A Second Order Sliding Mode Controller with Predefined-Time Convergence

This paper presents the basis to design a well-suited control law which guarantees predefined-time convergence for a class of second-order systems. In contrast to the case of finite-time and fixed-time controllers, a predefined-time controller allows to set the bound of the convergence time, explicitly during the control design. Furthermore, in the case of no disturbance, the least upper bound of the convergence time can be predefined directly from the control definition. A Lyapunov-like characterization for predefined-time stability is performed. Numerical results are discussed to show the reliability of the proposed method.Consejo Nacional de Ciencia y Tecnologí

Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems

The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly reduced compared to classical CLFs, which makes \emph{flexible CLFs} more suitable for stabilization of constrained discrete-time nonlinear systems and real-time control. The purpose of this overview is to highlight the potential of flexible CLFs for real-time control of fast mechatronic systems, with sampling periods below one millisecond, which are widely employed in aerospace and automotive applications.Comment: 2 figure

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

A class of predefined-time stable dynamical systems

This article introduces predefined-time stable dynamical systems which are a class of fixed-time stable dynamical systems with settling time as an explicit parameter that can be defined in advance. This concept allows for the design of observers and controllers for problems that require to fulfil hard time constraints. An example is encountered in the fault detection and isolation problem, where mode detection in a timely manner needs to be guaranteed in order to apply a recovery action. Furthermore, through the notion of strong predefined-time stability, the approach hereinafter presented permits to overcome the problem of overestimation of the convergence time bound encountered in previous methods for the analysis of finite-time stable systems, where the stabilization time is often an unbounded function of the initial conditions of the system. A Lyapunov analysis is provided together with a detailed discussion of the applications to consensus and first order sliding mode controller design