Some Applications of Hamilton–Jacobi Inequalities for Classical and Impulsive Optimal Control Problems

Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control

“…Integral relation in (2) is a sort of constraints that are sometimes called "soft" or "energetic bounds" [10], and makes sense of an a priori estimation (qualitatively expressed by a given positive real M ) of the total resource of controller over the time period T . Systems of type (1), (2) and related control problems arise in a series of real life applications of mathematical control theory in mechanics, economics and management (see, e.g., the monographs [8,14,22], and the bibliography therein).…”

Variable Time Impulse System Optimization with Continuous Control and Impulse Control

“…In the infinite time horizon optimization problem, conditions (6) to (14) are still valid. The boundary condition at the final time, given in (15), is no longer needed.…”

“…Studies on this topic can be traced back to the 1960s when optimal impulse orbit transfer was investigated [6]. Methods of dynamic programming [13,14] and maximum principle [15][16][17] have been studied in the literature. In recent decades, necessary conditions for optimality have been proposed for different classes of impulse systems [7][8][9][10][11][12].…”

“…In recent decades, necessary conditions for optimality have been proposed for different classes of impulse systems [7][8][9][10][11][12]. Methods of dynamic programming [13,14] and maximum principle [15][16][17] have been studied in the literature.…”

Invariance for impulsive control systems

“…This explains why a considerable body of theory for this class of systems (see, for example, [1,2,[8][9][10][11][12][13][14][15][16][17][18][19], and references therein) and supporting control strategies computation schemes, [20][21][22][23] have been developed so far.…”