A chebyshev polynomial method for optimal control with state constraints

Abstrsct--This paper presents a numerical technique for solving non-linear constrained optimal control problems. The method extends previous contributions to non-linear unconstrained optimal control problems and is based upon a Chebyshev series expansion of state and control. The differential and integral expressions from the system dynamics and the performance index, the boundary conditions and other general conditions are converted into some algebraic equations. State inequality constraints are transformed into equality constraints through the use of slack variables. The technique may start from a feasible or non-feasible trajectory and avoids problems of singular arcs. The applicability is illustrated on two well-known state variable inequality constrained optimal control problems. Extensions of the approach to problems with other equality and inequality constraints on state and control are described but have not yet been tested on practical examples.