Numerical methods for optimal control problems with state constraints
The author considers optimal control problems with pathwise state inequality constraints of the form \[ \min_u\Phi(x(1)), \] \[ x'(t)= f(t,x(t),u(t))\;\forall t\in [0,1],\;x(0)= x_0, \] \[ u(t)\in \Omega,\quad h^1_i(x(1))= 0,\quad h^2_j(x(1))\leq 0. \] For this problems, first- and second-order solution methods are discussed. The book has the following chapters: 1. Introduction, 2. Estimates on solutions to differential equations and their approximations, 3. First order method, 4. Implementation, 5. Second-order method, 6. Runge-Kutta based procedure for optimal control of differential-algebraic equations. In the Appendix A, a primal range-space method for piecewise-linear quadratic programming is given. The author gives also remarks on numerical software developed in connection with the derived methods.
scientific article; zbMATH DE number 1342607