Robust stabilization of uncertain nonlinear slowly-varying systems: application in a time-varying inertia pendulum.

This paper considers the problem of robust stabilization of nonlinear slowly-varying systems, in the presence of model uncertainties and external disturbances. The main contribution of this paper is an extension of the Slowly-Varying Control Lyapunov Function (SVCLF) technique to design a robust stabilizing controller for nonlinear slowly-varying systems with matched uncertainties. In the proposed strategy, the Lyapunov redesign method is utilized to design a robust control law. This method, originally, leads to a discontinuous controller which suffers from chattering. In this paper, this problem is removed by using a saturation function with a high slope, as an approximation of the signum function. Since, using the saturation function leads to loss of asymptotic stability and, instead, guarantees only the boundedness of the system's states; therefore, some sufficient conditions are proposed to guarantee the asymptotic stability of the closed-loop uncertain nonlinear slowly-varying system (without chattering). Also, in order to show the applicability of the proposed method, it is applied to a time-varying inertia pendulum. The efficiency of the designed controller is demonstrated through analysis and simulations.

Application of partial sliding mode in guidance problem.

In this paper, the problem of 3-dimensional guidance law design is considered and a new guidance law based on partial sliding mode technique is presented. The approach is based on the classification of the state variables within the guidance system dynamics with respect to their required stabilization properties. In the proposed law by using a partial sliding mode technique, only trajectories of a part of states variables are forced to reach the partial sliding surfaces and slide on them. The resulting guidance law enables the missile to intercept highly maneuvering targets within a finite interception time. Effectiveness of the proposed guidance law is demonstrated through analysis and simulations.

Partial stabilization-based guidance.

A novel nonlinear missile guidance law against maneuvering targets is designed based on the principles of partial stability. It is demonstrated that in a real approach which is adopted with actual situations, each state of the guidance system must have a special behavior and asymptotic stability or exponential stability of all states is not realistic. Thus, a new guidance law is developed based on the partial stability theorem in such a way that the behaviors of states in the closed-loop system are in conformity with a real guidance scenario that leads to collision. The performance of the proposed guidance law in terms of interception time and control effort is compared with the sliding mode guidance law by means of numerical simulations.

Stabilization of nonlinear systems with a slowly varying parameter by a control Lyapunov function.

Based on a control Lyapunov function (CLF) strategy, a novel approach for designing a controller for a slowly varying nonlinear system is proposed. The approach may be thought of as being in between the time-invariant and time-varying CLF techniques. If the time-invariant technique is used to control a slowly varying system, stability will not be guaranteed. On the other hand, the time-varying CLF technique, due to the control law, has complexity and needs to measure or estimate the derivative of system parameters. The advantage of the proposed method is its independence from the measurement or estimation of the derivatives of the system parameters. It is shown that the proposed control law can even be independent of the parameters of the system. In this paper, the conditions are derived that allow using the simple CLF formula that guarantees the stability of a slowly varying system. The efficiency of the approach is shown through some simulations.