Semi-Global Predefined-Time Stable Vector Systems

In this paper, we expose a control function which allows the semi-global predefined-time stabilization of first-order vector systems. The predefined-time stability is a stronger class of finite-time stability that has as main advantage the settling time as a tunable parameter of the proposed function. To design that stabilizing function, we use the unit control principle jointly to the inverse incomplete gamma function. For the resulting expression, the domain of definition the inverse incomplete gamma function can be made as large as wanted with an appropriate parameter selection, and, as consequence, the attraction domain of the systems. Therefore, we say that the system exhibits semi-global predefined-time stability. As an essential feature, the parameter which defines the settling time bound and those that tune the attraction domain are independent of each other. Finally, the constructed function is used to design predefined-time stabilizing controllers which are robust against vanishing and non-vanishing perturbations

Predefined-Time Backstepping Control for Tracking a Class of Mechanical Systems

The predefined-time exact tracking of unperturbed fully actuated mechanical systems is considered in this paper. A continuous second-order predefined-time stabilizing backstepping controller, designed using first-order predefined-time stabilizing functions, is developed to solve this problem. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show performance of the proposed control scheme.Consejo Nacional de Ciencia y Tecnologí

A Second Order Predefined-Time Control Algorithm

The predefined-time stabilization of second-order systems, i.e. the fixed-time stabilization with settling time as a function of the controller parameters, is revisited in this paper. The proposed controller is a time-based switched controller which first drive the system trajectories to a linear manifold in predefined time and then uses a nested second order controller. The application of the results is demonstrated for the trajectory tracking control in fully actuated mechanical systems. An illustrative example of the control of a two-link planar manipulator with predefined-time convergence shows the effectiveness of the proposed algorithm

Backstepping Design for the Predefined-Time Stabilization of Second-Order Systems

The backstepping design of a controller which stabilizes a class of second-order systems in predefined-time is studied in this paper. The origin of a dynamical system is said to be predefined-time stable if it is fixed-time stable and an upper bound of the settling-time function can be arbitrarily chosen a priori through an appropriate selection of the system parameters. The proposed backstepping construction is based on recently proposed Lyapunov-like sufficient conditions for predefined-time stability. Different from other approaches, the proposed backstepping design allows the simultaneous construction of a Lyapunov function which meets the conditions for guaranteeing predefined-time stability. A simulation example is presented to show the behavior of a developed controller, and to show its advantages against similar schemes.ITESO, A.C

Predefined-time stabilization of high order systems

The aim of this paper is to introduce a controller that stabilizes a class of arbitrary order systems in predefined-time. The proposed controller is designed with basis on the block-control principle yielding in a nested structure similar to high order sliding mode algorithms and terminal sliding mode algorithms. For this case, it is assumed the availability of the state and the absence of perturbations. Numerical simulations expose the desired performance of this controller

Predefined-time tracking of a class of mechanical systems

In this paper the problem of predefined-time exact tracking of fully actuated and unperturbed mechanical systems is solved by means of a continuous controller. It is assumed the availability of the state and the desired trajectory as well as its two first derivatives. This is accomplished introducing the idea of second-order predefined-time stable systems, which is based on the nested application of the first-order predefined-time stabilizing function. As an example, the proposed solution is applied over a two-link planar manipulator and numerical simulations are conducted to show its performance.ITESO, A.C.CINVESTA

A Note on Predefined-Time Stability

This note presents a new characterization for predefined-time-stable systems based on Lyapunov stability. In contrast to the previous results in predefined-time stability, the proposed characterization allows the construction of predefined-time stabilizing controllers with polynomial terms instead of exponential ones, removing the exponential nature hypothesis of predefined-time-stable systems. Moreover, the existing Lyapunov characterization of predefined-time stability is shown to be a consequence of the new theorem presented in this paper. Finally, the proposed approach is used for the construction of robust predefined-time stabilizing controllers for first-order systems. A simulation example shows the feasibility of the proposed methods.Consejo Nacional de Ciencia y Tecnologí

An Integral Sliding Mode Observer for Linear Systems

In this paper a sliding-mode observer for linear time-invariant systems is proposed. The observer is based on integral sliding modes and the equivalent control method. In order to induce a sliding mode in the output error, a second order sliding mode algorithm is used. Convergence proofs of the proposed observer are presented. In order to expose the features of this proposal, a design example over a DC motor model is exposed, noiseless and noisy measurements cases are considered. For this case, the simulation shows the high performance of the integral observer.ITESO, A.C.Universidad Nacional de ColombiaCINVESTAV-IP