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In this paper, an impulsive observer–based controller is designed for a class of Lipschitz nonlinear systems with time–varying uncertainties. The impulsive observer uses only sampled measurements of the system output. Sufficient conditions for the existence of the controller are given in terms of Linear Matrix Inequalities, obtaining exponential stability to the origin of the system state and the state estimation error. The performance of the proposed impulsive observer–based controller is tested via simulations.

Status epilepticus is an emergency condition in patients with prolonged seizure or recurrent seizures without full recovery between them. The pathophysiological mechanisms of status epilepticus are not well established. With this argument, we use a computational modeling approach combined with in vivo electrophysiological data obtained from an experimental model of status epilepticus to infer about changes that may lead to a seizure. Special emphasis is done to analyze parameter changes during or after pilocarpine administration. A cubature Kalman filter is utilized to estimate parameters and states of the model in real time from the observed electrophysiological signals. It was observed that during basal activity (before pilocarpine administration) the parameters presented a standard deviation below 30% of the mean value, while during SE activity, the parameters presented variations larger than 200% of the mean value with respect to basal state. The ratio of excitation-inhibition, increased during SE activity by 80% with respect to the transition state, and reaches the lowest value during cessation. In addition, a progression between low and fast inhibitions before or during this condition was found. This method can be implemented in real time, which is particularly important for the design of stimulation devices that attempt to stop seizures. These changes in the parameters analyzed during seizure activity can lead to better understanding of the mechanisms of epilepsy and to improve its treatments.

SUMMARYControlling a walking biped robot is a challenging problem due to the robot's complex and uncertain dynamics. In order to tackle this problem, we propose a sliding mode controller based on a dynamic model that we obtained using the conformal geometric algebra (CGA) approach. An important contribution of this paper is the development of algorithms using the CGA framework. The CGA framework permits us to use lines, points, and other geometric entities to obtain the Lagrange equations of the system. The references for the joints of the robot were obtained in a bio-inspired way following the kinematics of a walking human body. The first and second derivatives of the reference signal were obtained via an exact robust differentiator based on a high-order sliding mode. We analyzed the performance of the proposed control schemes by using bio-inspired walking patterns and simulations.

Recent studies suggest that the appearance of signals with high frequency oscillations components in specific regions of the brain is related to the incidence of epilepsy. These oscillations are in general small in amplitude and short in duration, making them difficult to identify. The analysis of these oscillations are particularly important in epilepsy and their study could lead to the development of better medical treatments. Therefore, the development of algorithms for detection of these high frequency oscillations is of great importance. In this work, a new algorithm for automatic detection of high frequency oscillations is presented. This algorithm uses approximate entropy and artificial neural networks to extract features in order to detect and classify high frequency components in electrophysiological signals. In contrast to the existing algorithms, the one proposed here is fast and accurate, and can be implemented on-line, thus reducing the time employed to analyze the experimental electrophysiological signals.

Continuous stirred tank bioreactors with non-monotonic growth kinetics can exhibit bifurcation and multiple equilibrium points. Maximum productivity for this bioreactor is located at the limit of a bifurcation. Therefore, when the desired operating point is near optimal productivity, even small perturbations may drive the system from stability to an undesired, unstable condition. This work describes a fuzzy servo controller that was designed based on sector nonlinearities to force the bioreactor to stay near its optimal productivity point. The designed controller enables tracking of a reference signal that switches between stable and unstable nodes and finally stabilizes at the optimal operating point. Two reference signals were evaluated for the substrate and the biomass respectively. The performance of the proposed controller was compared to PID and LQ controllers. Linear matrix inequalities were used to prove the closed-loop stability.

In this paper the problem of stabilization of continuous systems with time delay in input which are discretized is addressed. Using a predictor based controller capable of stabilizing and compensating the discrete model and continuous model as well, is obtained. This scheme allows using a digital controller for stabilizing an analog plant. The performance of such a control scheme is tested in the case of simplified attitude control of a vehicle.

