Suboptimal Robust Stabilization of Discrete-time Mismatched Nonlinear System

This paper proposes a discrete-time robust control technique for an uncertain nonlinear system. The uncertainty mainly affects the system dynamics due to mismatched parameter variation which is bounded by a predefined known function. In order to compensate the effect of uncertainty, a robust control input is derived by formulating an equivalent optimal control problem for a virtual nominal system with a modified costfunctional. To derive the stabilizing control law for a mismatched system, this paper introduces another control input named as virtual input. This virtual input is not applied directly to stabilize the uncertain system, rather it is used to define a sufficient condition. To solve the nonlinear optimal control problem, a discretetime general Hamilton-Jacobi-Bellman(DT-GHJB) equation is considered and it is approximated numerically through a neural network(NN) implementation. The approximated solution of DTGHJB is used to compute the suboptimal control input for the virtual system. The suboptimal inputs for the virtual system ensure the asymptotic stability of the closed-loop uncertain system. A numerical example is illustrated with simulation results to prove the efficacy of the proposed control algorithm.

Distributed fuzzy fault-tolerant consensus of leader-follower multi-agent systems with mismatched uncertainties

In this paper,the distributed fuzzy fault-tolerant tracking consensus problem of leader-follower multi-agent systems(MASs)is studied.The objective system includes actuator faults,mismatched parameter uncertainties,nonlinear functions,and exogenous disturbances under switching communication topologies.To solve this problem,a distributed fuzzy fault-tolerant controller is proposed for each follower by adaptive mechanisms to track the state of the leader.Furthermore,the fuzzy logic system is utilized to approximate the unknown nonlinear dynamics.An error estimator is introduced between the mismatched parameter matrix and the input matrix.Then,a selective adaptive law with relative state information is adopted and applied.When calculating the Lyapunov function’s derivative,the coupling terms related to consensus error and mismatched parameter uncertainties can be eliminated.Finally,a numerical simulation is given to validate the effectiveness of the proposed protocol.

Integral sliding mode control for flexible ball screw drives with matched and mismatched uncertainties and disturbances

The design of servo controllers for flexible ball screw drives with matched and mismatched disturbances and uncertainties is focused to improve the tracking performance and bandwidth of ball screw drives.A two degrees of freedom mass model is established based on the axial vibration characteristics of the transport ball screw,and the controller of an adaptive integral sliding mode is proposed combining the optimal design of state feedback gain matrix K to restrain the vibration and the matched disturbances and uncertainties.Then for the counteraction of the mismatched disturbances and uncertainties,a nonlinear disturbance observer is also developed.The trajectory tracking performance experiments and bandwidth analysis were conducted on experimental setup with the proposed control method.It is proved that the adaptive integral sliding mode controller has a high tracking performance and bandwidth especially for the axial vibration characteristics model of ball screw drives.And the ball screw tracking accuracy also has a considerable improvement with the application of the proposed nonlinear disturbance observer.

Sliding mode control for an aerodynamic missile based on backstepping design

In order to solve the mismatched uncertainties of a class of nonlinearsystems, a control method of sliding mode control (SMC) based on the backstepping design isproposed. It introduces SMC in to the last step of backstepping design to modify the backsteppingalgorithm. This combination not only enables the generalization of the backstepping design to beapplied to more general nonlinear systems, but also makes the SMC method become effective in solvingthe mismatched uncertainties. The SMC based on the backstepping design is applied to the flightcontrol system design of an aerodynamic missile. The control system is researched throughsimulation. The simulation results show the effectiveness of the proposed control method.

Integral sliding mode control of time-delay systems with mismatching uncertainties

A linear matrix inequality （LMI）-based sliding surface design method for integral sliding mode control of uncertain time- delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mis- matching norm bounded uncertainties in the state matrix as well as the input matrix, A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order slJdJng mode dynamics. An LMI characterization of the slid- ing surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.

Adaptive robust controller for supercavitating vehicle using guaranteed cost theory

Regarding to the problems that supercavitating vehicles have special characteristics from traditional underwater vehicles,robust control problem was studied in this paper for the supercavitating vehicles with mismatched uncertainties.The nonlinear dynamic model was improved.For mismatched uncertainties,the robust sliding mode function was proposed based on guaranteed cost theory,and sufficient condition for the existence was given in terms of linear matrix inequality (LMI).Continuous sliding mode controller was designed,with an adaptive technology which was used to estimate the unknown upper bound of mismatched uncertainties.Meanwhile,upper bound of parameter uncertainties was not required.Simulation results demonstrated that the system responds rapidly and has good robust stability.Due to application of guaranteed cost theory,the controlled plant is not only stable but also guarantees an adequate level of performance.Therefore,it provides theoretical references for further study on control problems of supercavitating vehicles.

Sliding mode control of supercavitating vehicles in the vertical plane using guaranteed cost theory

This paper focuses on robust control problems for supercavitating vehicles in the vertical plane. Firstly, for the mathematical model with mismatched uncertainties, the robust sliding mode function is designed based on the guaranteed cost theory, and a sufficient condition for the existence is given in terms of linear matrix inequality （LMI）. Secondly, a continuous sliding mode controller is proposed to handle the nonlinear, time - varying behavior of the vehicles. Simulation results demonstrate that the system responds rapidly and has good robust stability. Therefore, it provides theoretical references for further study on control problems of supercavitating vehicles.

An Adaptive Full Order Sliding Mode Controller for Mismatched Uncertain Systems

In this paper, an adaptive full order sliding mode （FOSM） controller is proposed for strict feedback nonlinear systems with mismatched uncertainties. The design objective of the controller is to track a specified trajectory in presence of significant mismatched uncertainties. In the first step the dynamic model for the first state is considered by the desired tracking signal. After the first step the desired dynamic model for each state is defined by the previous one. An adaptive tuning law is developed for the FOSM controller to deal with the bounded system uncertainty. The major advantages offered by this adaptive FOSM controller are that advanced knowledge about the upper bound of the system uncertainties is not a necessary requirement and the proposed method is an effective solution for the chattering elimination from the control signal. The controller is designed considering the full-order sliding surface. System robustness and the stability of the controller are proved by using the Lyapunov technique. A systematic adaptive step by step design method using the full order sliding surface for mismatched nonlinear systems is presented, Simulation results validate the effectiveness of the proposed control law.

Spiking-free HGO-based DSC for flexible joint manipulator

The tracking control problem for Flexible Joint Manipulator Control System(FJMCS)with unmeasurable states is addressed in this paper.Firstly,a High-Gain Observer(HGO)is constructed to estimate the unmeasurable states and the uncertainties.Then,a Dynamic Surface Control(DSC)scheme is developed by using the estimation of HGO.The newly proposed controller has two advantages over the existing methods:(A)a novel Spike Suppression Function(SSF)is developed to avoid the estimation spike problem in the existing HGO-based controllers.(B)Unlike the existing observer-based partial feedback control scheme that can only estimate the unmeasurable states,the proposed HGO can estimate both the unmeasurable states and uncertainties.The closed-loop system stability is proved by the Lyapunov theory.Simulation results demonstrate the effectiveness of the proposed controller.