• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.244-251
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• 2005

In this paper, we study the problem of stabilizing a general nonlinear control system by means of gradient descent control method which is a dynamic feedback control law. In this method, the general nonlinear control system can be considered as an affine nonlinear control systems. Then by using Sontag's formula we investigate the stability (asymptotic) of the general nonlinear control system.

• International Journal of Control, Automation, and Systems
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• v.5 no.4
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• pp.397-409
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• 2007

In this paper, we propose a nonlinear guidance law for missiles against maneuvering targets. First, we derive the equations of motion described in the line-of-sight reference frame and then we define the equilibrium subspace of the nonlinear system to guarantee target interception within a finite time. Using Sontag's formula, we derive a nonlinear guidance law that always delivers the state to the equilibrium subspace. If the speed of the missile is greater than that of the target, the proposed law has global capturability in that, under any initial launch conditions, the missile can intercept the maneuvering target. The proposed law also minimizes the integral cost of the control energy and the weighted square of the state. The performance of the proposed law is compared with the augmented proportional navigation guidance law by means of numerical simulations of various initial conditions and target maneuvers.