The problem of the nonlinear synthesis of speed-of-response-wise suboptimal bounded controls when there is interference (Q1921555)

A class of nonlinear control systems is considered in the presence of unknown but bounded perturbations. The following problem is considered: synthesize a robust control law satisfying given geometric constraints and taking the system from an arbitrary initial point of a given set \(D\) into a given equilibrium point in finite time. This problem is reduced (by means of nonlinear change of variables and a special choice of construction of the control laws) to solving a linear differential game problem. The minimum guaranteed stabilization time is estimated and sufficient conditions are proved. As an illustration, the proposed method is applied to a problem of reorientation of a spacecraft and the corresponding numerical results are presented.