Robust adaptive iterative learning control for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

A torque controller based on adaptive robust control is proposed for trajectory tracking of nonholonomic wheeled mobile robot with kinematic and dynamic uncertainties. In this controller, the parametric uncertainties are estimated by the adaptive control, and the non-parametric uncertainties are compensated by the adaptive robust control. The operation efficiency of the system is improved by distinguishing the differences between parametric and non-parametric uncertainties. Furthermore, the transient performance of adaptive control is optimized by the adaptive robust control and the measurements of uncertainties bounds are avoided, this strengthened the applicability of the controller. The uniformly ultimately bounded of closed-loop control system is proved by the Lyapunov theory. Simulations show that the adversely impacts of complex system uncertainties can be eliminated effectively and the high-precision trajectory tracking is guaranteed.

In this paper, we investigate the robust adaptive iterative learning control issue for discrete-time nonlinear systems with uncertainties by using an iteration-varying dead-zone approach. The uncertainties are dependent on both time index and iteration index, which can be expressed as the sum of a time-varying but iteration-invariant part and a bounded iteration-drift term. Then, a novel iteration-varying dead-zone approach is employed in the estimations of the iterationinvariant part and the drift bound simultaneously. The ultimate error bound is given explicitly with rigorous proof. Finally, simulation result has illustrated the efficacy of the proposed approach.

This article presents a method for guaranteeing the safety of a system with both parametric and nonparametric uncertainties, while at the same time decreasing the conservatism compared to existing approaches. This is obtained by combining robust adaptive control barrier functions (RaCBF) and Gaussian process control barrier functions (GPCBF). We provide a condition under which the considered system is safe with a given probability, and show that the proposed method is less conservative than GPCBF. We evaluate the method through a simulation study, where we consider a force controlled robot manipulator in contact with a partially unknown environment. The results show that our proposed GPRaCBF can guarantee bounds on the contact forces despite parametric and nonparametric uncertainties in the contact dynamics and outperforms GPCBF in terms of the conservatism.

In this paper, a new design of adaptive iterative learning control (ILC) for a class of uncertain nonlinear systems is proposed for the purpose of state tracking and improving convergence speed with both parametric and nonparametric uncertainties. The main feature of the design is that the controller signal is continuous due to the use of integral and employment of second-order sliding mode technique. Nonparametric uncertainties such as norm-bounded nonlinear uncertainties satisfying local Lipschitz condition can be effectively handled. In response to unknown bounded disturbances, a continuous sliding mode adaptive iterative learning control is more robust. By designing a suitable controller and composite energy function, the convergence of tracking error sequence within a small neighborhood of the origin is achieved in the iteration domain. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed ILC scheme.

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

Adaptive control has been developed for decades, and now it has become a rigorous and mature discipline which mainly focuses on dealing parametric uncertainties in control systems, especially linear parametric systems. Nonparametric uncertainties were seldom studied or addressed in the literature of adaptive control until new areas on exploring limitations and capability of feedback control emerged in recent years. Comparing with the approach of robust control to deal with parametric or nonparametric uncertainties, the approach of adaptive control can deal with relatively larger uncertainties and gain more flexibility to fit the unknown plant because adaptive control usually involves adaptive estimation algorithms which play role of “learning” in some sense. This chapter will introduce a new challenging topic on dealing with both parametric and nonparametric internal uncertainties in the same system. The existence of both two kinds of uncertainties makes it very difficult or even impossible to apply the traditional recursive identification algorithms which are designed for parametric systems. We will discuss by examples why conventional adaptive estimation and hence conventional adaptive control cannot be applied directly to deal with combination of parametric and nonparametric uncertainties. And we will also introduce basic ideas to handle the difficulties involved in the adaptive estimation problem for the system with combination of parametric and nonparametric uncertainties. Especially, we will propose and discuss a novel class of adaptive estimators, i.e. information-concentration (IC) estimators. This area is still in its infant stage, and more efforts are expected in the future for gainning comprehensive understanding to resolve challenging difficulties. Furthermore, we will give two concrete examples of semi-parametric adaptive control to demonstrate the ideas and the principles to deal with both parametric and nonparametric uncertainties in the plant. (1) In the first example, a simple first-order discrete-time nonlinear system with both kinds of internal uncertainties is investigated, where the uncertainty of non-parametric part is characterized by a Lipschitz constant L, and the nonlinearity of parametric part is characterized by an exponent index b. In this example, based on the idea of the IC estimator, we construct a unified adaptive controller in both cases of b = 1 and

