Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints

In this paper, smooth output feedback controllers are presented to stabilize a class of planar switched nonlinear systems with asymmetric output constraints (AOCs). A new common barrier Lyapunov function (CBLF) is developed to prevent the switched system from violating AOCs. Combining the adding a power integrator technique (APIT) and the CBLF, state feedback controllers are designed. Then, reduced-order nonlinear observers are constructed and smooth output feedback controllers are proposed to globally stabilize planar switched nonlinear systems under arbitrary switchings. Meanwhile, the system output meets the prescribed AOCs during operation. The method proposed in this paper is a unified tool because it works not only for switched nonlinear systems with asymmetric or symmetric output constrains but also for those without output constraints. Simulations are presented to verify the proposed method.     

A hybrid feedback control strategy for autonomous waypoint transitioning and loitering of unmanned aerial vehicles

We consider the problem of autonomously controlling a fixed-wing aerial vehicle to visit a neighborhood of a pre-defined waypoint, and when nearby it, loiter around it. To solve this problem, we propose a hybrid feedback control strategy that unites two state-feedback controllers: a transit controller capable of steering or transitioning the vehicle to nearby the waypoint and a loiter controller capable of steering the vehicle about a loitering radius. The aerial vehicle is modeled on a level flight plane with system performance characterized in terms of the aerodynamic, propulsion, and mass properties. Thrust and bank angle are the control inputs. Asymptotic stability properties of the individual control algorithms, which are designed using backstepping, as well as of the closed-loop system, which includes a hybrid algorithm uniting the two controllers, are established. In particular, for this application of hybrid feedback control, Lyapunov functions and hybrid systems theory are employed to establish stability properties of the set of points defining loitering. The analytical results are confirmed numerically by simulations.     

Lyapunov type functions for classes of autonomous parabolic feedback control problems and applications

In this note we provide sufficient conditions for the existence of a Lyapunov function for a class of parabolic feedback control problems. The results are applied to the long-time behavior of state functions for the following problems: (i) a model of combustion in porous media; (ii) a model of conduction of electrical impulses in nerve axons; and (iii) a climate energy balance model.     

Finite-time disturbance observer-based trajectory tracking control for quadrotor unmanned aerial vehicle with obstacle avoidance

This paper investigates the problem of trajectory tracking control for quadrotor unmanned aerial vehicle (UAV) in the presence of dynamic obstacles and external disturbance forces/torques. More specifically, two new sliding mode disturbance observers are firstly designed to estimate the external disturbances, in which the observation errors can converge to zero in finite time. Furthermore, utilizing the observation information, a new sliding mode surface-like variable-based position tracking control scheme and a novel nonsingular terminal sliding mode-based attitude synchronization control scheme are developed to drive the UAV tracking the reference trajectory with obstacle avoiding. Moreover, the tracking errors of the close-loop control system can converge to zero within finite time by the analyses of Lyapunov methodology. Finally, the numerical simulation results are presented to illustrate the effectiveness of the proposed control schemes.     

Adaptive tracking control for a class of switched uncertain nonlinear systems under a new state-dependent switching law

This paper deals with the problem of adaptive fuzzy tracking control for a class of switched uncertain nonlinear systems. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and the adaptive backstepping and dynamic surface control techniques are adopted. First, a new state-dependent switching method is proposed. By introducing convex combination technique and designing a state-dependent switching law, only the solvability of the adaptive tracking control problem for a convex combination of the subsystems is necessary. Second, a new common Lyapunov function with switched adaptive parameters is constructed to reduce the conservatism. Third, to avoid Zeno behavior, a modified state-dependent switching law with dwell time is proposed. It is shown that under the proposed control and switching laws, all the signals of the closed-loop system are bounded and all the state tracking errors can converge to a priori accuracy, even if some subsystems are uncontrollable. Finally, the effectiveness of the proposed method is illustrated through two simulation examples.     

