A two-level costate prediction algorithm for non-linear systems

Digital LQR control scheme to maintain the separation distance of the NASA benchmark tetrahedron constellation

“…The existence of the optimal control is obtained from the solution of the Hamilton-Jacobi equation which is defined everywhere to obtain a minimum-time problem, but the definitions for a minimum time problem in a digital control are defined differently as explained in Refs. [10,14]. The system of discrete linear equations can be defined from Eq.…”

Control of Complex Systems

“…When such problems are tackled by the Maximum Principle, nonlinear two-point-boundary-valueproblems appear and may be solved using several successive approximation methods (Meyer 1973, Falb andDe Jong 1969). There has also been much interest in the development of hierarchical algorithms for the dynamic optimization of nonlinear systems (Hassan and Singh 1977, Mahmoud 1978, Singh and Hassan 1978. The main disadvantage of all these techniques is that the solution is only possible numerically, i.e the obtained control law is in open-loop form.…”

A Survey of the Power System Control Problem

“…It is also quite evident that the hierarchical optimisation may lead to computational saving in both storage and computer time. Amongst these techniques are L _J the methods given in [6,13,14] which are characherised by the simplicity of the corresponding algorithms. These techniques are often limited to off-line computations of open-loop control laws.…”

“…However, a certain number of difficulties in this approach appear and especially in the on-line implementation. Hierarchical techniques [13][14][15][16][17] have been recently used to overcome some of these difficulties. This paper presents a comprehensive survey of the main different techniques, developed in the literature, for solving these types of problems stating the difficulties due to their applications.…”