On the continuity properties of the attainable sets of control systems with integral constraints on control

Attainable Sets of Integral Constrained Seir Control System With Nonlinear Incidence

“…Approximate computational techniques and some topological characteristics are present in attainable sets of affine control systems with integral limitations for control have been studied in [10], [11], [17]. In publications [12][13][14][15], these analyses are generalized for the fully nonlinear case, and [15] presents an approximation approach for computing the reachable sets in a specified terminal time.…”

On the compactness of the attainable sets of control systems with $p$-integrable controls

“…Linear systems are well studied and most properties of attainable sets are proved [4,5]. For nonlinear systems, attainable sets are still an object of active study (see, e. g., [1][2][3][6][7][8]). Consider a control system whose behavior is described by the differential equation where x 2 R n is the n-dimensional phase state vector of the system, u 2 R r is the r-dimensional control vector, t 2 OEt 0 ; T .t 0 < T < 1/ is the time, f .t; x/ is an ndimensional vector function, B.t; x/ is an .n r/-dimensional matrix function, and…”

The approximation of reachable sets of control systems with integral constraint on controls

“…In papers (see, [3,8,11,17] and references therein) the numerical methods for construction and estimation of the reachable sets of the control systems with geometrical constraints on control are considered. Control systems with integral constraints on control have been investigated in [2,6,7,9,10,12,13,16].…”