Controlling the pose of a manipulator involvesfinding the correct configuration of the robot’s elementsto move the end effector to a desired position and orientation.In order to find the geometric relationshipsbetween the elements of a robot manipulator, it is necessaryto define the kinematics of the robot. We presenta synthesis of the kinematical model of the pose forthis type of robot using the conformal geometric algebraframework. In addition, two controllers are developed,one for the position tracking problem and another for theorientation tracking problem, both using an error feedbackcontroller. The stability analysis is carried out forboth controllers, and their application to a 6-DOF serialmanipulator and the legs of a biped robot are presented.By proposing the error feedback and Lyapunov functionsin terms of geometric algebra, we are opening a newvenue of research in control of manipulators and robotlegs that involves the use of geometric primitives, suchas lines, circles, planes, spheres.

This paper presents a structurally stable scheme for nonlinear systems which do not satisfy the so-called FIB conditions for the existence of a linear solution to the structurally stable regulator solution, namely, the case when some necessary detectability condition with respect to the original system’s output does not hold. Under certain additional conditions, it is shown that the proposed scheme guarantees zero output tracking error between the actual output and the desired reference signal, in spite of the presence of parameter variations. Application to the model of a rotary inverted pendulum shows the effectiveness of the proposed scheme.

In this paper, we address the problem of stabilizing a continuous nonlinear Takagi-Sugeno fuzzy model, by means of its Takagi-Sugeno fuzzy discrete model. We extend the classic result for linear systems, namely, a feedback control law that stabilizes the discretization of a continuous linear system, stabilizes this continuous system as well.

This paper applies the block control technique to design a sliding mode regulator that guarantees asymptotic reference tracking for a class of linear delayed systems with disturbances. This class of systems are those presented in so-called block controllable form with delay. The block control technique is used to derive a sliding manifold on which the motion of the closed-loop system is stable, and the tracking error is zeroed. Examples of the application of the proposed control strategy and observer design are illustrated.

"Recently, technological advances have been focused on the cockpit of modern unmanned aerial vehicles (UAVs) in order to reduce pilot requirements and workload to operate them. First person view (FPV) flight represents a key point when UAVs perform tasks beyond the line of sight. This paper presents the design and implementation of a cockpit for a remotely operated quadrotor. We have developed an intuitive graphical user interface (GUI) for piloting the quadrotor encompassing the most relevant flight instruments as an altimeter, attitude, heading, and ground speed indicators. The GUI is developed using the programming development environment LabVIEW®."

In this paper, a block decomposition procedure for sliding mode control of a class of nonlinear systems with matched and unmatched uncertainties, is proposed. Based on the nonlinear block control principle, a sliding manifold design problem is divided into a number of sub-problems of lower dimension which can be solved independently. As a result, the nominal parts of the sliding mode dynamics is linearized. A discontinuous feedback is then used to compensate the matched uncertainty. Finally, a step-by-step Lyapunov technique and a high gain approach is applied to obtain hierarchical fast motions on the sliding manifolds and to achieve the robustness property of the closed-loop system motion with respect to unmatched uncertainty. Copyright © 2002 John Wiley & Sons, Ltd.

This paper combines the block control and sliding mode control techniques to design a discontinuous regulator for a class of nonlinear systems presented in so-called Nonlinear Block Controllable Form with matched and unmatched uncertainties. The Sliding Mode Regulation Problem is formulated, and the existence solution conditions are derived.

This paper presents a robust scheme for nonlinear systems which does not satisfy the so-called FIB conditions for the existence of a robust regulator solution, namely, the case when some necessary detectability condition with respect to the measurable output does not hold. Under certain additional condition, it is shown that the proposed scheme guarantees zero output tracking error between the actual output and the desired reference signal, in despite of the presence of parameter variations.

A robust control scheme for the output tracking of nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. It is shown that if perturbations and/or uncertainties appear on the system, the sliding mode controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.

This paper proposes the design of a fuzzy observer which uses both discrete and continuous measurements and updates the initial condition of the state of the system at each sampling instant to ensure the convergence of the estimation error. The proposed fuzzy observer is tested to estimate the substrate and biomass concentration of an anaerobic wastewater treatment process. The observer performance is compared via numerical simulation with two fuzzy observers which use only continuous measurements, showing a faster convergence rate. Finally, the whole estimation scheme is validated using experimental data from an anaerobic digestion process.

