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This paper deals with the problem of robust regulation of a Planar Vertical Takeoff and Landing (PVTOL) aircraft affected by crosswind disturbances. The proposed approach simultaneously exploits the advantages of passivity-based control and the integral sliding mode (ISM) control technique. We demonstrate that the passivity-based controller accomplishes the PVTOL regulation within a guaranteed stability region. At the same time, the ISM controller can effectively counteract the undesirable disturbances effect from the beginning of the operation since the disturbances are never seen in the measurable output. Using the passivity approach with LaSalle's Invariance Theorem, we construct the required Lyapunov function to establish the closed-loop system stability. The proposed combination of controllers results in a robust system that satisfactorily solves the regulation problem. Numerical simulations are provided to show that the proposed approach allows the tracking of different reference signals: pulse-train shaped trajectory and ellipse-shaped trajectory, considering the presence of perturbations (crosswind). Furthermore, to illustrate the effectiveness of the proposed technique, a comparative analysis considering two robust control strategies is provided. [ABSTRACT FROM AUTHOR]

In this work, we present a novel design of an explicit control strategy to solve the trajectory tracking problem for an uncertain second-order linear system with only partial availability of the state. The system parameters are unknown, and an additive constant disturbance is considered. Despite the apparent simplicity of this system, the solution requires an intricate combination of available methodologies. The proposed approach corresponds to a Lyapunov-based adaptive control strategy consisting of a reduced-order observer, a dynamic slave system and an adaptive controller with dynamic extension. Simulation results are provided to highlight the effectiveness of the proposed adaptive control strategy in accomplishing the regulation and trajectory tracking problems. [ABSTRACT FROM AUTHOR]

We present a proportional–integral–derivative-based controller plus an adaptive slide surface to solve the trajectory tracking control problem for a fully actuated vessel with unknown parameters perturbed by slowly varying external unknown dynamics. The controller design assumes that the vessel moves at low speed and frequency, its physical parameters are unknown, and its state is measurable. The control approach ensures error tracking convergence toward a small vicinity at the origin. We conduct the corresponding stability analysis using the Lyapunov theory and saturation functions. We tested the controller through two numerical experiments—a turning ellipse maneuver and a rest-to-rest maneuver—where the vessel parameters were unknown, and we obtained satisfactory results. [ABSTRACT FROM AUTHOR]

This paper presents the double chain–integrator finite-time convergence in a closed loop with a second-order bang–bang sliding control. The direct Lyapunov method carried out the stability analysis and the reaching time estimation using a suitable non-smooth strong Lyapunov function. That is, the proposed energy function is strictly positive definite, with a strictly definite negative time derivative. Additionally, the proposed function estimates the reaching time in the presence of matching bounded perturbations. Numerical comparisons with well-known approaches were performed to assess the proposed strategy's effectiveness. [ABSTRACT FROM AUTHOR]

We propose an adaptive stabilization solution for a linear second-order system with unknown parameters, where only the position and the sign of the constant associated with the control input are known. The control strategy consists in proposing a filter system with its whole state available and having the same structure as the uncertain system. Then, based on the Immersion & Invariance approach, and the Model Reference method, we design an adaptive controller to stabilize the filter system. Finally, using the backstepping approach, we stabilize the original uncertain system. We carry out the convergence analysis using the traditional Lyapunov method, in conjunction with the Barbalat’s Lemma. The obtained control strategy is simple and easy to implement. We assess the effectiveness of our adaptive control strategy through numerical simulations. [ABSTRACT FROM AUTHOR]

An algebra-based active disturbance rejection control approach for uncertain second-order flat systems, perturbed by a matching perturbation, is presented. This approach consists of proposing an online algebraic estimator for the uncertain system, together with an algebraic reconstructor for the unknown velocity. To assess the efficiency of the approach, numerical simulations to control an uncertain longitudinal vehicle system were carried out. [ABSTRACT FROM AUTHOR]

The adaptive stabilisation of uncertain second-order linear systems is addressed, under a lack of information from both states and parameters. The only standard assumptions are no zeros and the sign of the high frequency gain known. To the best of the authors' knowledge, there has been only an explicit solution proposed in the literature so far with proven stability. Despite the simplicity of the system, it does not fit in any of the standard nonlinear control methodologies available. Thus, this work is a complementary contribution providing a mixed control design strategy based on a reduced-order observer, adaptive Immersion & Invariance and Backstepping approaches. Hence, this solution depicts a transversal outlook of those nonlinear control strategies and provides a breakthrough for the generalisation of this non-trivial control problem. Numerical simulations are reported to assess the effectiveness of the adaptive strategy. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A nonlinear controller for the stabilisation of the Furuta pendulum is presented. The control strategy is based on a partial feedback linearisation. In a first stage only the actuated coordinate of the Furuta pendulum is linearised. Then, the stabilising feedback controller is obtained by applying the Lyapunov direct method. That is, using this method we prove local asymptotic stability and demonstrate that the closed-loop system has a large region of attraction. The stability analysis is carried out by means of LaSalle's invariance principle. To assess the controller effectiveness, the results of the corresponding numerical simulations are presented. [ABSTRACT FROM AUTHOR]

Abstract: The identification of the unknown parameters of the Duffing''s mechanical system, based on an algebraic approach, is presented. This approach is fast, accurate, and simple to numerically implement. Also, the method, combined with a suitable invariant filter, can became robust against high frequency output measurement noises. Our method uses the availability of one measurable output and produces an exact formula for the unknown parameters, which may be realized in terms of iterated convolutions. First, we show that the Duffing''s system parameters are linearly identifiable with respect to the position variable, then we obtain a linear system where the unknowns are the unavailable parameters. Suitable algebraic operations on the output differential equations makes the identification schema independent of the unavailable initial conditions of the underlying nonlinear dynamical system. [Copyright &y& Elsevier]

The authors are concerned in this study by bounded control of single input non‐linear under‐actuated mechanical systems. The authors focus the exposition on a feedback‐based stabilisation‐bounded control action shaped by saturation functions, and the proposed approach was illustrated via the design and the experimental evaluation of a simple stabilising controller for the cart–pendulum system, a well‐known control benchmark. The proposed simple control strategy is built around a lumped linear continuous time‐invariant description of the concerned under‐actuated non‐linear system. Namely, a model consisted of a cascade non‐linear dynamical system constituted by a chain of four integrators affected by a high‐order smooth non‐linear perturbation. Assuming initialisation of the under‐actuated system to the upper‐half plane, the proposed feedback‐based regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasi‐linear. Control boundedness is provided in both involved control actions by specifically designed saturation functions. The first bounded control action brings the non‐actuated coordinate near to the upright position and keep it inside of a well characterised small vicinity, whereas the second bounded control action asymptotically brings the whole state of the dynamical system to the origin. The necessary closed‐loop stability analysis uses standard linear stability arguments as well as the traditional well‐known Lyapunov method and the LaSalle's invariance principle. The proposed control law ensures global stability of the closed‐loop system in the upper‐half plane. [ABSTRACT FROM AUTHOR]