Elegant antidisturbance fault‐tolerant control for stochastic systems with multiple heterogeneous disturbances

In this article, the elegant antidisturbance fault‐tolerant control (EADFTC) problem is studied for a class of stochastic systems in the simultaneous presence of multiple heterogeneous disturbances and time‐varying faults. The multiple heterogeneous disturbances include white noise, norm bounded uncertain disturbances and uncertain modeled disturbances with multiple nonlinearities and unknown amplitudes, frequencies, and phases. The time‐varying fault signals are caused by lose efficacy of actuator. To online estimate uncertain modeled disturbances and time‐varying faults, a novel composite observer structure consisting of the adaptive nonlinear disturbance observer and the fault diagnosis observer is constructed. The novel EADFTC strategy is proposed by integrating composite observer structure with adaptive disturbance observer‐based control theory and H_∞ technology. It is proved that all the signals of closed‐loop system are asymptotically bounded in mean square under the circumstances of multiple heterogeneous disturbances and time‐varying faults occur simultaneously. Finally, the effectiveness and availability of proposed strategy are demonstrated by means of the numerical simulation and a doubly fed induction generators system simulation, respectively.     

Composite hierarchical antidisturbance control for a class of discrete‐time stochastic systems

In this paper, antidisturbance control and estimation problem are discussed for a class of discrete‐time stochastic systems with nonlinearity and multiple disturbances, which include the disturbance with partially known information and a sequence of random vectors. A disturbance observer is constructed to estimate the disturbance with partially known information. A composite hierarchical antidisturbance control scheme is proposed by combining disturbance observer and H_∞ control. It is proved that the 2 different disturbances can be rejected and attenuated, and the corresponding desired performances can be guaranteed for discrete‐time stochastic systems with known and unknown nonlinear dynamics, respectively. Simulation examples are given to demonstrate the effectiveness of the proposed scheme.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

H∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems

This paper addresses the problem of H_∞ boundary control for a class of nonlinear stochastic distributed parameter systems expressed by parabolic stochastic partial differential equations (SPDEs) of Itô type. A simple but effective H_∞ boundary static output feedback (SOF) control scheme with collocated boundary measurement is introduced to ensure the local exponential stability in the mean square sense with an H_∞ performance. By using the semigroup theory, the disturbance‐free closed‐loop well‐posedness analysis is first given. Then, based on the SPDE model, a general linear matrix inequality based H_∞ boundary SOF control design is provided via Lyapunov technique and infinite‐dimensional infinitesimal operator, such that the disturbance‐free closed‐loop system is locally exponentially stable in the mean square sense and the H_∞ performance of disturbance attenuation can also be achieved in the presence of disturbances. Finally, simulation results on a stochastic Fisher‐Kolmogorov‐Petrovsky‐Piscounov equation illustrate the effectiveness of the proposed method.     

Composite anti‐disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances

In this paper, the problem of composite anti‐disturbance resilient control is studied for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. The multiple disturbances include two types: one is in the input channel generated by an exogenous system with perturbations, and the other is belong to L ₂[0,∞ ). The first class of disturbances is estimated by designing a disturbance observer. Combining the disturbance estimation with conventional L ₂ ? L _∞ resilient control law, a composite anti‐disturbance control scheme is constructed such that the closed‐loop system is stochastically stable, and different types of disturbances can be attenuated and rejected. By using Lyapunov function method and linear matrix inequalities technique, some sufficient conditions for the desired controller and observer gains are developed. Finally, an application example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite hierarchical anti‐disturbance control for nonlinear systems with DOBC and fuzzy control

Anti‐disturbance control and estimation problem is introduced for a class of nonlinear system subject to disturbances. The adaptive disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance‐observer‐based control with fuzzy control, a novel type of composite hierarchical anti‐disturbance control scheme is presented for a class of nonlinear system with unknown nonlinear dynamics. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes.Copyright © 2012 John Wiley & Sons, Ltd.     

A generalized exact tracking control methodology for disturbed nonlinear systems via homogeneous domination approach

A generalized homogeneous exact set‐point tracking control methodology for a class of disturbed higher‐order nonlinear systems is investigated in this paper. By virtue of utilizing the disturbance estimation and active elimination approach, a homogeneous domination feedback technique is then integrated such that a generalized composite active anti‐disturbance control framework is proposed with a delicate handling procedure of the non‐vanishing nonlinearities. The proposed methodology has several new features. First, a genuine nonlinear composite controller employing the system nonlinearities will bring an improvement of the control performances. Second, the flexility of the design methodology renders its suitability for random output tracking with mismatched disturbances in every channel. Moreover, the control function is constructed in a neat nested form and hence easier to be implemented. Numerical simulation results affirm the output tracking control performances. Copyright © 2016 John Wiley & Sons, Ltd.     

