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Although sliding mode control has many drawbacks when applied to electrical drives due to real limitations of switches, as limited frequency of operation, turn on and turn off delays, some of its theory can be succesfully used in order to project a high performance controller, robust and with a reduced design effort. This paper shows the use of sigmoidal function, hyperbolic tangent, instead of the...
This paper presents the design procedure of the integral sliding mode controller with enhanced robustness properties for a class of nonlinear uncertain systems. The integral sliding mode control (I-SMC) is synthesized with the generalized disturbance attenuation scheme called robust internal-loop compensator (RIC) through the Lyapunov redesign framework, thus introducing a generalisation of the well-known...
A control strategy for the regulation of a PVTOL, based on output-feedback, is introduced. To this end, a couple of controllers or actuators that operate concurrently are proposed. One of them stabilizes the vertical variable in finite time, by means of a novel sliding mode controller. The other actuator uses the energy control approach to balance, simultaneously, the horizontal and angular variables...
This article proposes two control strategies to track a desired altitude of an Unmanned Aircraft System (UAS). These strategies are a Super-Twisting Sliding Mode Controller (Super Twisting-SMC) and a Modified Super-Twisting Sliding Mode Controller (Modified Super Twisting-SMC), both controllers are robusts and present a satisfactory effectiveness even under external disturbances. The Lyapunov Stability...
In this paper, the problem of designing robust non-fragile guaranteed cost state feedback controller for a class of continuous-time singular piecewise-affine systems is considered. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the robust non-fragile stabilization condition is established, and meanwhile, the condition of...
We consider a class of flexible joint manipulator system which is nonlinear and contains uncertainty. The inertial matrix can be used to construct Lyapunov function, even though some of the joints are prismatic. We construct subsystems via backstepping method and suggest a state transformation under which implanted control is used. From this state transformation, a robust controller, which is only...
This paper is devoted to the development of a new saturated control law for constrained Takagi-Sugeno fuzzy systems. These systems are subject to both control input and state constraints and also persistent disturbances bounded in amplitude. The design procedure is formulated through linear matrix inequalities (LMIs) form which can be solved by means of convex optimization techniques. Based on the...
This work is devoted to the construction of feedback laws which guarantee the robust global exponential stability of the uncongested equilibrium point for general discrete-time freeway models. The feedback construction is based on a control Lyapunov function approach and exploits certain important properties of freeway models. The developed feedback laws are tested in simulation. A comparison with...
We consider the design of self-triggered controllers for Lipschitz nonlinear systems subject to additive disturbances. The goal of the controller design is to avoid measurements and input changes as long as possible, while guaranteeing good performance subject to the worst case disturbances. Furthermore, the controller should be practically implementable. The controller is based on the emulation of...
For stabilizing model predictive control adjusting the prediction model requires the adjustment of the terminal set and terminal cost. However, the conventional methods to design these are not practical, and often impossible, to implement in microcontrollers. In this paper, we pre-compute the terminal cost and terminal set in a form that allows to adjust them with minimal computational effort, following...
This paper introduces a class of fixed-time stable dynamical systems with settling time as a explicit parameter, namely the inverse the gain. Those systems are defined as predefined-timed stable dynamical systems. Continuous and discontinuous are cases are presented. A detailed Lyapunov characterization of this class of systems is also shown. Finally, the application to the design of a class of first...
In this paper we show how to design robust and gain-scheduled controllers for linear continuous-time parameter-varying systems without quadratic stability. Parameter-independent Lyapunov functions are constructed, of which quadratic stability is a particular case. Examples illustrate the application of the resulting stabilization conditions, which are Linear Matrix Inequalities with a set of tuning...
This paper deals with the problem of control of partially known nonlinear systems, which have an open-loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main contribution is the identification of a class of systems for which a globally stable PI can be designed knowing only the systems input matrix and measuring only the actuated...
We present conditions for robust stability of a class of linear systems interconnected by uncertain nonlinear, norm-bounded functions. We show that such conditions can be reformulated as classical small gain like conditions for a related linear system. Under further assumptions that render the related linear system positive, we show that we can achieve sharp tractable conditions for robust stability...
This paper provides synthesis conditions of robust state feedback control law for continuous-time linear time-invariant systems with polytopic uncertainty. By conveniently expressing the Lyapunov stability condition of the closed-loop system and using the elimination lemma, a new LMI synthesis condition with scalar searches is proposed. As main novelty, the scalar search is constrained to the interval...
This paper deals with a robust synchronization problem for multistable systems evolving on manifolds in the context of Input-to-State Stability (ISS) framework. Based on a recent generalization of classical ISS theory to multistable systems (may have unstable equilibrium), a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system. The invariant...
Whereas synchronization (consensus, agreement) in linear networks has been thoroughly studied in recent years up to certain exhaustiveness, reaching a synchrony among general nonlinear agents still remains a hard open problems. In this paper, we propose a general criteria of synchronization in undirected networks with nonlinear nodes, based on the idea of incremental dissipativity. We show that our...
This work solves the obstacle avoidance problem extending the Potential Field (PF) method for a mobile robot. The usual definition of the PF has been modified to have a field which is continuous everywhere. It is shown that the system has an attracting equilibrium at the target point, repelling equilibriums in the centers of the obstacles and saddle points on the borders. Those unstable equilibriums...
This paper presents a stabilizing Model Predictive Control (MPC) algorithm based on the off-line computation of a sequence of 1-step controllable sets and a condition that enables flexible, non-monotone convergence towards a suitably chosen terminal set. Such an off-line computed sequence of sets leads to a large region where the MPC algorithm is feasible, regardless of the length of the prediction...
This paper addresses the problem of robust output feedback controller design with guaranteed cost and multiple quadratic Lyapunov function for linear switched systems in the continuous-time domain. The approach followed in this paper looks at the existence of switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality...
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