Some robust control methods have been developed in the past in order to increase tracking performance in the presence of parametric uncertainties. In the presence of parametric uncertainty, unmodelled dynamics and other sources of uncertainties, robust control laws are used. Corless-Leitmann [1] approach is a popular approach used for designing robust controllers for robot manipulators. In early application of Corless-Leitmann [1] approach to robot manipulators [2, 3], it is difficult to compute uncertainty bound precisely. Because, uncertainty bound on parameters depends on the inertia parameters, the reference trajectory and manipulator state vector. Spong [4] proposed a new robust controller for robot manipulators using the Lyapunov theory that guaranties stability of uncertain systems. In this approach, Leithmann [5] or Corless-Leithman [1] approach is used for designing the robust controller. One of the advantage of Spong’s approach [4] is that uncertainty on parameter is needed to derive robust controller and uncertainty bound parameters depends only on the inertia parameters of the robots. Yaz [6] proposed a robust control law based on Spong’s study [4] and global exponential stability of uncertain system is guaranteed. However, disturbance and unmodelled dynamics are not considered in algorithm of [4, 6]. Danesh at al [7] develop Spong’s approach [4] in such a manner that control scheme is made robust not only to uncertain inertia parameters but also to robust unmodelled dynamics and disturbances. Koo and Kim [8] introduce adaptive scheme of uncertainty bound on parameters for robust control of robot manipulators. In [8], upper uncertainty bound is not known as would be in robust controller [4] and uncertainty bound is estimated with estimation law in order to control the uncertain system. A new robust control approach is proposed by Liu and Goldenerg [9] for robot manipulators based on a decomposition of model uncertainty. Parameterized uncertainty is distinguished from unparameterized uncertainty and a compensator is designed for parameterized and unparameterized uncertainty. A decomposition-based control design framework for mechanical systems with model uncertainties is proposed by Liu [10]. In order to increases tracking performance of uncertain systems, design of uncertainty bound estimation functions are considered. For this purpose, some uncertainty bound estimation functions are developed [11-15] based on a Lyapunov function, thus, stability of

An integrated direct/indirect adaptive robust controller (DIARC) is proposed to further improve the achievable posture trajectory tracking control performance of a parallel manipulator driven by pneumatic muscles. Due to the model errors of the static forces and friction forces of pneumatic muscles, the simplified average flow rate characteristics of valves, and the unknown disturbances of entire system, there exist large extent of parametric uncertainties and rather severe uncertain nonlinearities in the modeling of the parallel manipulator. To address these problems, in this paper, an indirect type parameter estimation is used to obtain reliable estimates of effective model parameters for reducing the parametric uncertainties while an integrated direct/indirect ARC with dynamic compensation type fast adaptation is utilized to further attenuate the influences of uncertain nonlinearities for better tracking performance. Considering that the conventional parameter estimation algorithm based on single error minimizing criterion normally fails to provide reliable parameter estimation for the parallel manipulator with symmetric structure due to the difficulty in satisfying the persistent exciting conditions all the time-the theoretical requirement for the convergence of online parameter estimation, additional practical constraints are imposed to further condition the parameter estimation process and a new parameter estimation algorithm based on composite error minimizing criterion in task-space is developed. Experimental results demonstrate that the parallel manipulator under the control of the proposed integrated DIARC has strong self-adaptability and robustness with the steady-state posture tracking error being less than 0.01deg, average tracking error less than 0.1deg, and maximum tracking error less than 0.3deg, which are significantly better than those of the direct ARC.

A robust model-free adaptive iterative learning control (R-MFAILC) algorithm is proposed in this work to address the issue of laterally controlling an autonomous bus. First, according to the periodic repetitive working characteristics of autonomous buses, a novel dynamic linearized method used in the iterative domain is utilized, and a time-varying data model with a pseudo gradient (PG) is given. Then, the R-MFAILC controller is designed with a proposed adaptive attenuation factor. The proposed algorithm's advantage lies in the R-MFAILC controller, which solely utilizes the input and output data of the regulated entity. Moreover, the R-MFAILC controller has strong robustness and can handle the nonlinear measurement disturbances of the system. In simulations based on the Truck-Sim simulation platform, the effectiveness of the proposed algorithm is verified. A rigorous mathematical analysis is employed to demonstrate the stability and convergence of the proposed algorithm.

An adaptive learning control algorithm is developed for a class of high-order nonlinear systems with both parametric and non-parametric uncertainties. The unknown time-varying parameters are estimated by a periodic repetitive learning strategy. To tackle the non-parametric uncertainties, the unknown periodic reference input signal is expanded with the sum of finite Fourier series and bounded truncation error, which is adaptively learned by estimating its Fourier coefficients. The hyperbolic function is introduced to eliminate the influences of truncation errors. By constructing a Lyapunov-like function, we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to nonlinear systems with unknown control coefficient. Two simulation examples are supplied to illustrate the effectiveness of the proposed control scheme.

In this paper, the uncertain model of the robotic system is decomposed into repetitive and non-repetitive parts, and the norm model of the system is taken into account. By using the Lyapunov method, an adaptive robust iterative learning control scheme is presented for the robotic system with both structured and unstructured uncertainty, and the overall stability of the system in the iteration domain is established. In the scheme the bound parameters estimated as well as the iterative learning control input are adjusted in the iteration domain. The validity of the scheme is illustrate through a simulation example.

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

Adaptive robust motion control of linear motors for precision manufacturing

In this article, a robust adaptive output-feedback control approach is presented for a class of nonlinear output-feedback systems with parameter uncertainties and time-varying bounded disturbances. A reduced-order filter driven by control input is proposed to reconstruct unmeasured states. The state estimation error is shown to be bounded by dynamic signals driven by system output. The bound estimation technique is employed to estimate the unknown disturbance bound. Based on the backstepping design with three sets of tuning functions, an adaptive output-feedback control scheme with the flat-zone modification is proposed. It is shown that all the signals in the resulting closed-loop adaptive control systems are bounded, and the output tracking error converges to a prespecified small neighborhood of the origin. Two simulation examples are provided to illustrate the effectiveness and validity of the proposed approach.