Adaptive–adaptive robust boundary control for uncertain mechanical systems with inequality constraints

In this paper, adaptive–adaptive robust boundary control is proposed for uncertain mechanical systems with inequality constraints. First, inequality constraints are taken into consideration, which are derived from the system or environment constraints on state bounds and control input bounds. Moreover, the original system with inequality constraints is transformed into a novel system with merely equality constraints by constraint reorganization techniques. Second, an adaptive robust control with a two-layer adaptive law is initiated. Here, the lower-layer adaptive law is used to overcome the (possibly rapidly time-varying) system uncertainty, which is bounded but unknown. Additionally, the adaptive law design parameters are chosen online by the upper-layer adaptive law, rather than according to the empirically set fixed values. Finally, the performance of the controller with uniform boundedness and uniform ultimate boundedness is theoretically and experimentally verified. The control strategy allows the electric cylinder-driven pitch system to achieve highly accurate and error-controllable motion within the motor drive capability.

     

Quantization-based tracking control for fuzzy singularly perturbed Markov jump systems with incomplete transition information and packet dropout

In this article, the tracking control problem for discrete-time singularly perturbed systems with a piecewise-homogeneous Markov chain subject to the effect of quantization and packet dropout is addressed based on Takagi–Sugeno (T–S) fuzzy-approximation. Firstly, the stochastic variation of mode transition probabilities with time-varying peculiarities is considered in a finite set, which is dominated by a higher-level homogeneous Markov chain. Moreover, partially unknown information in higher-level transition probabilities (HTPs) matrix is resolved by constructing a unified framework, which covers the stochastic switching and arbitrary switching as special cases, simultaneously. Secondly, considering the burden of network communication between components, the quantization impact and packet dropout caused by network network-induced constraints are integrated into the co-design of fuzzy tracking controller, which is mode-dependent and variation-dependent. Several criteria for the stochastic stability and \({\mathcal {H}}_{\infty }\) performance of the augmented system are deduced by establishing a series of linear matrix inequalities. Ultimately, two simulation examples are given to verify the practicability and effectiveness of the proposed control design schemes.

     

Property and evolution of the running-in attractor in an actual dynamic system

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

     

Truncated predictor stabilization control for interconnected nonlinear systems with time-varying input delay

This paper deals with control design for interconnected nonlinear systems with time-varying input delay. Based on the truncated prediction of the system state over the delay period, the state feedback control law is constructed. In the framework of the Lyapunov–Krasovskii function, the stability equations of closed-loop system under state feedback law are established, and the feasibility of the controller is transformed into the problem of establishing a set of linear matrix inequality (LMI) conditions. Based on the Lyapunov stability theorem, it is proved that the closed-loop system is asymptotically stable. Finally, a simulation example is provided to demonstrate the effectiveness of the control scheme.

     

Velocity-based tuning of degree of homogeneity for finite-time stabilization and fault tolerant control of an ROV in the presence of thruster saturation and rate limits

This paper introduces a homogeneous controller along a fixed-time state and fault observer for finite-time stabilization and fault accommodation of a remotely-operated vehicle in the presence of actuator saturation and rate limits. For this, a novel tuning algorithm is improvised for manipulating the degree of homogeneity in homogeneous controllers to effectively acquire different properties from the overall control system. The tuning of degree of homogeneity is based on vehicle’s velocity. The proposed algorithm results in a switching-type controller, which undergoes three different stages during the operation, to eliminate the sensitivity of conventional finite-time and fixed-time controllers to large initial errors in the presence of thruster constraints. In addition, a new fixed-time fault and state observer is designed for the realization of output feedback control and fault tolerance by combining a fixed-time state observer with a fault estimation unit. In contrast to conventional extended-state observers, this observer considers the dynamics of the thruster system in its formulation so that better performance can be provided for the control system upon thruster failures. Control allocation is utilized to accommodate thruster failures and faults and to take account of thruster saturation and rate limits. Stability analyses are carried out for the overall control system and the proposed observer. It is shown that the closed-loop control system would be globally finite-time stable. The state estimation subsystem is fixed-time stable and the fault estimation unit is input-to-state stable. Simulations are carried out and comparisons are made with several finite-time and fixed-time controllers to outline the advantages of the proposed homogeneous controller and the benefits of the overall fault-tolerant control system.

     

Controller design for fractional-order interconnected systems with unmodeled dynamics

This paper focuses on the output feedback tracking control for fractional-order interconnected systems with unmodeled dynamics. The reduced order high gain K-filters are designed to construct the estimation of the unavailable system state. Unmodeled dynamics is extended to the general fractional-order dynamical systems for the first time which is characterized by introducing a dynamical signal r(t). An adaptive output feedback controller is established using the fractional-order Lyapunov methods and proposed by novel dynamic surface control strategy. Then, it is confirmed that the considered system is semi-globally bounded stable and the errors between outputs and the desired trajectories can concentrate to a small neighborhood of the origin. Finally, a simulation example is introduced to demonstrate the correctness of the supplied controller.

