Class Of Nonlinear Parameter Systems Research Articles

Fixed-time stabilizing control for a class of nonlinearly parameterized systems

Fixed-time stabilizing control for a class of nonlinearly parameterized systems

Adaptive quantized control for a class of high‐order nonlinear systems

AbstractIn this article, the adaptive stabilization problem is addressed for a class of nonlinearly parameterized systems with quantized input. The quantizer parameters and virtual control coefficients are unknown, and the linearization of the nonlinear systems is uncontrollable. A novel nonlinear time‐varying model is proposed to deal with the quantized input. Through the proposed nonlinear model, the quantized adaptive control problem is converted into the adaptive stabilization problem for nonlinear high‐order system with unknown virtual control coefficients. Then, based on the tuning function approach and adding power integrator technique, adaptive laws and an adaptive state feedback controller are designed. Further, it is shown that by adjusting some design parameters, the proposed scheme enables the stabilization error converges to an arbitrarily small neighborhood of the origin. Simulation is also provided to verify the validity of proposed scheme.

Model reference safety‐critical adaptive control for a class of nonlinearly parameterized systems

AbstractSafety is the most fundamental problem of safety‐critical systems. Safety control addresses the problem whether a given unsafe region of the state space can be avoided by a specific control‐input. Moreover, linearly parameterized dynamical system is a general assumption in most safety‐critical adaptive control literature; however, unknown parameters in real systems are usually nonlinear. The control problem of nonlinearly parameterized systems is really difficult without linear‐in‐the‐parameters (LIP) assumptions, which tends to be complicated and computationally intensive. In this paper, a novel model reference safety‐critical adaptive control (MRAC) approach is proposed for a class of nonlinearly parameterized systems. The proposed approach involves a novel controller architecture with a modified update law, which specifically filters out the unsafe behavior (the system is in a state which the system cannot operate normally, i.e., the given unsafe region), while preserving favorable tracking capability and robustness. The novelty of this paper is that the nonlinearly parameterized systems can be enforced safety, without LIP assumptions and complex calculations. Most importantly, this approach is effective for nonlinearly parameterized systems as well as linearly parameterized systems. Finally, three illustrative numerical examples are presented to demonstrate the effectiveness of the proposed design approach.

Dynamic surface control for a class of nonlinearly parameterized systems with input time delay using neural network

By using the radial basis function neural network (RBF NN), this paper presents tracking control problem of the nonlinear systems with the input time delay, in which the unknown continuous functions may be nonlinearly parameterized. Different from the existing results which deal with the nonlinearly parameterized functions by using the separation principle, in this paper, the nonlinearly parameterized functions are lumped into the continuous functions, and then, the neural networks (NNs) are applied to approximate them. Moreover, through a state transformation the system can be easily transformed into a system without the input time delay. Finally, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive NN backstepping control scheme is developed, and only two parameters need to be adjusted online in the controller design procedure. Thus, the proposed control method cannot only overcome the problem of “explosion of complexity” inherently existing in traditional backstepping design methods, but also reduce the computational burden greatly. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of the origin with an appropriate choice of design parameters. Finally, three examples are used to show the effectiveness of the proposed approach.

A [formula omitted]-filter-based adaptive control for nonlinear systems with unknown parameters in state and output equations

Adaptive stabilization by output feedback is investigated for a class of nonlinear systems with parametric uncertainty in both state and output equations. Different from the existing work, the precise knowledge of the unknown parameter at the output, including its sign, is not required. The nonlinear system under consideration is assumed to be linear in the unmeasured states but does permit to be nonlinear with respect to the system output. To achieve global state regulation with stability, we employ the idea of K-filter and develop a universal-like output feedback control scheme using the Nussbaum gain. The proposed adaptive control strategy is then applied to tackle the problem of adaptive output tracking for the same class of uncertain nonlinear systems. Further extensions are also included, which address the adaptive output feedback control of a wider class of nonlinearly parametrized systems with output parametric uncertainty.