Optimal output tracking control for nonlinear systems via successive approximation approach

This paper deals with the optimal output tracking control (OOTC) problem of a class of nonlinear systems whose reference input to be tracked is produced by a generalized linear exosystem. To solve the nonlinear OOTC problem, the nonlinear two-point boundary value (TPBV) problem derived from the necessary conditions of the OOTC problem is transformed into two decoupled iterative sequences of linear differential equations. The OOTC law obtained consists of accurate feedforward and feedback terms and a nonlinear compensation term. The former can be found by solving a Sylvester equation and a Riccati equation, and the latter can be approximated using a successive approximation approach (SAA). A reduced-order reference input observer is constructed to make the feedforward control law physically realizable. A simulation example is employed to illustrate the validity of the results.     

Output tracking control of Boolean control networks with impulsive effects

This paper studies the output tracking problem of Boolean control networks (BCNs) with impulsive effects via the algebraic state‐space representation approach. The dynamics of BCNs with impulsive effects is converted to an algebraic form. Based on the algebraic form, some necessary and sufficient conditions are presented for the feedback output tracking control of BCNs with impulsive effects. These conditions contain constant reference signal case and time‐varying reference signal case. The study of an illustrative example shows that the obtained new results are effective.     

A new method for control of nonlinear state-dependent switched systems

In this paper, a new method for the control of input-affine nonlinear switched systems is introduced. The system switching conditions are assumed to be state-dependent, rather than the simpler input-dependent case. The main contribution of this research is that the effects of switched dynamics are interpreted as a model uncertainty bounded within a polynomial of states norms, with unknown coefficients. In order to prevent extra conservativeness, coefficients are tuned adaptively, so that a minimal state-varying bound could be achieved. This is unlike the conventional sliding mode control (SMC) scheme, where the existence of a constant and usually large upper bound must be presumed. To address the challenge of coping with such a new concept of uncertainty, an extended form of the original adaptive fuzzy sliding mode control scheme is proposed. Adaptation laws are used to tune a fuzzy controller and also real-time estimation of the instantaneous bound of uncertainties. Closed-loop stability is guaranteed by proposing a group of multiple Lyapunov functions (MLF) with tunable parameters. Except for the mild condition that the largest difference between the magnitudes of the sub-manifolds of the switched system is bounded by a polynomial of states with uncertain coefficients, the proposed method has the distinct advantage that no information about the dynamic equations or switching conditions is required in the control design stage. The proposed method is applied to the two challenging case studies, depicting the outstanding effectiveness of the method.     

Fixed-time stability of switched systems with application to a problem of formation control

The problem of fixed-time stability of switched systems is studied. With the aid of the multiple Lyapunov function method, constraints on switching signals are derived under which global fixed-time stability of zero solutions of considered systems can be guaranteed. Sufficient conditions of fixed-time stability for Persidskii-type systems are obtained. The developed approaches are applied to the problem of the fixed-time deployment of mobile agents over a line segment under protocols with switched communication topology. Efficiency of the obtained results is demonstrated by a numerical simulation.     

Fuzzy guaranteed cost output tracking control for fuzzy discrete‐time systems with different premise variables

This article investigates the problem of output tracking control for a class of discrete‐time interval type‐2 (IT2) fuzzy systems subject to mismatched premise variables. Based on the IT2 Takagi–Sugeno (T–S) fuzzy model, the criterion to design the desired controller is obtained, which guarantees the closed‐loop system to be asymptotically stable and satisfies the predefined cost function. Moreover, the controller to be designed does not need to share the same premise variables of the system, which enhances the flexibility of controller design and reduces the conservativeness. Finally, two examples are provided to demonstrate the effectiveness of the method proposed in this article. © 2015 Wiley Periodicals, Inc. Complexity 21: 265–276, 2016     

Multiple delay-dependent guaranteed cost control for uncertain switched random nonlinear systems against intermittent sensor and actuator faults