     

A new reduction-based LQ control for dynamic systems with a slowly time-varying delay

Time delays in the feedback control often dete- riorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly time-varying input delay based on a transformation, which sire-plifies the time-delay system the relation is discussed for into a delay-free one. Firstly, two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.     

Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology

For the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults, a fuzzy controller based on command filtered and event-triggered technology is designed to improve the tracking error of the system. Concurrently, a fault-tolerant control scheme is introduced to effectively solve the problem of sudden output sensor failure. Additionally, the proposed controller can also greatly avoid complexity explosion problem of derivations of virtual control laws, which makes the design of the controller simpler. Furthermore, an effective observer is designed to solve the problem of system state immeasurability. Therefore, the proposed control scheme makes the design of the controller more convenient and flexible. According to Lyapunov stability theory, it is proved that all closed-loop signals are uniformly and ultimately bounded. Finally, two simulation examples of second-order nonlinear system and single-link robot show the effectiveness of the proposed scheme.

     

Backstepping control for the optoelectronic stabilized platform based on adaptive fuzzy logic system and nonlinear disturbance observer

A composite controller based on a backstepping controller with an adaptive fuzzy logic system and a nonlinear disturbance observer is proposed in this paper to address the disturbance and uncertainty issues in the control of the optoelectronic stabilized platform. The matched and unmatched disturbances and system uncertainty are included in the stabilized platform model. The system's uncertainty and disturbance are approximated and estimated using an adaptive fuzzy logic system and a nonlinear disturbance observer. Moreover, the backstepping control algorithm is utilized to control the system. The simulations are performed in four states to confirm the viability of the proposed control technique. The proportional integral controller, proportional integral-disturbance observer controller, and fuzzy backstepping controller are contrasted with the proposed controller. It has been noted that the proposed controller's instantaneous disturbance's highest value is 5.1°/s. The maximal value of the coupling output for the two gimbals utilizing the proposed controller, however, is 0.0008°/s and 0.0018°/s, respectively. The findings presented here demonstrate that the backstepping controller, which is based on an adaptive fuzzy logic system and a nonlinear disturbance observer, is capable of precise tracking and dynamic tracking of a stabilized platform under disturbance and uncertainty.

     

Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection

For the barrier Lyapunov function-based control of full-state time-varying constrained systems via the traditional backstepping technology, due to repeated differentiations of virtual control functions involving time-varying barriers, the adverse effects of “explosion of complexity” caused by the backstepping iteration are more serious, which even makes it impossible to implement for high-order systems. In order to eliminate this negative influence, we take advantage of the command filtered backstepping approach which introduces a command filter to approximate the constructed virtual control law in each procedure of the backstepping design. More importantly, the approximate errors arising from the introduced filters will be removed by constructing a series of compensating signals. Meanwhile, some relatively conservative assumptions will be released compared with existing control strategies. Furthermore, largely unknown external disturbances that may exist in the system will be estimated in real-time via high-gain disturbance observers and then compensated feedforwardly in designing the controller. Specially, the scheme of the resulting control algorithm is simple and online computation time is saved. Finally, the stability of the whole closed-loop system and the control performance is strictly certificated, respectively.

     

BLS-based formation control for nonlinear multi-agent systems with actuator fault and input saturation

This paper studies the formation control of a nonlinear multi-agent system based on a broad learning system under actuator fault and input saturation. Firstly, the multi-agent tracking error is proposed based on graph theory. Besides, fault tolerance should be considered when actuator fault exists. Meanwhile, the broad learning system is put forward to approximate the unknown nonlinear function in the multi-agent system. Then, an input saturation auxiliary system is introduced to reduce the adverse effects of input saturation constraints. At the same time, the disturbance observer technology is used to estimate the actuator failure as a lumped uncertainty. At last, dynamic surface control is introduced to realize formation control with actuator fault and input saturation. Obviously, it is difficult to design a controller with unknown nonlinear function, input saturation, and actuator fault existing in the multi-agent system. The Lyapunov method can prove the stability of the formation control. The simulation results verify the effectiveness of the controller.

