With a special choice for the system state equations, the use of the simplest quadratic form as candidate Lyapunov function directly leads to the definition of very simple, smooth and effective closed loop control laws for unicycle-like vehicles, suitable to be used for steering, path following, and navigation. The authors provide simulation examples to show the effectiveness and, in a sense, the “natural behavior” of the obtained closed loop motions (when compared with everyday driving experience

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The increased demand on robotic manipulator performances leads to the use of advanced control structures. An adaptive model following control system for robotic manipulators is developed via hyperstability theory. A new control algorithm is proposed that produces a discontinuous control signal, similar to a pulse amplitude signal, so that particular trajectories, referred as sliding modes, occur. The design procedure is simple and effective and always assures the asymptotic stability in the large. The decoupling properties can be achieved by a suitable choice of the reference model. A case study is developed by numerical simulation.