Robust block decomposition sliding mode control design

The paper examines the problem of sliding mode manifold design for uncertain nonlinear system with discontinuous control. The original plant first is decomposed such that the problem is divided into a number of simpler sub-problems. Then the block control recursive procedure is presented in which nonlinear sliding manifold is derived. Finally combined high gain and Lyapunov functions techniques are applied to establish hierarchy of the control gains and to estimate the upper bounds of the sliding mode equation solutions

Recurrent neural networks with fixed time convergence for linear and quadratic programming

In this paper, a new class of recurrent neural networks which solve linear and quadratic programs are presented. Their design is considered as a sliding mode control problem, where the network structure is based on the Karush-Kuhn-Tucker (KKT) optimality conditions with the KKT multipliers considered as control inputs to be implemented with fixed time stabilizing terms, instead of common used activation functions. Thus, the main feature of the proposed network is its fixed convergence time to the solution. That means, there is time independent to the initial conditions in which the network converges to the optimization solution. Simulations show the feasibility of the current approach.Consejo Nacional de Ciencia y Tecnologí

On optimal predefined-time stabilization

This paper addresses the problem of optimal predefined-time stability. Predefined-time stable systems are a class of fixed-time stable dynamical systems for which the minimum bound of the settling-time function can be defined a priori as an explicit parameter of the system. Sufficient conditions for a controller to solve the optimal predefined-time stabilization problem for a given nonlinear system are provided. These conditions involve a Lyapunov function that satisfies a certain differential inequality for guaranteeing predefined-time stability. It also satisfies the steady-state Hamilton–Jacobi–Bellman equation for ensuring optimality. Furthermore, for nonlinear affine systems and a certain class of performance index, a family of optimal predefined-time stabilizing controllers is derived. This class of controllers is applied to optimize the sliding manifold reaching phase in predefined time, considering both the unperturbed and perturbed cases. For the perturbed case, the idea of integral sliding mode control is jointly used to ensure robustness. Finally, as a study case, the predefined-time optimization of the sliding manifold reaching phase in a pendulum system is performed using the developed methods, and numerical simulations are carried out to show their behavior

A discontinuous recurrent neural network with predefined time convergence for solution of linear programming

The aim of this paper is to introduce a new recurrent neural network to solve linear programming. The main characteristic of the proposed scheme is its design based on the predefined-time stability. The predefined-time stability is a stronger form of finite-time stability which allows the a priori definition of a convergence time that does not depend on the network initial state. The network structure is based on the Karush-Kuhn-Tucker (KKT) conditions and the KKT multipliers are proposed as sliding mode control inputs. This selection yields to an one-layer recurrent neural network in which the only parameter to be tuned is the desired convergence time. With this features, the network can be easily scaled from a small to a higher dimension problem. The simulation of a simple example shows the feasibility of the current approach.Consejo Nacional de Ciencia y Tecnologí

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

Integral high order sliding mode control of a brake system

The aim of this paper is to present the design of a robust sliding mode control scheme for a vehicle system which consists of active brake systems. The proposed control strategy is based on the combination of high order sliding mode control methods and integral sliding mode control, taking advantage of the block control principle. The brake controller induces the antilock brake system feature by means of tracking the slip rate of the car, improving the stability in the braking process and preventing the vehicle from skidding.Cinvesta

Sliding mode control for Antilock Brake System

A Sliding Mode (SM) Block Control is proposed to control an Antilock Brake System (ABS). The control problem is to achieve reference tracking for the slip rate, such that, the friction between tyre and road surface is good enough to control the car. The closed-loop system is robust in presence of matched and unmatched perturbations. To show the performance of the proposed control strategy, a simulation study is carried on, where results show good behavior of the ABS under variations in the road friction.CINVESTAVUniversidad de Guadalajar

Semi-Global Predefined-Time Stable Systems

A Lyapunov-based construction of a predefined-time stabilizing function (a function that stabilizes a system in fixed-time with settling time as function of the controller parameters) for scalar systems is considered in this paper. The constructed function involves the inverse incomplete gamma function, causing this function to be semi-global, i.e., the domain of definition of the function can be made as large as wanted with an appropriate parameter selection. Finally, the constructed function is used to design predefined-time stabilizing controllers which are robust against vanishing and non-vanishing perturbations

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