Research on Robust Adaptive and Efficient Control System: A Theoretical Approach

In this paper, a robust adaptive repetitive control algorithm is presented for periodically time-varying systems. Periodic time-varying parameter estimation through periodic learning algorithm, and the uncertainty of aperiodic was robust adaptive method. Different from the existing repetitive control, this paper introduces the design of a new variable cycle number control. Convergence error when the number increase will gradually decrease due to the cyclical repetition character system, in order to ensure the global asymptotic stability. Further, this method is applied to a class of nonlinearly parameterized systems with non-parametric disturbances, and the tracking error converges asymptotically. The results verify the simulation model of the inverse pendulum. In addition, it is proved that the proposed design method is applied to eliminate the influence of approximation error of neural network. Theoretical analysis shows that the system output is convergent to the desired one and all signals in the network based robust adaptive repetitive control system are bounded. The experimental result illustrates the effectiveness of our proposed methodology.

Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems

This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network’s weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given

Switching adaptive learning control for nonlinearly parameterized systems with disturbance of unknown periods

SummaryIn this paper, a logic‐based switching adaptive learning control mechanism is proposed for a class of nonlinearly parameterized systems with disturbance of unknown periods. The switching algorithms include two parts: one is to stabilize the nonlinearly parameterized uncertainties, the other is to learn the periodic bounded disturbance. An adaptive control method with fully saturated periodic adaptation law is presented to take advantage of the periodic and bounded property of the disturbance. It is shown that under the proposed control designs, the asymptotic convergence is ensured irrespective of initial conditions with all the signals in the closed‐loop system bounded. An illustrative example is given to show the validity of the switching adaptive learning control. Copyright © 2014 John Wiley & Sons, Ltd.

A New AILC for a Class of Nonlinearly Parameterized Systems with Unknown Delays and Input Dead-Zone

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of deadzone nonlinearity is presented. The assumption of identical initial condition for ILC is removed by introducing boundary layer functions. The uncertainties with time-varying delays are compensated for with assistance of appropriate Lyapunov-Krasovskii functional and Young’s inequality. The hyperbolic tangent function is employed to avoid the possible singularity problem. According to a property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while maintaining all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

FBFN-based adaptive repetitive control of nonlinearly parameterized systems

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network (FBFN). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delay and unknown control direction

This paper proposes a new adaptive iterative learning control approach for a class of nonlinearly parameterized systems with unknown time-varying delay and unknown control direction. By employing the parameter separation technique and signal replacement mechanism, the approach can overcome unknown time-varying parameters and unknown time-varying delay of the nonlinear systems. By incorporating a Nussbaum-type function, the proposed approach can deal with the unknown control direction of the nonlinear systems. Based on a Lyapunov-Krasovskii-like composite energy function, the convergence of tracking error sequence is achieved in the iteration domain. Finally, two simulation examples are provided to illustrate the feasibility of the proposed control method.

A Combined Multiple Model Adaptive Control Scheme and Its Application to Nonlinear Systems With Nonlinear Parameterization

A combined multiple model adaptive control (CMMAC) scheme, which is a proper combination of the estimator-based MMAC scheme and the unfalsified MMAC scheme, has been proposed with the aim of taking advantage of the strength of each scheme while avoiding their weaknesses. The major novelty of the CMMAC scheme lies in the fact that it monitors not only the adequacy of candidate models in terms of their estimation performances but also the performance of the active candidate controller. As an application of the CMMAC scheme and one example of such new multiple model adaptive controllers, a CMMAC based controller has been designed for a class of nonlinear systems with nonlinear parameterization. Under some sufficient conditions, a strong finite time switching result (which provides a characterization on the maximum number of switching) and the closed-loop stability have been established. A constructive design based on back-stepping is provided for the adaptive control problem of a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability.

Adaptive Repetitive Control of Nonlinearly Parameterized Systems Based on Fuzzy Basis Function Networks

In this note, an adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on fuzzy basis function networks (FBFNs). The parameters of the fuzzy rules are tuned with adaptive schemes. The adaptive repetitive control law is derived by using Lyapunov synthesis method to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, the controller singularity problem is solved as it avoids the nonlinear parameterization from entering into the adaptive control and repetitive control. The proposed approach has the added advantage that it does not require an exact structure of the system dynamics. The proposed controller is applied to control a model of permanent-magnet linear synchronous motor (PMLSM) subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method in terms of significant reduction in chattering while maintaining asymptotic convergence.

