A computationally effective suboptimal control algorithm for linear-quadratic regulator problems with state variable inequality constraints can be developed through collocation and approximation of the state and control variables by cubic splines.
Summary--A suboptimal control algorithm for linearquadratic regulator problems with state variable inequality constraints (SVIC) is developed. The state and control variables are approximated by cubic splines on an uniform mesh. Through collocation at the knots, the dynamic equations and SVIC are reduced to a set of linear algebraic equations and the suboptimal control is constructed from the solution of a quadratic programming problem with sparse matrices. The number of non-zero storage elements required for these matrices varies linearly with the number of mesh points.
Computational experience for specific examples is presented and compared with other approaches described in the literature. Good to excellent accuracy is obtained with modest computational requirements. Memory considerations and on-line implementation are discussed. From both the computational and storage aspects, the approach offers an effective alternative for SVIC problems. Extensions of the algorithm to more general control problems are suggested.
1. Introduction
IN THE past 10 years there has been a marked interest in developing practical computational techniques for optimal control problems. While considerable success has been achieved for uncon-*