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We introduce an algebraically active disturbance rejection-based control solution for the trajectory tracking problem of an uncertain second-order flat system with unknown external disturbances. To this end, we first algebraically identify the system’s unknown dynamics and the external disturbances with a linear set of time-varying integral expressions for the output and the control signal. We use the identified dynamics on an online feedback cancellation scheme to linearize the second-order system and cancel the uncertainties. With a proportional-integral controller we stabilize the linearized system without the need to estimate the velocity and have feedback from it. We carry out the stability analysis using linear systems theory. Finally, we evaluate the effectiveness of the proposed controller in a partially known 2-DOF manipulator.

We introduce a control strategy to solve the regulation control problem, from the perspective of trajectory planning, for an uncertain 3D overhead crane. The proposed solution was developed based on an adaptive control approach that takes advantage of the passivity properties found in this kind of systems. We use a trajectory planning approach to preserve the accelerations and velocities inside of realistic ranges, to maintaining the payload movements as close as possible to the origin. To this end, we carefully chose a suitable S-curve based on the Bezier spline, which allows us to efficiently handle the load translation problem, considerably reducing the load oscillations. To perform the convergence analysis, we applied the traditional Lyapunov theory, together with Barbalat’s lemma. We assess the effectiveness of our control strategy with convincing numerical simulations.

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]

We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension‐one and codimension‐two bifurcation analysis, and chaos control in a predator‐prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension‐two 1 : 2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results. [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]

The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.

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]

This work proposes a robust controller to solve the trajectory‐tracking control problem of planar vertical take‐off and landing (PVTOL) aircraft under crosswind. The controller combines input–output feedback linearization and active disturbance rejection control techniques. The former linearizes the PVTOL dynamics and the latter actively estimates and compensates for the crosswind effects. Numerical simulations assess the effectiveness of the proposed approach. [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]