Finite-time optimal control of polynomial systems using successive suboptimal approximations
The paper is focused on the problem of time-optimal control of polynomial systems. It shows that this optimalization problem may be solved on the way of creation of a sequence of optimal control problems for the linear problem. The subject of the paper is the controlled object \[ \dot{x}=p(x,u,t) \] where \(x \in R^{n}, u \in R^{m}\). The problem deals with a quadratic criterion of optimality. As problem solution it has been presented an iterative procedure. The proposed method consists of the following steps: i. Quasi-linearization of the polynomial system at the step \(k \rightarrow 1\) around of the solution of iteration \(k\). ii. Solution of the optimal control problem. A proof of the convergence is presented, i.e., the iteration converges if the weight \(R\) on the control inputs is large. Numerical examples interpret the idea of problem solution.
scientific article; zbMATH DE number 1523638