Moving horizon numerical observers of nonlinear control systems

In this note, we develop moving horizon numerical observers and analyze the error. In the error estimation, we take into consideration both the integration error and the optimization error. The design facilitates the use of a variety of numerical algorithms to form different observers. As a special case, an Euler-Newton observer is introduced. The numerical observer is independent of any optimization software or toolbox. Furthermore, the observer is formulated in a way that is especially efficient for systems with sampled measurement.     

Composite nonlinear feedback control for strict-feedback nonlinear systems with input saturation

This paper focuses on composite nonlinear feedback (CNF) controller design for tracking control problem of strict-feedback nonlinear systems with input saturation to address the improvement of transient performance. First, without considering the input saturation, a stabilisation control law is designed by using standard backstepping technique for the nonlinear system, then a feedforward control law is added to the backstepping-based stabilisation control law to construct a tracking control law. The tracking control law is tuned to drive the output of the closed-loop system to track a command input with quick response. Then, an additional nonlinear feedback law is constructed and combined with the tracking control law to obtain a CNF control law. The role of this additional nonlinear feedback law is to smoothly change the damping ratio of the closed-loop system while the system output approaches the command input, and to reduce overshoot caused by the tracking control law. It is shown that the extra-adding nonlinear feedback part does not cause the loss of stability of the closed-loop system in its attractive basin.     

Design of a control algorithm for objects with parametric uncertainty,disturbances, and input signal saturation

We design a control algorithm for objects under parametric uncertainty, external bounded disturbances, and saturation of the controlled signal. We assume that the object model is described by a linear dynamical system with arbitrary relative degree and several inputs and outputs. The developed algorithm provides approximate tracking of the output of the control object for a reference signal. We obtain sufficient stability conditions for the closed system that depend on object parameters, reference model, and the controller. We show modeling results that illustrate the operation of the developed scheme.     

受饱和输入约束的非线性系统滑模自适应控制

利用神经网络和滑模控制,研究带有饱和输入的一类非线性系统。为了便于问题分析,引入饱和约束模型输出与控制输入的差值这个变量,分5种情况讨论,求得神经网络权值的在线调节律,得到保证闭环系统稳定的控制律。利用Lyapunov函数,证明了闭环系统的稳定性;仿真实验说明了算法的有效性。     

A fast nonlinear control method for linear systems with input saturation

We present a novel, fast saturating nonlinear feedback law for single input systems with linear dynamics and input saturation. It is fast in the sense that it yields a better performance than a saturating linear control law. The control law is based on implicit soft variable-structure control. A convex optimization procedure for the controller synthesis based on linear matrix inequalities (LMIs) is derived at the price of some conservatism. As an example, we consider the control of a submarine.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

Adaptive neural network control of uncertain MIMO nonlinear systems with input saturation

In this paper, an adaptive neural network (NN) tracking controller is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with input saturation. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions in the MIMO system. A novel auxiliary system is developed to compensate the effects induced by input saturation (in both magnitude and rate) during tracking control. Endowed with a switching structure that integrates two existing representative auxiliary system designs, this novel auxiliary system improves control performance by preserving their advantages. It provides a comprehensive design structure in which parameters can be adjusted to meet the required control performance. The auxiliary system signal is utilized in both the control law and the neural network weight-update laws. The performance of the resultant closed-loop system is analyzed, and the bound of the transient error is established. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive neural network control.     

Robust control for spacecraft rendezvous with disturbances and input saturation

This paper deals with the stabilization problem of spacecraft rendezvous in the presence of disturbances and input saturation. A dead zone operator based model is used to describe the saturation phenomenon. By using Lyapunov method, two groups of control laws are obtained, which ensure the input-to-state stability and the input-to-state practical stability of the closed-loop systems respect to disturbance acceleration, respectively. Simulation results are provided to illustrate the effectiveness of the proposed approaches.     

Moving horizon estimation for switching nonlinear systems

This paper is concerned with moving horizon estimation for a class of constrained switching nonlinear systems, where the system mode is regarded as an unknown discrete state to be estimated together with the continuous state. In this work, we establish the observability framework of switching nonlinear systems by proposing a series of concepts about observability and analyzing the properties of such concepts. By fully applying the observability properties, we prove the stability of the proposed moving horizon estimators. Simulation results are reported to verify the derived results.     

Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation

This paper studies the problem of adaptive neural network finite-time control for a class of non-triangular nonlinear systems with input saturation. Under the assumption that the nonlinearities have strict increasing smooth bounding functions, the backstepping technique can be used to design the state feedback controller and adaptive laws. Neural networks are adopted to approximate some unknown nonlinear functions. With the help of the finite-time Lyapunov stability theorem, it can be proved that the state of the closed-loop system can converge to an arbitrarily small neighborhood of the origin in a finite time. Finally, a numerical simulation example is given to show the effectiveness of the proposed design method.

     

Adaptive neural control of stochastic nonlinear systems with multiple time-varying delays and input saturation

This paper investigates the problem of adaptive neural control for a class of strict-feedback stochastic nonlinear systems with multiple time-varying delays, which is subject to input saturation. Via the backstepping technique and the minimal learning parameters algorithm, the problem is solved. Based on the Razumikhin lemma and neural networks’ approximation capability, a new adaptive neural control scheme is developed. The proposed control scheme can ensure that the error variables are semi-globally uniformly ultimately bounded in the sense of four-moment, while all the signals in the closed-loop system are bounded in probability. Two simulation examples are provided to demonstrate the effectiveness of the proposed control approach.     

