输入受限的非仿射纯反馈不确定系统自适应动态面容错控制

针对存在执行器故障和输入饱和受限的非仿射纯反馈不确定动态系统,提出了一种自适应动态面容错控制策略.在不损失模型精度和考虑系统输入饱和受限的前提下,基于中值定理将非仿射系统转化为具有线性结构的时变不确定系统,在此基础上,再利用参数自适应投影技术对有界不确定时变参数进行在线估计,参数估计误差和外界扰动采用非线性动态阻尼技术进行补偿,并利用双曲正切函数和Nussbaum函数处理系统输入饱和受限和控制增益函数方向未知的问题,同时将反演法和动态面法相结合设计鲁棒自适应控制器,消除了反演法的计算膨胀问题,并且在系统出现执行器失效故障的情况下可确保稳定跟踪.最后,根据解耦反推法,基于Lyapunov稳定性定理证明了闭环系统的半全局一致最终有界.仿真结果验证了所设计控制方案的可行性与有效性.     

一类纯反馈非线性系统的反推控制

研究了一类纯反馈非线性系统的输出跟踪问题.通过引入一个新的坐标变换,提出了一种基于反推设计的状态反馈控制算法.所得控制算法不仅保证了系统跟踪误差全局渐近稳定,同时使得闭环系统所有信号有界.最后,一个仿真实例验证了本文控制算法的有效性.     

输入饱和及输出受限的纯反馈非线性系统控制

针对具有输入饱和和输出受限的纯反馈非线性系统,设计了神经网络自适应控制器.首先利用隐函数定理和中值定理将非仿射形式的纯反馈非线性系统转换成有显式输入的非线性系统,基于李雅普诺夫第二方法以及反推法并采用障碍型李雅普诺夫函数进行控制器的设计,最后通过稳定性分析证明了闭环控制系统是半全局一致最终有界的,利用仿真例子验证了控制...     

一类纯反馈非线性系统的自适应动态面控制

针对一类完全非仿射纯反馈非线性系统,提出了一种新的自适应动态面控制方法.应用中值定理将未知非仿射输入函数进行分解,使其含有显式的可控制输入参数;引入Nussbaum增益函数,解决了虚拟控制增益符号未知的问题,同时避免了反馈线性化方法中可能出现的控制器奇异性问题;动态面控制消除了传统反推设计中的"微分爆炸"问题.采用解耦反推方法,基于李亚普诺夫稳定性定理证明了闭环系统的半全局稳定性,数值仿真验证了方法的有效性.     

一类纯反馈非线性系统的简化自适应神经网络动态面控制

针对一类完全非仿射纯反馈非线性系统,提出一种简化的自适应神经网络动态面控制方法.基于隐函数定理和中值定理将未知非仿射输入函数进行分解,使其含有显式的控制输入;利用简化的神经网络逼近未知非线性函数,对于阶SISO纯反馈系统,仅一个参数需要更新;动态面控制可消除反推设计中由于对虚拟控制反复求导而导致的复杂性问题.通过Lyapunov稳定性定理证明了闭环系统的半全局稳定性,数值仿真验证了方法的有效性.     

MIMO非线性系统的直接自适应控制

本文给出模型未知多输入多输出非线性系统的一种动态线性逼近方法，提出了基于该线性化方法的自适应控制律。讨论了在一定假设条件下自适应控制律的收敛性。     

非线性系统的反演自适应动态滑模控制

为削弱非线性系统中由滑模控制引起的抖振现象,提出自适应动态滑模控制方案.动态滑模方法是通过设计新的切换函数或将常规滑模变结构控制中的切换函数s通过微分环节构成新的切换函数,该切换函数与系统控制输入的一阶或高阶导数有关,可将不连续项转移到控制的一阶或高阶导数中去,得到在时间上本质连续的动态滑模控制律.该方案利用自适应技术和反演法,设计动态滑模控制器,有效地削弱了系统的抖振.最后仿真结果证明了该方案是正确的.     

一类纯反馈非线性系统的动态面控制

针对一类非仿射输入纯反馈非线性系统,提出了一种动态面控制算法.不同于运用中值定理,该算法通过引入一个辅助系统,将原系统转化为输入仿射系统,结合动态面控制与反推设计法,消除了反推法中"计算膨胀"问题.所设计控制器保证了闭环系统所有信号半全局一致最终有界,且通过选择合适的设计参数可使跟踪误差收敛到原点的一个小邻域内.一个仿真实例进一步验证了所提控制算法的有效性.     

基于ADP的导引控制一体化全状态受限反演控制

针对导引控制一体化设计中状态受限及非线性最优问题，提出了一种结合反演控制与自适应动态规划（ADP）技术，考虑全状态受限的新型导引控制一体化设计方法.首先，将状态受限的严格反馈系统通过坐标变换转化为非状态受限系统.然后，采用前馈反演控制与反馈最优控制相结合的设计思路，利用ADP技术在线求解非线性HJB方程得到最优解.最后通过李亚普诺夫理论证明了系统的闭环稳定性与所有信号的一致有界性.与传统方法的对比仿真验证了该设计方法的可行性与优越性.     

Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme.     

Adaptive receding horizon control for constrained MIMO systems

An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented.     