In this paper, guaranteed cost control is investigated for switched random nonlinear systems against multiple state delays, model uncertainties, intermittent sensor and actuator faults. Other factors containing nonlinear dynamics, external disturbances as well as measurement noise are also considered. This is the first try to realize guaranteed cost control for uncertain switched random nonlinear systems against multiple time delays. In practice, color noise is more common than white noise in some specific situations. Thus, this paper considers random systems with color noise. In contrast to the previous study works, the suggested system can be applied to a wider range. First, a dynamic full-order output feedback controller is established to make the system stable. And an entire closed-loop system is got to achieve guaranteed cost control. Then, the multiple delay-dependent sufficient conditions are acquired through the piecewise Lyapunov function in the framework of linear matrix inequalities (LMIs). In the meantime, controller gain matrices are obtained. At last, two simulation examples are presented to verify the availability of the suggested approach.     

Robust optimal control for a batch nonlinear enzyme-catalytic switched time-delayed process with noisy output measurements

In this paper, we consider a nonlinear switched time-delayed (NSTD) system with an unknown time-varying function describing the batch culture. The output measurements are noisy. According to the actual fermentation process, this time-varying function appears in the form of a piecewise-linear function with unknown kinetic parameters and switching times. The quantitative definition of biological robustness is given to overcome the difficulty of accurately measuring intracellular material concentrations. Our main goal is to estimate these unknown quantities by using noisy output measurements and biological robustness. This estimation problem is formulated as a robust optimal control problem (ROCP) governed by the NSTD system subject to continuous state inequality constraints. The ROCP is approximated as a sequence of nonlinear programming subproblems by using some techniques. Due to the highly complex nature of these subproblems, we propose a hybrid parallel algorithm, based on Nelder–Mead method, simulated annealing and the gradients of the constraint functions, for solving these subproblems. The paper concludes with simulation results.     

具外部扰动的变时滞不确定奇异系统的滑动模态控制

研究了含有多个变时滞的不确定奇异系统的滑动模态问题.该系统相比文献中已研究的系统更为复杂,具有多个变时滞,且分别含有匹配和不匹配的外部扰动项.通过对系统进行等价分解化为两个子系统,对分解后的系统进行切换函数的设计,再通过定义Lyapunov函数得到使得系统的滑模运动渐近稳定的充分条件.由此证明了所设计的滑模控制率能够保证状态轨迹在优先时间内被驱动到指定的切换面上且保持运动.设计过程简单,且结果以线性矩阵不等式呈现,相比文献中已有的结论更易于实现.最后通过例子验证结论的正确性.     

RBF‐based discrete sliding mode control for robust tracking of uncertain time‐delay systems with input nonlinearity

In this article, a control scheme combining radial basis function neural network and discrete sliding mode control method is proposed for robust tracking and model following of uncertain time‐delay systems with input nonlinearity. The proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties, and external disturbances. The salient features of the proposed controller include no requirement of a priori knowledge of the upper bound of uncertainties and the elimination of chattering phenomenon and reaching phase. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. © 2015 Wiley Periodicals, Inc. Complexity 21: 194–201, 2016     

Distributed adaptive formation tracking using quantized feedback communication for networked mobile robots with unknown wheel slippage

In this study, we consider a quantized-feedback-communication-based control design problem for the distributed adaptive formation tracking of multiple nonholonomic mobile robots with unknown slippage constraints under capacity-limited network control environments. Uniform-hysteretic quantizers are employed to quantize all the inputs and states of robots and the quantized position information of each robot is only transmitted to neighboring robots through directed networks. Compared with existing literature related to the robot formation, the primary contribution of this paper lies in establishing a novel local adaptive control design methodology to deal with the discontinuity problem caused by using the quantized states of each follower and the quantized position communication of neighboring robots. In the proposed strategy, the communication of the orientations and velocities of neighboring robots is not required for the local control design of follower robots. Moreover, quantized-states-based adaptive compensation schemes are constructed for the effects of signal quantization and wheel slippage. Based on the analysis of quantization errors, the practical stability strategy of the overall closed-loop formation system is derived with the convergence of local tracking errors. Simulation results clarify the proposed formation strategy.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016