nonlinear systems

The model-based controllers need a mathematical model of the system, whereas the data-driven controllers operate based on measuring the input-output data. Nowadays, considering complexity of the industrial systems and unavailability of an accurate mathematical model of the system, scientists try to reduce dependency of the controllers on the mathematical model. In this paper, an adaptive sliding-mode data-driven controller for a class of unknown multi-input multi-output nonlinear discrete-time systems is proposed. Because the chattering phenomenon is the main challenge of the sliding-mode controllers, an adaptive sliding-mode controller is used to solve this problem. In addition, to solve the dependencies of the controller on the mathematical model, the proposed adaptive sliding-mode controller is combined with a data-driven controller. Next, the new adaptive laws for the switching gain and the Pseudo Jacobian Matrix (PJM) are calculated. In addition, the closed-loop stability based on the Lyapunov theory is investigated. To show performance of the controller, the proposed method is applied to a three-tank system. The proposed controller has some advantages in comparison with similar methods in references, such as reducing the conservatism and complexity in the controller design and simplifying the closed-loop stability analysis. The simulated results show that the proposed method better tracks the reference signals and improves rejection of the external disturbances. Furthermore, the chattering phenomenon is considerably reduced.

In this paper, a new algorithm of Gaussian sum filters for state estimation of nonlinear systems is presented. The proposed method consists of several parallel Cubature Kalman filters each of which is implemented according to the simplex spherical-radial rule. In this method, the probability density function is the sum of the weights of several Gaussian functions. The mean value, covariance, and weight coefficients of these Gaussian functions are calculated recursively over time, and each of the Cubature Kalman filters are responsible for updating one of these functions. Finally, the performance of the proposed filter is investigated using two nonlinear state estimation problems and the results are compared with conventional nonlinear filters. The simulation results show the appropriate accuracy of the proposed algorithm in state estimation of nonlinear systems.

This paper considers the work entitled “Dynamic Sliding Mode Control Design for Nonlinear Systems Using Sliding Mode Observer” that is published in Tabriz Journal of Electrical Engineering where the authors try to design a sliding mode control design with sliding mode observer for a class of nonlinear systems. In this paper, we first give a brief overview of the proposed approach of aforementioned paper to the observer design. For the convergence of the estimation error, there is a proposition that we will discuss the validity of its proof. Finally, with a change in dynamic error equations of observer, its stability is proven.

This paper focuses on designing multiple-controller for nonlinear dynamic systems. An algorithm is proposed that integrates two stages of selecting the nominal local models and designing the local controllers. The proposed algorithm does not need to a priori knowledge about the system and a prior experience to choose the gridding threshold. In order to design the local controllers, the stability and performance criteria are integrated and the local controllers have a simple Proportional-Integral (PI) structure. Although the simple local PI controllers lead to have a simple global multiple-controller, but the bump phenomenon occurs when switching between the active local controller in the closed-loop and another controller in the off-line controllers set waiting to take over the control loop. In order to solve the lift-off and landing issues by switching among different local controllers, a linear quadratic bumpless transfer method is used in the closed-loop. The off-line local controllers were not fed by the error signal to have a bumpless switch. Therefore, the proposed multiple-controller design method provides support to have a gentle switch among different local controllers. To evaluate the proposed method a nonlinear CSTR is simulated. The simulation results demonstrate the success of the proposed method in set-point tracking with a smooth control signal in comparison with the opponents.

In this paper, a robust model predictive control (MPC) algorithm is designed for nonlinear uncertain systems in presence of the control input constraint. To achieve this goal, first, the additive and polytopic uncertainties are formulated in the nonlinear uncertain system. Then, the control policy is chosen as a state feedback control law in order to minimize a given cost function at each known sample-time. Finally, the robust MPC problem is transformed into another optimization problem subject to some linear matrix inequality (LMI) constraints. The controller gains are determined via the online solution of the proposed minimization problem in real-time. The suggested method is simulated for a second order nonlinear uncertain system. The closed-loop performance is compared to other control techniques. The simulation results show the effectiveness of the proposed algorithm compared to some existing control methods.

Lyapunov method is an effective method to prove the stability of the equilibrium points of dynamical systems. One of the applications of the Lyapunov analysis, is estimation of the region of attraction. In general, based on the selected Lyapunov function, a portion of the region of attraction is estimated that may not be the best. In this paper, via proposing an algorithm for generating Lyapunov candidate functions in a series from, a method is developed by which, in each step ahead, a modified estimation of the region of attraction is presented. The main idea of generation of the mentioned entries, is constructing a new Lyapunov function using a linear combination of the current Lyapunov function with its derivative. According to each candidate Lyapunov function, a region of attraction is constructed so that in the generation process of the new functions, every estimated region of attraction is subset of the next estimation. Finally, to show the effectiveness of the obtained results, some numerical examples are simulated.