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delays

First of all, an adaptive iterative learning control strategy is developed for a class of nonlinearly parameterized systems with two unknown time-varying parameters and one unknown time-varying delay. The proposed control law includes a PID-type feedback term in time domain and an adaptive learning term used to estimate the unknown time-varying vector in iteration domain. By constructing a Lyapunov-Krasovskii-like composite energy function, we prove the stability of the closed-loop system and the convergence of the tracking error. Then, the design idea is further extended to a broader class of systems with mixed parameters in which the unknown time-invariant vector is estimated by a PI-type learning law in time domain. The simulation results, for a time-delay chaotic system, confirm the effectiveness of the proposed control scheme.

ADAPTIVE CONTROL DESIGN FOR NONLINEARLY PARAMETERIZED SYSTEMS WITH A TRIANGULAR STRUCTURE

ABSTRACTA novel adaptive backstepping design for a class of nonlinearly parameterized systems with a triangular structure is proposed. Under the Lipschitz condition with respect to unknown parameters of the system, an effective adaptive controller is designed without the requirement on the compactness of the unknown parametric set. Especially, the proposed adaptive control enables the advantage of “tuning function concept”, which results in only one estimation law for the unknown parameters. Our simulation with induction motor model particularly shows the viability of the obtained results.

Switching Logic-based Adaptive Robust Control of Nonlinearly Parameterized Uncertain Systems

In this paper, a switching logic-based adaptive robust control is proposed for a class of nonlinearly parameterized systems (NFS). Specifically, the controller mainly consists of a robust type term to address the system uncertainty, and a switching logic tuning mechanism to update the involved control gain. The constructed controller achieves a global uniformly ultimate boundedness (GUUB) result for the system errors, and simulation results are included to demonstrate the effectiveness of the control law.

Adaptive Repetitive Control for a Class of Nonlinearly Parametrized Systems

In this note, Lyapunov-based adaptive repetitive control is presented for a class of nonlinearly parametrized systems. Through the use of an integral Lyapunov function, the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control. Global stability of the adaptive system and asymptotic convergence of the tracking error are established, and tracking error bounds are provided to quantify the control performance. Both partially and fully saturated learning laws are analyzed in detail, and compared analytically

Robust adaptive control of nonlinearly parameterized systems with unmodeled dynamics

Many physical systems such as biochemical processes and machines with friction are of nonlinearly parameterized systems with uncertainties. How to control such systems effectively is one of the most challenging problems. This paper presents a robust adaptive controller for a significant class of nonlinearly parameterized systems. The controller can be used in cases where there exist parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The design of the controller is based on the control Lyapunov function method. A dynamic signal is introduced and adaptive nonlinear damping terms are used to restrain the effects of unmodeled dynamics, nonlinear uncertainties and unknown bounded disturbances. The backstepping procedure is employed to overcome the complexity in the design. With the proposed method, the estimation of the unknown parameters of the system is not required and there is only one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are. It is proved theoretically that the proposed robust adaptive control scheme guarantees the stability of nonlinearly parameterized system. Furthermore, all the states approach the equilibrium in arbitrary precision by choosing some design constants appropriately. Simulation results illustrate the effectiveness of the proposed robust adaptive controller.

Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization

We address the problem of output tracking for a class of nonlinearly parameterized systems with unstabilizable linearization. To achieve practical output tracking globally in the case when both the bound of reference signals and the bound of unknown time-varying parameters are not known a priori, we present a robust adaptive control method that is based on the idea of universal control combined with the new adaptive feedback design method developed recently for controlling uncertain systems with nonlinear parameterization. Continuous adaptive tracking controllers are explicitly constructed in this paper. The proposed adaptive tracking controllers use only the information of a prescribed reference signal but not its derivatives, nor its bound.

새로운 형태의 Lyapunov 함수를 이용한 직접 적응 제어기의 설계

We propose a direct adaptive controller for a class of nonlinearly parametrized systems. A normalized output error is added to the previous control law to construct the proposed adaptive controller. The transient performance of the resulting closed-loop system can be guaranteed by suitably choosing a novel kind of Lyapunov function while the tracking performance of the adaptive control system is improved using the proposed algorithm. Finally, the effectiveness of the proposed algorithm is illustrated with computer simulation.