The development of a nonlinear controller of stabilization of underactuated mechanical systems (UMSs) is a challenging endeavor due to a larger number of output variables to be controlled than the control input space. This paper proposes an adaptive sliding mode control based on a higher-order nonlinear disturbance observer (HONDO) for stabilizing the rotational pendulum (RP) system falling under the class of UMSs. Firstly, the HONDO is designed in such a way that it can improve accuracy in estimations with its incremental order. As a result, the proposed controller obtained from the sliding surface which is developed with system’s states and estimations, forces the states attaining the sliding mode and hence keeps them to their origin forever against disturbances. To achieve this, the sliding coefficients are obtained using inertia matrix of the system. The zero dynamics is stabilized by the proposed controller. This alleviates the chattering problem in the control input. Finally, numerical performance on the underactuated RP model is analyzed to show the efficiency of the proposed controller and it is compared with the established control technique found in the literature.

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In this article, a sliding mode control–based nonlinear guidance scheme for controlling both impact angle and impact time simultaneously is proposed. The problem of impact angle control is first transformed to that of controlling line-of-sight angle and its rate, while the requirement of impact time is achieved by tracking the desired time-to-go. The chosen time-to-go estimate accounts for the curvature required to meet the impact angle requirements toward the target interception. In order to satisfy both of these terminal constraints, the sliding surface is defined as a combination of impact time error and the variable pertaining to the errors in line-of-sight angle and its rate, with appropriate gains assigned to them. The interceptor first performs necessary maneuvers to meet the impact time requirements and then steers its course to achieve the target interception at a desired impact angle. The guidance law is initially derived using nonlinear engagement kinematics against stationary targets and then extended to cater to constant velocity targets using the concept of predicted interception point. Numerical simulations are performed to validate the efficacy of the proposed guidance scheme for various initial engagement geometries. The performance of the proposed guidance scheme is also compared with those of the existing guidance laws and shown to be superior.

This paper proposes predefined-time convergent guidance schemes that can drive the pursuer on a collision course corresponding to the target interception from a pre-specified impact direction, irrespective of initial engagement geometries. The target interception at the desired impact angle is first transformed into a problem of controlling the line-of-sight angle and its rate. Then, guidance commands are derived using sliding mode control (SMC) to ensure the convergence of corresponding errors to zero within a predefined time. A nonlinear disturbance observer is used to estimate the target’s maneuver, and the estimation error is treated as an uncertainty while rejecting its effect by virtue of SMC. Guidance commands are also derived for the case where the target maneuver is completely unknown except for its upper bound. It was shown that the gain could be selected based on the maximum bound on target maneuver to enforce sliding mode on the chosen surface, and thus guarantees target interception at a pre-specified impact angle, provided the closing speed of the engagement is positive. Owing to the use of a nonlinear framework while deriving pursuer guidance commands, the proposed guidance strategies remain valid even for engagements with large initial deviations where schemes based on linearized dynamics may fail or have degraded performance. The efficacy of the proposed guidance methods is validated through simulations for the pursuers having constant speed and time-varying speed, for various engagement geometries. The results of proposed strategies are compared with those of existing guidance and shown to be superior.