Beibei Ren

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control.

Adaptive Neural Control for Output Feedback Nonlinear Systems Using a Barrier Lyapunov Function

In this brief, adaptive neural control is presented for a class of output feedback nonlinear systems in the presence of unknown functions. The unknown functions are handled via on-line neural network (NN) control using only output measurements. A barrier Lyapunov function (BLF) is introduced to address two open and challenging problems in the neuro-control area: 1) for any initial compact set, how to determine a priori the compact superset, on which NN approximation is valid; and 2) how to ensure that the arguments of the unknown functions remain within the specified compact superset. By ensuring boundedness of the BLF, we actively constrain the argument of the unknown functions to remain within a compact superset such that the NN approximation conditions hold. The semiglobal boundedness of all closed-loop signals is ensured, and the tracking error converges to a neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed approach.

Brief paper: Control of nonlinear systems with time-varying output constraints

This paper presents output tracking control for strict feedback nonlinear systems with time-varying output constraint. A Barrier Lyapunov Function (BLF), which depends explicitly on time, is employed at the outset to prevent the output from violating the time-varying constraint. Specifically, we allow the barrier limit to vary with the desired trajectory in time. Through a change of coordinates for the tracking error, we then eliminate the time dependence, therefore simplifying the analysis. We show that asymptotic output tracking is achieved without violation of the time-varying constraint, and that all closed loop signals remain bounded. The performance of the proposed control is illustrated through a simulation example.

Adaptive Neural Control for a Class of Uncertain Nonlinear Systems in Pure-Feedback Form With Hysteresis Input

In this paper, adaptive neural control is investigated for a class of unknown nonlinear systems in pure-feedback form with the generalized Prandtl-Ishlinskii hysteresis input. To deal with the nonaffine problem in face of the nonsmooth characteristics of hysteresis, the mean-value theorem is applied successively, first to the functions in the pure-feedback plant, and then to the hysteresis input function. Unknown uncertainties are compensated for using the function approximation capability of neural networks. The unknown virtual control directions are dealt with by Nussbaum functions. By utilizing Lyapunov synthesis, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of zero. Simulation results are provided to illustrate the performance of the proposed approach.

Adaptive Neural Control for a Class of Nonlinear Systems With Uncertain Hysteresis Inputs and Time-Varying State Delays

In this paper, adaptive variable structure neural control is investigated for a class of nonlinear systems under the effects of time-varying state delays and uncertain hysteresis inputs. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design, and the effect of the uncertain hysteresis with the Prandtl-Ishlinskii (PI) model representation is also mitigated using the proposed control. By utilizing the integral-type Lyapunov function, the closed-loop control system is proved to be semi globally uniformly ultimately bounded (SGUUB). Extensive simulation results demonstrate the effectiveness of the proposed approach.

Stabilization and Gevrey Regularity of a Schrödinger Equation in Boundary Feedback With a Heat Equation

We study stability of a Schrödinger equation with a collocated boundary feedback compensator in the form of a heat equation with a collocated input/output pair. Remarkably, exponential stability is achieved for both positive and negative gains, namely, as long as the gain is non-zero. We show that the spectrum of the closed-loop system consists only of two branches along two parabolas which are asymptotically symmetric relative to the line Reλ = -Imλ (the 135° line in the second quadrant). The asymptotic expressions of both eigenvalues and eigenfunctions are obtained. The Riesz basis property and exponential stability of the system are then proved. Finally we show that the semigroup, generated by the system operator, is of Gevrey class δ >; 2. A numerical computation is presented for the distributions of the spectrum of the closed-loop system.

Robust Control for a Class of Nonaffine Nonlinear Systems Based on the Uncertainty and Disturbance Estimator

In this paper, the uncertainty and disturbance estimator (UDE)-based robust control is applied to the control of a class of nonaffine nonlinear systems. This class of systems is very general and covers a large range of nonlinear systems. However, the control of such systems is very challenging because the input variables are not expressed in an affine form, which leads to the failure of using feedback linearization. The proposed UDE-based control method avoids the inverse operator construction, which might result in the control singularity problem. Moreover, the general assumption on the uncertainty and disturbance term is relaxed, and only its bandwidth information is required for the control design. The asymptotic stability of the closed-loop system is established. The proposed approach is easy to be implemented and tuned while bringing very good robust performance. The important features and performance of the proposed approach are demonstrated through both simulation studies and experimental validation on a servo system with nonaffine uncertainties.

Stabilization of an ODE–Schrödinger Cascade

In this paper, we consider a problem of stabilization of an ODE-Schrodinger cascade, where the interconnection between them is bi-directional at a single point. By using the backstepping approach, which uses an invertible Volterra integral transformation together with the boundary feedback to convert the unstable plant into a well-damped target system, the target system in our case is given as a PDE-ODE cascade with exponential stability at the pre-designed decay rate. Instead of one-step backstepping control, which results in difficulty in finding the kernels, we develop a two-step backstepping control design by introducing an intermediate target system and an intermediate control. The exponential stability of the closed-loop system is investigated using the Lyapunov method. A numerical simulation is provided to illustrate the effectiveness of the proposed design.

Anti-disturbance control of hypersonic flight vehicles with input saturation using disturbance observer

This paper proposes an anti-disturbance control scheme for the near space vehicle (NSV) based onterminal sliding mode (TSM) technique and disturbance observer method. To tackle the system uncertainty andthe time-varying unknown external disturbance of the NSV, a disturbance observer based on TSM technique isdesigned which can render the disturbance estimate error convergent in finite time. Furthermore, an auxiliarydesign system is introduced to analyze the input saturation effect. Based on the developed disturbance observerand the auxiliary design system, an anti-disturbance attitude control scheme is developed for the NSV usingthe TSM technique to speed up the convergence of all signals in closed-loop system. For the closed-loop system,the stability is rigorously proved by using the Lyapunov method and we guarantee the finite time convergenceof all closed-loop system signals in the presence of the integrated affection of the system uncertainty, the inputsaturation, and the unknown external disturbance. Simulation study results are given to show the effectivenessof the developed TSM anti-disturbance attitude control scheme using the disturbance observer and the auxiliarysystem for the NSV.

Adaptive Neural Network Control of Hard Disk Drives With Hysteresis Friction Nonlinearity

In this brief, an adaptive neural network (NN) friction compensator is presented for servo control of hard disk drives (HDDs). The existence of the hysteresis friction nonlinearity from pivot bearing, which is represented as the LuGre hysteresis friction model here, increases the position error signal of read-write head and deteriorates the performance of HDD servo systems. To compensate for the effect of the hysteresis friction nonlinearity, NN is adopted to approximate its unknown bounding function. With the proposed control, all the closed-loop signals are ensured to be bounded while the tracking error converges into a neighborhood of zero. Comprehensive comparisons between the conventional proportional-integral-derivative control (without friction compensator) and the proposed adaptive NN control (with friction compensator) are provided in experiment results. It is shown that the proposed control can mitigate the effect of the hysteresis friction nonlinearity and improve the track seeking performance.