Abstract In this paper an active controller for ground vehicles stability is presented. The objective of this controller is to force the vehicle to track a desired reference, ensuring safe driving conditions in the case of adhesion loss during hazardous maneuvers. To this aim, a nonlinear discrete-time inverse optimal control based on a neural network identification is designed, using a recurrent high order neural network (RHONN) trained by an Extended Kalman Filter. The RHONN ensures stability of the identification error, while the controller ensures the stability of the tracking errors. Moreover, a discrete-time reduced order state observer is utilized to reconstruct the lateral vehicle dynamic not usually available. For the control problem, the references of the lateral velocity and yaw rate are given by a dynamic system mimicking an ideal vehicle having not-decreasing tire lateral characteristics. The proposed approach avoids the identification of the Pacejka’s lateral parameters of the tires, so simplifying the input control determination. Moreover, an optimal control is proposed to optimize the actuator effort and power, usually bounded. Control gains are determined using optimal “nature-inspired" algorithms such as particle swarm optimization. Test maneuvers, performed through the full vehicle simulator CarSim®, have been used to test correctness, quality and performances of the observer, the neural identifier and the inverse optimal controller. Robustness of the reduced order discrete-time state observer is also discussed for different sample times. Finally, a fair comparison between optimal and non-optimal control schemes is presented, highlighting the numerical results obtained in simulation.

Controlling walking biped robots is a challenging problem due to its complex and uncertain dynamics. In order to tackle this, we propose a sliding mode controller based on a dynamic model which was obtained using the conformal geometric algebra approach (CGA). 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 bio-inspired in the kinematics of a walking human body. The first and second derivatives of the reference signal were obtained through an exact robust differentiator based on high order sliding modes. The performance of the proposed control scheme is illustrated through simulation.

Trajectory tracking has been long ago set into a formal mathematical framework through the nonlinear output regulation theory. Results thereby derived have been hardly implemented in a systematic way due to their complexity, which forces the designer to lead with expressions which are not necessarily computationally tractable. Fuzzy regulation has intended to fill this gap by introducing systematic procedures based on Takagi-Sugeno models and linear matrix inequalities. This paper offers a systematic approach to solve the nonlinear output regulation problem via state feedback and convex representations of the required mappings; in contrast with former results, this one takes full advantage of the time-derivatives of the membership functions. Moreover, it is fully based on element-wise linear matrix inequalities which are numerically solvable by interior-point-based methods.

The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.

In this paper, a fuzzy nonlinear ripple-free regulator is proposed to solve the sample-data structurally stable regulation problem for the case of nonlinear or generalized immersion. This regulator guarantees asymptotic tracking of time-varying references and rejection of disturbances while maintaining the closed-loop stability. Such a regulator is based on a continuous fuzzy error feedback controller, which updates its states at each sampling period and relies on the existence of an internal model. The internal model is obtained by determining, if possible, an observable generalized immersion of the exosystem dynamics. A key feature is that this immersion allows the generation of all the possible steady-state inputs for all admissible values of the system parameters. The robustness of the proposed fuzzy controller, under parameter uncertainties and changes on disturbance signals, is tested in an illustrative example.

An adaptive tracking controller for a discrete-time direct current (DC) motor model in presence of bounded disturbances is presented. A high order neural network is used to identify the plant model; this network is trained with an extended Kalman filter. Then, the discrete-time block control and sliding modes techniques are used to develop the reference tracking control. This paper includes also the respective stability analysis and a strategy to avoid specific adaptive weights zero-crossing. The scheme is illustrated via simulations for a discrete-time nonlinear model of an electric DC motor.

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.

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 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.

This paper is concerned with the design of a robust regulator capable of achieving trajectory tracking for discrete-time nonlinear systems under parameter uncertainty. By assuming that the behavior of the nonlinear system is described, at least locally, by a Takagi-Sugeno dynamic fuzzy model, an approach based in the combination of this fuzzy modeling and the regulator theory is presented. Conditions for the existence of a robust regulator under this approach are then derived and extended to include the use of the linear matrix inequality (LMI) technique.

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.