Aldo-Jonathan Muñoz-Vázquez

Uniformly continuous differintegral sliding mode control of nonlinear systems subject to Hölder disturbances

An integral sliding mode controller based on fractional order differintegral operators is proposed. This controller generalizes the classical discontinuous (integer order) integral sliding mode scheme. By using differintegral operators, their topological properties lead to a uniformly continuous controller that enforces an integral sliding mode for any initial condition. In addition, it is demonstrated that the proposed scheme is robust against matched Holder continuous, but not necessarily differentiable, disturbances and uncertainties. Also, asymptotic convergence of tracking errors is assured for any initial condition by means of an ideal controller, even in presence of anomalous but Holder continuous disturbances. It is worth to mention that the salient properties of our proposal (i.e. invariance at any initial condition, uniform continuity, and robustness to non-differentiable disturbances) are not provided by any existing integer order sliding mode based controller of the literature. The viability of the proposed scheme is shown in a representative simulation study.

Continuous fractional sliding mode-like control for exact rejection of non-differentiable Hölder disturbances

Exploiting algebraic and topological properties of differintegral operators as well as a proposed principle of dynamic memory resetting, a uniform continuous sliding mode controller for a general class of integer order affine non-linear systems is proposed. The controller rejects a wide class of disturbances, enforcing in finite-time a sliding regime without chattering. Such disturbance is of Hölder type that is not necessarily differentiable in the usual (integer order) sense. The control signal is uniformly continuous in contrast to the classical (integer order) discontinuous scheme that has been proposed for both fractional and integer order systems. The proposed principle of dynamic memory resetting allows demonstrating robustness as well as: (i) finite-time convergence of the sliding manifold, (ii) asymptotic convergence of tracking errors, and (iii) exact disturbance observation. The validity of the proposed scheme is discussed in a representative numerical study.

Attitude tracking control of a quadrotor based on absolutely continuous fractional integral sliding modes

The model-free sliding mode control based on fractional order sliding surface is built upon: i) An absolutely continuous control structure that does not require the exact dynamic model to induce a fractional sliding motion in finite time, and ii) A methodology to design fractional references with a clear counterpart in the frequency domain is proposed. This in order to improve the system response, in particular the transient period, and to generate a high-performance during the sliding motion. Numerical simulations support the proposal and illustrates the closed-loop system, which provides a better insight of the proposed scheme.

Free-model fractional-order absolutely continuous sliding mode control for euler-lagrange systems

Euler-Lagrange systems, such as robots, exhibit benign structural properties, including passivity, which allow us to design robust and efficient energy-shaping controllers. A great variety of passivity-based control schemes are available and recently model-based fractional order discontinuous sliding mode control has been proposed. In this paper, a fractional order absolutely continuous control scheme for Euler-Lagrange systems is proposed, without depending on the dynamic model, which enforces in finite-time a commensurable rational fractional order regime. Additionally, a frequency domain analysis is addressed, which is very useful for some applications. A numerical simulation assessment is presented, including the frequency domain response based on Bode plots. Final concluding remarks are discussed in view of the state of the art in fractional order controllers.

A novel continuous fractional sliding mode control

ABSTRACT A new fractional-order controller is proposed, whose novelty is twofold: (i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodelled dynamics, and (ii) based on a principle of dynamic memory resetting of the differintegral operator, it is enforced an invariant sliding mode in finite time. Both (i) and (ii) account for exponential convergence of tracking errors, where such principle is instrumental to demonstrate the closed-loop stability, robustness and a sustained sliding motion, as well as that high frequencies are filtered out from the control signal. The proposed methodology is illustrated with a representative simulation study.

Generalized order integral sliding mode control for non-differentiable disturbance rejection: A comparative study

Aiming at clarifying recent advances on disturbance rejection, we analyze a class of non-differentiable disturbances. We expose some subtle but fundamental differences between the fractional order (FO) and integer order (IO) integral sliding modes (ISM) to control a general class of nonlinear dynamical systems. This comparative study suggests that our proposed FOISM outperforms the extremely popular IOISM scheme when the dynamical system is subject to Hölder continuous but not necessarily differentiable disturbances. The drawbacks and advantages of the FOISM are discussed, including its capacity to reject Hölder disturbances with chattering alleviation. It is shown that the proposed method provides a uniform continuous control signal assuring robustness and invariance for any initial condition. Simulation results reveal the structural differences of these schemes, showing the viability of our proposal.

A passive velocity field for navigation of quadrotors with model-free integral sliding mode control

Velocity field (VF) control has proved effective for mobile robots and robot arms, aiming essentially at navigation and obstacle avoidance under position and velocity control in cluttered environment, however additional features are required for quadrotors due to its underactuated flight dynamics. The design of a VF control then comprises of two aspects, the design of the desired trajectories based on the VF and the design of the controller that guarantees tracking of such trajectories. In this paper, we propose a constructive method to design a passive VF for desired underactuated translational velocities; for desired orientation trajectories and due to the underactuation, those depend on the VF and the position controller from the analytical solution of the derivative of the rotation matrix. The controller uses model-free and chattering-free integral sliding modes for position and for attitude dynamics without requiring derivative of the VF nor assumption on boundedness on the integral of the VF nor the quadrotor dynamic model to withstand robustness against parametric and model uncertainties. It is shown that the controller steers the quadrotor onto the VF for all time and any initial conditions so as to the quadrotor behaves accordingly to the properties of the VF, such as exponential convergence toward the time-invariant nominal spatial contour for a robust and fast, yet smooth, approaching for easy manoeuvring. Simulations are discussed, and remarks address the viability of the proposed approach.

Passive Velocity Field Control for contour tracking of robots with model-free controller

A simple, fast and robust Passive Velocity Field Control (PVFC) scheme for contour tracking in 2D and 3D is presented. A model-free and chattering-free second order sliding mode controller is proposed, which enforces an invariant manifold for all time such that the generalized velocity tracks the spatial velocity field. A constructive simple and intuitive method to design this velocity field is built upon a fuzzy aggregation of orthogonal vectors to guide the end-effector subject to a dissipative map. Stability properties in the sense of Lyapunov establish the fast and yet smooth tracking with typical robustness of sliding modes. In this way, the closed-loop system exhibits the mildness of PVFC but it evades the subtle complexities of the original approach PVFC. A simulation study is discussed, and experimental results highlight the characteristics of the proposed approach.

Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Holder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Holder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

A Passive Velocity Field Control for Navigation of Quadrotors with Model-free Integral Sliding Modes

Velocity field (VF) control has proved effective for kinematic robots, aiming essentially at providing desired velocities for navigation along the field, and for obstacle avoidance in cluttered environments. When robot dynamics are involved, it is usually considered either that dynamics are known and that robot is fully actuated, thus it is not clear how to deal with VF control (VFC) for unknown underactuated dynamics, such as for a quadrotor. Moreover, passive VF (PVF) stands for an attractive methodology for quadrotors because of it yields time-invariant nominal spatial field for smooth approaching and easy manoeuvring. In this paper, we propose a constructive method to design a PVF-based controller with a chattering-free integral sliding modes for local exponential position tracking. The salient feature of our proposal is the passive nature of the field as well as the controller is model-free for the complete standard quasi-Lagrangian dynamic model of the quadrotor. The controller does not require the derivative nor any assumption on boundedness on the integral of the VF, yet the closed-loop withstands robustness against parametric and model uncertainties. Simulations are discussed, and remarks address the viability of the proposed approach.