Existence of solutions to MIMO relay feedback systems

This note studies the existence of solutions to MIMO linear systems under decentralized relay feedback containing hysterisis. A necessary and sufficient condition is presented to guarantee the extended solutions at the so-called intersecting instant. The suggested method is to examine the sign of the first non-zero derivative of each output right after the switches occur. Illustrative examples are given to show the cases of non-existence and non-uniqueness of solutions.     

Output feedback receding horizon control of constrained systems

This paper considers output feedback control of linear discrete-time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors. We show that the non-convex problem of finding a constraint admissible affine output feedback policy over a finite horizon, to be used in conjunction with a fixed linear state observer, can be converted to an equivalent convex problem. When used in the design of a time-varying robust receding horizon control law, we derive conditions under which the resulting closed-loop system is guaranteed to satisfy the system constraints for all time, given an initial state estimate and bound on the state estimation error. When the state estimation error bound matches the minimal robust positively invariant (mRPI) set for the system error dynamics, we show that this control law is time-invariant, but its calculation generally requires solution of an infinite-dimensional optimization problem. Finally, using an invariant outer approximation to the mRPI error set, we develop a time-invariant control law that can be computed by solving a finite-dimensional tractable optimization problem at each time step that guarantees that the closed-loop system satisfies the constraints for all time.     

Nonlinear feedback in simple locomotion systems

The purpose of this short paper is to analyze postural stability and periodic motion of a simple model of a locomotion system. Nonlinear feedback is used to linearize the system. The effects of discretization, quantization and noise are studied via simulation of a compound inverted pendulum with realistic actuator models.     

Crossover frequency limitations in MIMO nonminimum phase feedback systems

This paper investigates limitations and design tradeoffs of the closed-loop sensitivity/performance of linear-time-invariant nonminimum-phase uncertain multiple-input-multiple-output plants, with I inputs and m outputs, where m /spl les/ l. It is shown that if rows i/sub 1/...,i/sub k/ of the plant transfer function form a k /spl times/ l nonminimum phase transfer matrix, and if the design is such that the sensitivity gain of k - 1 rows among the rows i/sub 1/,...,i/sub k/ of the closed-loop transfer function is low, then by necessity the sensitivity gain of the remaining row is high. This sensitivity constraint is quantified with the help of the crossover frequency restriction of a specially constructed single-input-single-output transfer function that includes the right half plane zeros and poles of the k /spl times/ l transfer matrix.     

Nonlinear output regulation for invertible nonlinear MIMO systems

In this paper, we address the problem of output regulation for a broad class of multi‐input multi‐output (MIMO) nonlinear systems. Specifically, we consider input–affine systems, which are invertible and input–output linearizable. This class includes, as a trivial special case, the class of MIMO systems which possess a well‐defined vector relative degree. It is shown that if a system in this class is strongly minimum phase, in a sense specified in the paper, the problem of output regulation can be solved via partial‐state feedback or via (dynamic) output feedback. The result substantially broadens the class of nonlinear MIMO systems for which the problem in question is known to be possible. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust feedback model predictive control of constrained uncertain systems

We propose a novel procedure for the solution to the problem of robust model predictive control (RMPC) of linear discrete time systems involving bounded disturbances and model-uncertainties along with hard constraints on the input and state. The RMPC (outer) controller – responsible for steering the uncertain system state to a designed invariant (terminal) set – has a mixed structure consisting of a state-feedback component as well as a control-perturbation. Both components are explicitly considered as decision variables in the online optimization and the nonlinearities commonly associated with such a state-feedback parameterization are avoided by adopting a sequential approach in the formulation. The RMPC controller minimizes an upper bound on an H₂/H_∞-based cost function. Moreover, the proposed algorithm does not require any offline calculation of (feasible) feedback gains for the computation of the RMPC controller. The optimal Robust Positively invariant set and the inner controller – responsible for keeping the state within the invariant set – are both computed in one step as solutions to an LMI optimization problem. We also provide conditions which guarantee the Lyapunov stability of the closed-loop system. Numerical examples, taken from the literature, demonstrate the advantages of the proposed scheme.     

Nonlinear regulation in constrained input discrete-time linear systems

The use of composite linear and non-linear feedback laws for the control of constrained input discrete-time linear systems is re-examined. By making use of the delta operator formulation of a discrete-time system, an apparent restriction on the magnitude of the non-linear control law is removed, and the similarities between the continuous and discrete-time solutions to the problem are elucidated. In order to develop the results, unconstrained systems are treated initially, but it is shown that, locally, the sufficient conditions for the stabilization of such systems are actually equivalent to those for the stabilization of the corresponding constrained systems.     

Limits of generalized state space systems under proportional and derivative feedback

In this paper we study the high-gain feedback classification problem for generalized state space systems. We solve this problem for proportional and derivative feedback transformations of regularizable systems, i.e., we give necessary and sufficient conditions for a regularizable system to be a limit of a given system under high-gain proportional and derivative feedback. We also derive a new complete set of invariants for proportional feedback equivalence and specify a set of necessary conditions for a system to be the limit of another system under these feedback transformations. The necessary conditions are sufficient for arbitrary state space systems and for controllable singular systems.