Anti-windup synthesis for linear control systems with input saturation: Achieving regional, nonlinear performance

In this paper, we present LMI-based synthesis tools for regional stability and performance of linear anti-windup compensators for linear control systems. We consider both static and dynamic compensators. Algorithms are developed that minimize the upper bound on the regional L₂ gain for exogenous inputs with L₂ norm bounded by a given value, and that minimize this upper bound with a guaranteed reachable set or domain of attraction. Based on the structure of the optimization problems, it is shown that for systems whose plants have poles in the closed left-half plane, plant-order dynamic anti-windup can achieve semiglobal exponential stability and finite L₂ gain for exogenous inputs with L₂ norm bounded by any finite value. The problems are studied in a general setting where the only requirement on the linear control system is well-posedness and internal stability. The effectiveness of the proposed techniques is illustrated with an example.     

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

In this paper, we present a design procedure of composite nonlinear feedback control for general multivariable systems with actuator saturation. We consider both the state feedback case and the measurement feedback case without imposing any restrictive assumption on the given systems. The composite nonlinear feedback control consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with faster rise time, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to reduce overshoot and undershoot caused by the linear part. As such, a highly desired tracking performance with faster settling time and smaller overshoot can be obtained. The result is illustrated by a numerical example, which shows that the proposed design method yields a very satisfactory performance.     

Distributed receding horizon control of large-scale nonlinear systems: Handling communication delays and disturbances

This paper studies the robust distributed receding horizon control (DRHC) problem for large-scale continuous-time nonlinear systems subject to communication delays and external disturbances. A dual-mode robust DRHC strategy is designed to deal with the communication delays and the external disturbances simultaneously. The feasibility of the proposed DRHC and the stability of the closed-loop system are analyzed, and the sufficient conditions for ensuring the feasibility and stability are developed, respectively. We show that: (1) the feasibility is affected by the bounds of external disturbances, the sampling period and the bound of communication delays; (2) the stability is related to the bounds of external disturbances, the sampling period, the bound of communication delays and the minimum eigenvalues of the cooperation matrices; (3) the closed-loop system is stabilized into a robust invariant set under the proposed conditions. A simulation study is conducted to verify the theoretical results.     

Constrained receding horizon predictive control for systems with disturbances

A receding horizon predictive control method for systems with input constraints and disturbances is proposed. A polyhedral feasible set of states which is invariant with respect to a given state feedback control law is derived in the presence of bounded disturbances. The proposed predicted control algorithm deploys a strategy in which the current state is steered into the polyhedral invariant feasible set within a finite number N of feasible control moves, despite the presence of disturbances. The future control moves over the horizon N are represented as the sum of the state feedback control and a perturbation; the perturbation term provides the degrees of freedom with which to enlarge the stabilizable set of initial states. The control algorithm is formulated in linear matrix inequalities so that it can be solved using semidefinite programming.     

Receding horizon control of nonlinear systems

The receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems. The method is especially useful for the control of slow nonlinear systems, such as chemical batch processes, where it is possible to solve, sequentially, open-loop fixed-horizon, optimal control problems online. The method has been shown to yield a stable closed-loop system when applied to time-invariant or time-varying linear systems. It is shown that the method also yields a stable closed-loop system when applied to nonlinear systems     

Adaptive output feedback quantised tracking control for stochastic nonstrict-feedback nonlinear systems with input saturation

This paper is concerned with the problem of adaptive output feedback quantised tracking control for a class of stochastic nonstrict-feedback nonlinear systems with asymmetric input saturation. Especially, both input and output signals are quantised by two sector-bounded quantisers. In order to solve the technical difficulties originating from asymmetric saturation nonlinearities and sector-bounded quantisation errors, some special technique, approximation-based methods and Gaussian error function-based continuous differentiable model are exploited. Meanwhile, an observer including the quantised input and output signals is designed to estimate the states. Then, a novel output feedback adaptive quantised control scheme is proposed to ensure that all signals in the closed-loop system are 4-moment (2-moment) semi-globally uniformly ultimately bounded while the output signal follows a desired reference signal. Finally, the effectiveness and applicability of the design methodology is illustrated with two simulation examples.     

Adaptive fuzzy command filtered control for incommensurate fractional-order MIMO nonlinear systems with input saturation

Neural Computing and Applications - In this paper, an adaptive fuzzy control approach for incommensurate fractional-order multi-input multi-output (MIMO) systems with unknown nonlinearities and...     

Composite nonlinear feedback control for linear systems with input saturation: theory and an application

We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.     

Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of interconnected large-scale uncertain nonlinear time-delay systems with input saturation. RBF neural networks (NNs) are used to tackle unknown nonlinear functions, then the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The stability analysis subject to the effect of input saturation constrains are conducted with the help of an auxiliary design system based on the Lyapunov–Krasovskii method. The proposed controller guarantees uniform ultimate boundedness (UUB) of all the signals in the closed-loop large-scale system, while the tracking errors converge to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, and three problems of “computational explosion”, “dimension curse” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.