This paper proposes a new computed torque strategy to control the robotic manipulators using polytopic linear parameter varying (LPV) modeling method. An LPV representation of the robot is generated by identification of its dynamic in different workspace points about an arbitrary full-path trajectory. Identification of the models is done by using the least square of errors  algorithm. By utilization of parameter set mapping based on parameter component analysis (PCA) a reduced polytopic LPV model is obtained that reduces the complexity of the implementation. In the conventional computed torque control, it is necessary to know the dynamical model of the robot while in the proposed method an estimation of the required torque is computed based on the obtained LPV model. The control gain matrix is derived by solving a set of linear matrix inequalities (LMIs) that takes the time derivative of the Lyapunov function to the sufficiently small value. Sufficient conditions are provided to ensure the asymptotic stability of the closed loop LPV system against the torque estimation error. The proposed scheme is applied to trajectory tracking control of a six degree of freedom (DOF) PUMA 560 robot manipulator.

In the investigation presented with a focus on the applicability of adaptive control based on neural network to nonlinear systems in the presence of uncertainties, an adaptive control in association with intelligent tools with the key goal of adjusting nonlinear system’s parameters under control is designed. For having a novel idea in this area, at first, an exact consideration is made in one such case concerning the similar works that have all provided to deal with the similar systems under control and then the proposed control approach is designed based on the neural networks. Using Lyapunov theory, adaptive laws suitable for the convergence of the closed loop system is provided. Using this theory, it is proved that all signals in the closed loop system are bounded and the error signal converges to zero as asymptotically. At the end, the results of simulation programs via MATLAB verifies the effectiveness of the control approach proposed.

The main purpose of this paper is to present an adaptive-neural controller for strict-feedback nonlinear systems with unknown time delays and in the presence of external disturbances and actuator failure. The proposed adaptive-neural controller is constructed based on DSC design technique. Radial Basis Functions (RBF) networks are utilized to approximate unknown nonlinear functions. Adaptive rules are obtained based on Lyapunov design for updating the parameters of neural networks. Disturbances are unknown functions which their bounds are partially known. Therefore, continuous robust terms are applied in order to minimize their effects. Furthermore, due to the existence of unknown time delays in the system, Lyapunov–Krasovskii functionals are utilized in the process of designing the controller and proofing the stability of the system. In addition, the controller is designed so that it can compensate its effect if the considered actuator failure happens. For the designed controller, the boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighborhood of the origin.

In this paper, based on the state-dependent Riccati equation (SDRE) technique, a new method is proposed to design nonlinear observers in a  broadclass of networked control systems. Towards this end, an inequality condition is obtained to detect the time-instants of sending messages from the sensors to the controller. In this way, the data transmission is done in some specific instants and therefore, the proposed method can considerably reduce the information exchange between the sensors and the controller in a nonlinear networked control system. It is also proved that the obtained estimation converges to the system state. Two numerical simulations are worked to illustrate the design procedure and the flexibility of the proposed observer.

In this paper, an observer-based adaptive fuzzy back-stepping controller for a class of strict-feedback nonlinear delayed systems with unknown control coefficientis proposed. The system has unknown delayed nonlinear terms and unknown disturbances. The goal is to design an appropriate controller such that the system output tracks the desired trajectory with prescribed bounds while the closed-loop signals remain bounded. An adaptive mechanism is designed such that by using Fuzzy approximators, the unknown functions are approximated via adaptation laws. In addition, an observer is designed such that immeasurable states are estimated. In order to avoid the “explosion of complexity” that exists in traditional back-stepping controllers, the so-called Dynamic Surface Control is used at each steps of the traditional back-stepping approach. Furthermore, Barrier Lyapunov function is employed to consider constraints on the system output. Besides, Nussbaum function is utilized to address the unknown control gain problem. The proposed adaptive controller guarantees that all signals in the closed-loop are semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation results on a delayed nonlinear system with unknown control coefficient confirm the effectiveness of the proposed approach.

This paper presents an adaptive state feedback control scheme for a class of nonlinear systems with unknown parameters, variable control gains and in the presence of unknown time varying actuator failures. The designed controller compensates unknown loss of effectiveness failures as well as unknown time varying stuck failures in actuators. The considered actuator failure can cover most failures that may occur in actuators of the practical systems. The proposed adaptive controller is constructed based on a backstepping design method. Appropriate Lyapunov-Krasovskii functionals are introduced to design new adaptive laws to compensate the unknown actuator failures and unknown parameters. The offered method ensures the asymptotic output tracking and the boundedness of all the closed-loop signals. The proposed design approach is employed for a wing rock control of an aircraft in the presence of time varying actuator failures. The simulation results verify the effectiveness and correctness of the proposed adaptive control method.