Optimal control, via Riccati equations, by doubling, Newton's and Smith methods

报告人： Dr Eric King Wah Chu（Monash University，澳大利亚）

报告题目: Optimal control, via Riccati equations, by doubling, Newton's and Smith methods

报告时间：12月12日 下午3：00—4：00
报告地点： D座207

摘要: The optimal control problem for continuous- or discrete-time systems can be solved via algebraic, differential or difference Riccati equations. For small systems, many methods have been successful for the solution of these equations. For large-scale problems, notably from PDE boundary control, only a couple of techniques are available. Newton's method leads to some associated Lyapunov equations which can then be solved by ADI or Galerkin projection methods. The approach requires a difficult initial stabilization step and a heuristic choice of ADI parameters. The structure-preserving doubling algorithm proves to be a competitive alternative. For systems with stochastic disturbances, the problem becomes even more difficult and no good method is available, especially for large systems. In this talk, we shall review the techniques for the solution of stochastic algebraic, differential and difference Riccati equations, ending with a Newton's method and a homotopy method for the stochastic optimal control problem.