具有双控制输入通道高阶不确定非线性系统控制设计

Adaptive asymptotic tracking control design for high-order uncertain nonlinear systems

This paper is concerned with data-driven methods for virtual reference controller design of high-order nonlinear systems via neural network. Virtual reference feedback tuning (VRFT) is a one-shot direct data-based method to design controller of linear or nonlinear systems. In this paper, we recall the model reference control problem of high-order nonlinear systems and design a new objective function of VRFT. In ideal conditions, the two problems are demonstrated to have the same solution. For the first time, we prove that the value of the optimization problem for model reference control is bounded by that of the objective function of VRFT. A three-layer neural network is employed as a general approximator of the designed controller and two simulations are given to verify the validity of our method.

International audience

The μ analysis method is applied to a class of multivariable separable autonomous nonlinear feedback systems. The nonlinear element is replaced by its sinusoidal input describing function (SIDF) to develop a quasilinear nominal model for control analysis and design. Some properties of the ∞ -norm and structured singular values (SSVs) are shown to hold for the type of systems where the output is a function of control input-signal amplitude and frequency. The model uncertainty induced by the SDIF approximation is calculated and incorporated in the control design as an input multiplicative perturbation to the quasilinear nominal model. The μ analysis technique is then employed to study the stability and performance robustness of the nonlinear control system. Using small gain theorem, the condition for the absence of limit cycle is derived. The information obtained from this analysis is then used to design a bank of controllers using the H ∞ optimization-based μ synthesis technique. These controllers are designed such that the closed loop system is robust over a range of control-input amplitude. A simple scheme is then proposed to select the appropriate controller for the operating range. The simulation results illustrate that the proposed technique may be used to design a high performance robust controller for nonlinear systems and the absence of the limit cycle oscillation may be ensured.

This article discusses the adaptive fuzzy asymptotic tracking control for high-order nonlinear time-delay systems with full-state constraints. Fuzzy-logic systems and a separation principle are utilized to relax growth assumptions imposed on unknown nonlinearities. The adverse effect caused by unknown time delays is eliminated by choosing appropriate Lyapunov-Krasovskii functionals. By integrating nonlinear-transformed functions with a key coordinate transformation into the control design and constructing a specific compact set on the initial values of system states, the desired trajectory and parameter estimates, it is rigorously proved that all closed-loop signals are semiglobally bounded, the fuzzy approximation is valid, the full-state constraints are not violated without feasibility conditions on virtual controllers, and asymptotic tracking is achieved. The effectiveness and advantages of this control scheme are confirmed by two examples including a single-link robotic system.

Global output-feedback stabilization for high-order nonlinear systems with unknown control coefficients

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 addresses the problem of state feedback control for a class of stochastic high-order feedforward nonlinear systems with multiple time-varying delays. A distinct property of the system to be investigated is that the control coefficients are not restricted to 1. By introducing the sign function and the adding one power integrator, a delay-independent state feedback controller is constructed. By Lyapunov-Krasovskii theorem and homogeneous domination approach, the global stochastic asymptotic stability of the closed-loop system under the above-mentioned controller is proved. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.

Due to the difficulty encountered in dealing with unstructured system dynamics with unmeasured system state variables, this paper presents a novel observer-based neural network finite-time output control strategy for general high-order nonlinear systems (HNSs). The suggested technique is performed based on the backstepping-like control (BSC) scheme with a hybrid nonlinear disturbance-state observer and norm estimation-based radial basis function neural network (RBFNN). This helps not only reduce the number of estimated parameters but also relax the restriction of using inequality when exploiting the norm estimation concept in a conventional way; thus, retaining the same properties of the original system. Therefore, an observer-based finite-time output feedback control is established to deal with the unstructured dynamical behaviors and satisfying the output tracking regulation with the semi-global practically finite-time stability (SGPFS) guaranteed for the closed-loop system. The effectiveness and workability of the proposed algorithm is verified by a numerical simulation on a specific practical application.

