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Increasing pursuer capturability by using hybrid dynamics

Glizer V. Y., Turetsky V.

International Journal of Applied Mathematics and Computer Science

2015

Vol. 25, no. 1

77--92

A robust interception of a maneuverable target (evader) by an interceptor (pursuer) with hybrid dynamics is considered. The controls of the pursuer and the evader are bounded. The duration of the engagement is prescribed. The pursuer has two possible dynamic modes, which can be switched once during the engagement, while the dynamics of the evader are fixed. The case where for both dynamic modes there exists an unbounded capture zone was analyzed in our previous work. The conditions under which the pursuer can increase its capturability by utilizing the hybrid dynamics were established and the new robust capture zone was constructed. In the present paper, we extend this result to the cases where at least for one dynamic mode of the pursuer the capture zone is bounded. For these instances, conditions of increasing the pursuer’s hybrid capturability are derived. Respective capture zones are constructed. Illustrative examples and results of extensive simulation for a realistic non-linear engagement model in the presence of a random wind are given.

Correctness of a constrained control Mayer's problem for a class of singularly perturbed functional-differential systems

Glizer V. Y.

Control and Cybernetics

2008

Vol. 37, no 2

329-351

A Mayer's problem for a singularly perturbed controlled system with the general type of a small state delay is considered. The control is subject to geometrical constraints. The cost functional is a function of the terminal value of the slow state variable. A simpler parameter-free optimal control problem (the reduced problem) is associated with the original problem. A convergence of the optimal value of the cost functional in the original problem to the optimal value of the cost functional in the reduced problem, as a parameter of singular perturbation tends to zero, is established. An asymptotic suboptimality of the optimal control of the reduced problem in the original problem is shown. These results are extended to some more general optimal control problems. An illustrative example is presented.