The dynamics of the electric motors and generators (synchronous and induction) are highly nonlinear and content uncertainties including plant parameters variations magnetic saturation and external disturbances (load torque). On the other hand, the electric machine models are described by a class of nonlinear minimum phase systems which include the strict-feedback form or the nonlinear block controllable form (NBC-form) and stable residual stable. Therefore, in this case, to design a stabilized controller it is naturally to applied some feedback linearization (FL) technique: input-output (IO) linearization [9], backstepping (BS) [11] or block control (BC) ( [13]- [15]). It is interesting to note that the BC approach has some advantage comparing with the IO and BS ones.

In this work an integrated attitude control of a vehicle is designed. The actuators considered are the active front steering, the rear torque vectoring, and the semi–active suspensions. We design also an algorithm for the saturation management. The resulting controller is hybrid. In nominal conditions, when saturation conditions do not occur, a feedback guarantees exponential tracking of the reference trajectories. In critical conditions, a hybrid feedback law assigns higher priority to some states to improve the tracking. It is shown that the saturation management improves the controller performance. Some simulations results are provided, showing the performance of the proposed controller.

In this paper a controller based on the so–called robust or structurally stable regulation theory is designed. The ground vehicle motion control is reformulated as a tracking problem of a desired reference, generated by an external system. Moreover, the disturbance acting on the vehicle is supposed to be modeled, i.e. unknown but with a known structure, as happens in many typical situations. The use of immersion techniques eliminates the dependence of the controller on parameters, so obtaining a controller ensuring zero tracking error. Since an immersion for the designed control law can not be easily determined, in this paper we consider the immersion of an approximate expression of the control, so obtaining a bounded tracking error.

Analogously to the formulation of the so-called classical servomechanism problem, the problem of tracking a reference signal while rejecting the effect of a disturbance signal by means of the VSS technique is studied by formulating the sliding mode servomechanism problem for which conditions for the existence of a solution for in general case and for a classes of nonlinear system presented in the Regular Form or in the Nonlinear Block Controllable Form are derived. The effectiveness of the proposed method is demonstrated by the application to the Pendubot system.

Conventional internal combustion engines use mechanical camshafts to command the opening and closing phases of the intake and exhaust valves. The lift valve profile is designed to reach a good compromise among various requirements of the engine operating conditions. In principle, optimality in every engine condition can be attained by camless valvetrains. In this context, electromagnetic valves offer an interesting solution, although there are still some relevant open problems to be solved before they can be introduced in production. One of the main problem is due to the fact that valve position and velocity sensors should not be used, due to the constraint in terms of actuator cost and space limitations. In this work an observer-based controller is proposed, ensuring the so called "soft-landing". This controller, based on a state controller derived making use of the regulation theory, exploits an observer of the the state variables not measured and of the disturbance acting on the system.

In this work, the output regulation theory is combined with a dynamic neural identifier, in order to improve the robustness properties for trajectory tracking on SISO nonlinear system's. A neural network is used to identify the dynamics of the nonlinear system, by a suitable on-line training, which ensures small identification error. Then, the output regulation technique is applied to the neural network to obtain a controller that, when applied to the original system, guarantee also a bounded output tracking error despite the presence of parameter variations and external perturbations. Simulation results on a model of a chaotic system are presented showing the viability and effectiveness of the proposed technique.

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the nonlinear regulation theory are combined in order to construct a controller capable of taking the output of the fuzzy plant to the reference signal generated by an external system. The fuzzy modelling allows the controller to be designed by means of numerical techniques while the resulting stability region is larger than those obtained when simple linear controllers are used to stabilize nonlinear systems. On the other hand, it is well-known that a fuzzy regulator constructed from linear controllers does not solve the regulation problem in general. Therefore, a fully nonlinear regulator is considered in this work. The results are applied on the pendubot, which is an under-actuated electromechanical system with very complex nonlinear dynamics.

