Predictive sliding mode controller design for nonlinear systems

International audience

The work deals finite frequency H<sub>∞</sub> control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H<sub>∞</sub> lower can be by our method obtained developed where further comparison.

A practical reinforcement learning control design for nonlinear systems with input and output constraints

This paper studies the linear feedback control strategies for nonlinear systems. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function, which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations the Duffing oscillator and the nonlinear automotive active suspension system are provided to show the effectiveness of this method.

This study presents robust control architecture in the sense of variable structure control via a backstepping design. By using systematic backstepping design techniques, closed-loop behavior of an n-order nonlinear system can be transformed into a stability and convergence problem of a fast switched 2nd order system. There are two main parts contained within the proposed control algorithm; one is a nominal control effort generated according to the Lyapunov stability criterion during recursive backstepping processes, and the other belongs to a smooth robust control law designed to eliminate the effects of unknown lumped perturbations. Finally, a Genesio system is used as an illustrated example to demonstrate the robustness of the control algorithm. The feasibility and properties of the proposed method are given by numerical simulations.

An H∞ tracking-based adaptive fuzzy sliding mode controller (H∞ AFSMC) is proposed for a class of nonlinear systems involving system uncertainties and external disturbances. The H∞ tracking control design method and the adaptive fuzzy sliding mode control technique are combined in the design of the H∞ AFSMC controller. By the Lyapunov theory, it is shown that the proposed controller has the following advantages: it can inhibit the chattering phenomenon and can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Subsequently, the problem of H∞ AFSMC design is characterised in terms of an eigenvalue problem, which can be efficiently solved by using convex optimisation techniques. Finally, an inverted pendulum system is simulated to demonstrate the validity and effectiveness of the proposed controller.

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.

This paper proposes an adaptive sliding mode fault tolerant control design for lipschitz nonlinear system subject to simultaneous actuator and sensor faults. First, in order to estimate the system states, actuator and sensor faults, only one observer with an adaptive nonlinear gain is required where the minimum phase condition is relaxed to delectability and the matching condition is weakened to become a condition related to the system dimensions. Furthermore, our approach is applicable where there are faults greater than outputs. Next, a virtual sensor technique is developed to replace a failed, missing or corrupted sensor to provide a signal having the same effect of the nominal sensor. Then, this study provides an adaptive sliding mode fault tolerant control to achieve an optimal interaction between observer, virtual sensor and controller models. Thus, using the LMI technique with multiobjective optimization performance, sufficient conditions are derived to ensure the closed-loop Lipschitz nonlinear system stability and guarantee that the Lipschitz set of the adaptive sliding mode observer is a subset of the adaptive sliding mode control Lipschitz set. Two illustrative examples the first is the robotic manipulator model and the second is the longitudinal dynamics of the following vehicle system were performed to verify the effectiveness of the proposed approach.

In this paper, a nonlinear robust control technique is proposed for a class of affine nonlinear systems. This technique tries to increase tracking control performance by combining the benefits of sliding mode control (SMC) with model predictive control (MPC), for a class of nonlinear systems, in terms of smooth control law, a zero steady-state error, a faster convergence rate, and more robustness for the closed-loop system against external disturbances and model uncertainties. Furthermore, this paper provides a comparative study with the previously mentioned control methods. The controllers SMC and Model Predictive Sliding Mode Control (MPSMC) have been tested in simulation under Matlab/Simulink environment. Simulations are carried out on a nonlinear affine benchmark to evaluate the suggested technique and demonstrate its efficacy in achieving the required control performances.

The Delta robot is an over-actuated parallel robot with highly nonlinear kinematics and dynamics. Designing the control for a Delta robot to carry out various operations is a challenging task. Various advanced control algorithms, such as adaptive control, sliding mode control, and model predictive control, have been investigated for trajectory tracking of the Delta robot. However, these control algorithms require a reliable input–output model of the Delta robot. To address this issue, we have created a control-affine neural network model of the Delta robot with stepper motors. This is a completely data-driven model intended for control design consideration and is not derivable from Newton’s law or Lagrange’s equation. The neural networks are trained with randomly sampled data in a sufficiently large workspace. The sliding mode control for trajectory tracking is then designed with the help of the neural network model. Extensive numerical results are obtained to show that the neural network model together with the sliding mode control exhibits outstanding performance, achieving a trajectory tracking error below 5 cm on average for the Delta robot. Future work will include experimental validation of the proposed neural network input–output model for control design for the Delta robot. Furthermore, transfer learnings can be conducted to further refine the neural network input–output model and the sliding mode control when new experimental data become available.

In this article, two dual-loop control methods are proposed for attitude control and reaction wheels momentum management of the spacecraft simulator by assimilating the advantages of sliding mode and model predictive control (MPC). In the first method, by utilizing the high accuracy and constrained features of the MPC, an optimal controller is designed in the inner loop. MPC drives the angular velocity to the desired value while keeping the reaction wheel velocity to a small region near the origin, considering the constraints of the actuators. Furthermore, based on the fixed-time terminal sliding mode (TSM) the proper angular velocity is produced in the outer layer of this composite controller for the MPC part. In the second method, contrary to the first one, in the exterior loop MPC and in the interior loop finite-time TSM have been designed. The incorporated twofold nonlinear controllers’ policy insures a good dynamic and robustness against external disturbances. The high yielding of the control algorithms has been analyzed by simulation and experimental validation utilizing MATLAB software with real-time connection based on LabVIEW.

This paper presents a wavelet cerebellar model articulation controller (WCMAC) based adaptive control design for nonlinear systems using a particle swarm optimization (PSO). The WCMAC is the main tracking controller and a robust compensation controller is used to compensate for the residual error. In the WCMAC, the adaptive laws of controller parameters are derived using the gradient descent method. However, the initial values of learning rates of these adaptive laws are very important and they affect much to the performance of control systems. In this paper, the particle swarm optimization algorithm is applied to find the optimal learning rates of the parameter adaptation laws. To show the effectiveness of the proposed approach, numerical simulations of magnetic levitation system and inverted pendulum are provided to confirm the applications of the proposed PSO-WCMAC-based control system. The superiority of the proposed control scheme is also evaluated by quantitative comparison with other control schemes.

Fuzzy control design of nonlinear systems under unreliable communication links: A systematic homogenous polynomial approach

Analysis on existence of compact set in neural network control for nonlinear systems

Control Design for Nonlinear Systems via Controller with Quasi-fixed Parameters