An SQP method for optimal control of weakly singular Hammerstein integral equations
The authors consider the following nonlinear optimal control problem: \[ \text{Minimize} \qquad \int^T_0 \varphi(t,x(t), u(t))dt \] subject to \[ x(t)= \int^t_0 k(t,s) b(s,x(s), u(s))ds, \qquad \text{and }|u(t)|\leq 1, \] where \(x\in C[0,T]\), \(u\in L_\infty (0,T)\), \(\varphi\), \(b\) and \(k\) are real-valued functions with certain smoothness and growth properties. The local convergence of an SQP method for solving this problem is discussed. Sufficient conditions for local quadratic convergence of that technique are derived.
scientific article; zbMATH DE number 883409
scientific article