Parametric variational procedure to solve index-3 semi explicit linear-regulator control problem with constrained robot illustration

Abstract

The aim of this work is to solve 2-dimensional, 3-links linearized constrained robot problem. This problem is of index-three linear descriptor control problem. Since the aim is to regulate its output, a quadratic performance index is proposed to form an index-3 linear regulator optimal control problem. Firstly, the problem has been transformed into standard constrained optimal control problem over class of consistent initial condition with solvability assumptions. Secondly, the solution of differential-algebraic equation has been shown as equivalent to find the critical points of some variational formulation and vise- versa. Then aggregating all functional (performance one) with consistent initial conditions in one performance (weighted) index. Under standard topology of the solvability, a parametric approach has been proposed to approximate the state-space solutions with control over the class of constraints. Hence, an infinite dimensional problem is transformed into finite one, and then an approximate solutions is obtained by solving the class of linear algebraic equations. The proposed approach is easily implemented and accurate up to decision maker selections of the parameterization basis functions and their numbers.