A two-stage Active Disturbance Rejection Control (ADRC) design procedure is presented for the output trajectory tracking control problem in Single Input Single Output (SISO) nonlinear systems. Aside from the given scalar system output, the plant is assumed to exhibit a second, physically measurable, internal scalar output variable. The system output is controlled in an ADRC manner from an implicit static, or dynamic, nonlinear feedback controller using, in general, a nonlinear differential expression of the internal output variable. A desired internal output trajectory is thus generated. The internal output variable, in turn, is controlled from the original input and forced to track the desired trajectory synthesized in the previous step by the auxiliary controller. Each ADRC controller design is based on a simplified model of the corresponding subsystem, usually relegating interaction variables and additive nonlinearities to be part of a local (total) disturbance input term. The control scheme is reduced to a set of linear ADRC controllers with, possibly, cancellation of nonlinear input gains which are assumed to be known. Two illustrative aerospace examples are presented where the proposed procedure is illustrated via digital computer simulations.

Neuro-adaptive non-singular terminal sliding mode control for distributed fixed-time synchronization of higher-order uncertain multi-agent nonlinear systems

This paper studies the problem of finite-time fuzzy adaptive dynamic surface control (DSC) design for a class of single-input and single-output (SISO) high-order nonlinear systems with output constraint. Fuzzy logic systems (FLSs) are utilized to identify the unknown smooth functions. By adopting Barrier Lyapunov function (BLF), the problem of output constrain is handled. Combining adding a power integrator and adaptive backstepping recursion design technique, a novel fuzzy adaptive finite-time DSC algorithm is proposed. Based on finite-time Lyapunov stable theory, the developed control algorithm means that all the signals of the closed-loop system are semi-global practical finite-time stable (SGPFS) and the tracking error converges to a small neighborhood of origin in finite time. In addition, the output does not violate the given constrain bound. Finally, both numerical and practical simulation examples are given to illustrate the effectiveness of the proposed control algorithm.

Reduced-order observer-based control design for nonlinear stochastic systems

Good transparency performance (e.g., position tracking and force feedback) is an important issue in the control design of teleoperation systems. The four-channel architecture has advantages in the achievement of good transparency performance for teleoperation systems. However, most of the existing four-channel architectures are used in the linear teleoperation system, which cannot be well applied to execute tasks in the increasingly complicated operation environments. Thus, designing the four-channel architecture to achieve good transparency performance for nonlinear teleoperation systems with uncertainties is still a challenging issue. In this paper, the disturbance-observer-based sliding mode control design with a novel four-channel architecture is developed for the nonlinear bilateral teleoperation system to achieve a good transparency performance in the consideration of uncertainties and external disturbance, where the operating torque, master position, slave position, and the environment torque signals are transmitted through the communication channel. The reference tracking planner is designed in both the master and slave sides to produce the passive reference trajectories, and the disturbance-observer-based sliding mode controller is subsequently designed for the master and slave robots to achieve the good position tracking performance. The good force feedback performance can be achieved by the proper selection of plan parameters in the master reference tracking planner. Thus, the good transparency performance with both position tracking and force feedback can be achieved for the nonlinear bilateral teleoperation system with this novel four-channel architecture. The comparative simulation and experiment are implemented, and the results demonstrate good transparency performance achievement with the proposed control design.

This paper investigates the problem of the global stabilization via state feedback and adaptive technique for a class of high-order stochastic nonlinear systems with more uncertainties/unknowns. First of all, two stochastic stability concepts are slightly extended to allow the systems with more than one solution. To solve the stabilization problem, a lot of substantial technical obstacles should be overcome since the presence of severe uncertainties/unknowns and stochastic noise. By introducing the appropriate control Lyapunov function and suitable adaptive updated law for an unknown design parameter, and using the method of adding a power integrator, an adaptive continuous (nonsmooth) state feedback controller without overparameterization is successfully designed, which guarantees that the closed-loop states are bounded and the original system states eventually converge to zero, both with probability one.