     

车辆主动悬架设计的约束H∞控制方法

针对线性离散时间系统,研究其时域硬约束下的H∞输出反馈控制问题。假定外界扰动能量有限,基于线性矩阵不等式处理方法,提出并证明了时域硬约束下H∞输出反馈控制器存在的充分条件,并应用于车辆主动悬架设计。四分之一车辆模型数值仿真结果表明,即使车辆模型参数存在不确定性,本文提出的控制器在提高车辆乘坐舒适性的同时,仍能很好地兼顾车辆的其他性能要求。     

Prescribed-time adaptive neural tracking control for a class of uncertain robotic manipulators with dead zone input

This paper solves the prescribed-time control problem for a class of robotic manipulators with system uncertainty and dead zone input. To make the system stable within a given convergence time T, a novel prescribed-time adaptive neural tracking controller is proposed by using the temporal scale transformation method and Lyapunov stability theory. Unlike the finite-time and the fixed-time stability where the convergence time depends on the controller parameters, the convergence time constant T is introduced into the proposed controller so that the closed-loop system will be stable within T. To cope with the system uncertainty, radial basis function neural networks (RBFNNs) are used and only need to update one parameter online. In addition, by choosing the same structure and parameters of RBFNNs, the proposed method can shorten the convergence time of the neural networks. Finally, simulation results are presented to demonstrate the effectiveness of the prescribed-time controller.

     

Robust H ∞ output tracking control for fuzzy networked systems with stochastic sampling and multiplicative noise

In this paper, the problem of robust sampled-data H _?? output tracking control is investigated for a class of fuzzy networked systems with stochastic sampling, multiplicative noise and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and they can be extended to the case with multiple stochastic sampling periods. By using an input-delay method, the probabilistic system is transformed into a stochastic continuous time-delay system. A?new linear matrix inequality(LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H _??. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H _?? output tracking design.     

Finite-time non-fragile boundary feedback control for a class of nonlinear parabolic systems

In this paper, the finite-time non-fragile boundary feedback control problem is investigated for a class of nonlinear parabolic systems, where both the multiplicative and additive controller gain variations are considered to describe the actuator parameter perturbation. Non-fragile boundary control strategies are designed with respect to two controller gain variations via collocated or non-collocated boundary measurement, respectively. In light of the finite-time stability and Lyapunov-based techniques, some sufficient conditions are presented in terms of linear matrix inequalities such that the resulting closed-loop system is well-posedness and practically finite-time stable. Finally, numerical examples are given to verify the effectiveness of the proposed design method.

     

Dynamic control for permanent magnet synchronous generator system using novel modified recurrent wavelet neural network

Because permanent magnet synchronous generator (PMSG) system driven by permanent magnet synchronous motor (PMSM) based on wind turbine emulator (WTE) is a nonlinear and time-varying system with high complication, an accurate dynamic model of the PMSG system directly driven by WTE is difficult to establish for the linear controller design. In order to conquer this difficulty and improve the robustness of dynamic system, the PMSG system controlled by the online-tuned parameters of the novel modified recurrent wavelet neural network (NN)-controlled system is proposed to control output voltages and powers of controllable rectifier and inverter in this study. First, a closed-loop PMSM-driven system based on WTE is designed for driving the PMSG system to generate output power. Second, the rotor speeds of the PMSG, the voltages, and currents of the two power converters are detected simultaneously to yield maximum power output. In addition, two sets of the online-tuned parameters of the modified recurrent wavelet NN controllers in the controllable rectifier and inverter are developed for the voltage-regulating controllers in order to improve output performance. Finally, some experimental results are verified to show the effectiveness of the proposed novel modified recurrent wavelet NN controller for the power output of the PMSG system driven by WTE.     

Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters

The problem of output feedback control for a class of second-order nonlinear systems is investigated in this paper. Using the techniques of finite-time control and finite-time convergent observer, an observer-based finite-time output feedback controller is proposed which can guarantee that the system’s state converges to the equilibrium in a finite time. As an application of the proposed theoretical results, the problem of finite-time control without current signal for the DC–DC buck converters is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach

In this paper, an adaptive sliding mode control method is introduced to ensure robust synchronization of two different fractional-order chaotic systems with fully unknown parameters and external disturbances. For this purpose, a fractional integral sliding surface is defined and an adaptive sliding mode controller is designed. In this method, no knowledge of the bounds of parameters and perturbation is required in advance and the parameters are updated through an adaptive control process. The proposed scheme is global and theoretically rigorous. Two examples are given to illustrate effectiveness of the scheme, in which the synchronizations between fractional-order chaotic Chen system and fractional-order chaotic Rössler system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.

     

An output-feedback adaptive actuator failure compensation controller for systems with unknown state delays

This paper presents an output-feedback adaptive controller for a class of linear systems with unknown time-varying state delay and in the presence of actuator failures. We consider a common type of actuator failure in which some unknown system inputs may be stuck at some unknown fixed values and at unknown time instants. The adaptive controller is designed based on SPR–Lyapunov approach for relative degree one and two cases. Closed-loop system stability and asymptotic output tracking are proved using suitable Lyapunov–Krasovskii functional for each case. Simulation results are provided to demonstrate the effectiveness of the proposed results.