Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

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An algorithm, based on sliding mode control and graph algebraic theories, for the provision of consensus to a swarm of self-propelling agents is presented. Swarms, comprised of agents with first-order dynamics, that can be described by fully-connected and connected graphs with time-invariant topologies are considered. For consensus, the agents' inputs are designed to enforce sliding mode on surfaces that depend on the graph Laplacian matrix. The property of sliding mode occurring within a finite time interval, which can be varied, is lent to the swarm and it is this facet that distinguishes the proposed algorithm. As will be shown, applying this algorithm results the swarm achieving a constant consensus value equal to the average of the largest and smallest initial states of the agents. Owing to this result, by introducing a virtual agent with a precalculated initial condition, the algorithm allows for the tuning of the consensus value.