method), the author solves the first-order necessary conditions for optimality. The effectiveness of the numerical procedure is demonstrated via some examples.