In this paper, the problem of sensor faults detection (SFD) to non-linear systems is addressed using a modified dedicated observers approach originally proposed by Clark [1], The new approach use sliding mode fuzzy dedicates observers for the Takagi-Sugeno fuzzy model of the non-linear dynamic system to generate the signal residuals that indicate a fault condition in the system. This approach provides robustness to parametric variations in the plant.

This paper addresses a linear matrix inequalities (LMI) based fuzzy robust regulation as a control method to synchronize two Lorenz' chaotic attractors. On basis of the so called internal model approach, a methodology for the controller design is presented. By means of a combination of an exact Takagi-Sugeno (T-S) fuzzy model for the Lorenz attractor and the fuzzy regulation, a control law for the original nonlinear system is proposed. Concerning the stability property of the overall control system, sufficient conditions in the form of LMI's are derived. By the design of local controllers for each subsystem, the regulation feature is achieved. The controller construction is described and the synchronization objective verified by numerical simulations

In this work we design a controller for sliding mode output regulation of induction motors. The rotor fluxes are not measured and the load torque is a known perturbation term generated by an exosystem, which generates also the reference signals to be tracked. The sliding mode regulator problem is briefly revisited and then solved for the induction motor. The control here designed tracks any reference and rejects any disturbance generated by the exosystem

The Error Feedback Sliding Mode Regulation Problem has been introduced. Solution conditions are derived for linear systems and different classes of nonlinear systems including systems presented in the Regular and NBC-forms. In particular, the combination of VSS and block control techniques allows straightforward solutions to be obtained, specially when compared to the classical solutions of the error feedback regulator problem. Additionally the sliding mode based controller achieves robustness with respect to the uncertainty.

In this paper we present the design of a robust discretized controller based in the theory of regulation for nonlinear systems. In the general command tracking and disturbance rejection problem, it is known that a sample data controller using zero order holder may only guarantee asymptotic tracking at the sampling instances. We show that by means of a so-called exponential holder, we are able to guarantee asymptotic zero output tracking error, not only in the sampling instant, but also between these instant. Some considerations on the design of exponential holders are presented. The application in simulation to some typical nonlinear systems shows the good performance of the proposed scheme.

The problem of controlling an underactuated system, the so-called seesaw-inverted pendulum, consisting in two cars, one of them with an inverted pendulum and placed on a balancing seesaws, is addressed. The simulation and experimental results for tracking a reference signal are presented.

Underactuated mechanisms provide significant challenges to control engineers. In this paper a nonlinear controller, based on regulation theory is applied to an underactuated system, the so-called Pendubot, consisting in a double pendulum actuated only at the first joint. Simulation and experimental results for tracking a reference signal are presented.

The problem of output regulation with sliding mode is studied. The proposed solution to this problem is based in a set of linear reduced order matrix equations in the case of linear systems, and for a class nonlinear systems in the so-defined regular form, in a set of partial differential equations. A discontinuous dynamical feedback control law is constructed to provide the output asymptotic tracking and disturbance rejection requirements.

The combination of a recurrent neural network with the output regulation control theory is proposed so that a robust controller for general nonlinear discrete time systems is obtained. It is intended with this approach to profit from the identification capabilities of neural networks with the stability properties of the output regulation theory. Given the universal approximation properties, a recurrent neural network is applied for modelling nonlinear systems. Learning is implemented online, based on input-output data, ensuring that the learning error converges to zero. Due to the combination of the adaptive neural learning procedure aspect and the output regulator technique the proposed control scheme behaves with strong robustness with respect to unknown dynamics and nonlinear characteristics. To solve the regulator equations a new iterative procedure is presented. The proposed algorithm, based on the recurrent neural network ensures the convergence of the regulator equations. Experimental results collected from a laboratory heating system confirm the viability and effectiveness of the proposed methodology.

This paper focuses on the design of an error feedback sliding mode regulator able to achieve the asymptotic tracking of a reference trajectory for linear systems. It is assumed that the reference trajectory is generated by means of neutrally stable unforced systems. The solution conditions are derived for linear systems presented in general, Regular and Block controllable forms.