Feedback control of nonlinear differential algebraic systems using Hamiltonian function method

Many complex dynamic systems, such as power systems, robotic systems, etc. can be modeled as the following nonlinear differential algebraic systems (NDAS) [1-4](1) where the vector 1 x1 ∈ X 1 ? Rn represents the state variable, and x2 ∈X2? Rn2 is the al…     

Composite hierarchical anti-disturbance control for robotic systems with multiple disturbances

Various sources of disturbances exist simultaneously in robotic systems, such as vibrations, frictions, measurement noises, and equivalent disturbances from unmodeled dynamics and nonlinearities. However, most results on anti-disturbance control focus on only one type of disturbances, which cannot reflect the real applications and may lead to design conservativeness due to partial use of the disturbance information. In this paper, we propose a composite hierarchical anti-disturbance control (CHADC) strategy for robotic systems in the presence of multiple disturbances as well as system uncertainties. Particularly, we assume the existence of two types of disturbances, where the first type represents disturbances from exogenous systems with model perturbations, while the second type includes other random disturbances satisfying the L2-norm bound condition. Accordingly, the CHADC control architecture is composed of a nonlinear disturbance observer (NDO) and an H _∞ based PID controller, where the NDO is constructed to estimate the first type of disturbances and provide feed forward compensation, while the feedback PID loop is optimized using H _∞ theory to minimize the second type of disturbances. Robustness against system uncertainties is also considered in this hierarchical control structure. The proposed control approach is applied to a two-link robotic manipulator and compared with the conventional DOBC (disturbance observer based control) strategies.     

Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances

In this paper, the problem of composite anti-disturbance resilient control is addressed for time-varying delay Markovian jump nonlinear systems with multiple disturbances. The disturbances are assumed to include two parts: the first one in the input channel is described by an external system with perturbations; the second one is supposed to be bounded H₂ norm. By combining disturbance observer and L₂–L_∞ control method, the disturbances are attenuated and rejected, simultaneously, and the desired dynamic performance can be obtained for time-varying delay Markovian jump nonlinear systems. Moreover, the gains of the resilient controller and the observer are acquired by applying linear matrix inequalities (LMIs) technology. Finally, an application example is presented to show the effectiveness of the proposed approach.     

Robust control of nonlinear semi‐strict feedback systems using finite‐time disturbance observers

The output tracking controller design problem is dealt with for a class of nonlinear semi‐strict feedback systems in the presence of mismatched nonlinear uncertainties, external disturbances, and uncertain nonlinear virtual control coefficients of the subsystems. The controller is designed in a backstepping manner, and to avoid the shortcoming of ‘explosion of terms’, the dynamic surface control technique that employs a group of first‐order low‐pass filters is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input‐to‐state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite‐time disturbance observer that estimates the disturbance term in a finite‐time. The properties of the composite control system are analyzed theoretically. Furthermore, by exploiting the cascaded structure of the control system, a simplified robust controller is proposed where only the first subsystem employs a disturbance observer. The performance of the proposed methods is confirmed by numerical examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties

In this paper, an adaptive fuzzy output feedback control approach based on backstepping design is proposed for a class of SISO strict feedback nonlinear systems with unmeasured states, nonlinear uncertainties, unmodeled dynamics, and dynamical disturbances. Fuzzy logic systems are employed to approximate the nonlinear uncertainties, and an adaptive fuzzy state observer is designed for the states estimation. By combining backstepping technique with the fuzzy adaptive control approach, a stable adaptive fuzzy...     

Robust passivity‐based H∞ control for uncertain switched nonlinear systems

In this paper, we investigate the H_∞ control problem for uncertain switched nonlinear systems with passive and non‐passive subsystems. For any given average dwell time, any given passivity rate and any given disturbance attenuation level, we design feedback controllers of subsystems, which may depend on the pre‐given constants, to solve the H_∞ control problem for the uncertain switched nonlinear systems for all admissible uncertainties. For linear systems, the exponential small‐time norm‐observability is shown to be preserved under disturbance. Two examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite DOBC with fuzzy fault‐tolerant control for stochastic systems with unknown nonlinear dynamics

A class of stochastic nonlinear systems with fault and multisource disturbances is concerned. The fault is a general bounded actuator fault, and the multiple disturbances include partial‐known information disturbance and white noise. A stochastic adaptive disturbance observer is constructed to estimate the partial‐known information disturbance, based on which the partial‐known information disturbance can be compensated in the feed‐foreword channel immediately. Also, the multiplicative white noise can be attenuated by the designed feedback controller. To make the composite system is satisfactory, a composite disturbance based‐observer control with fuzzy fault‐tolerant control is proposed. The pole placement and LMI method is applied to attenuate and reject the disturbance. Furthermore, the fault can be compensated simultaneously. To verify the feasibility and availability of the designed control scheme, a simulation example is shown finally.     

Output tracking of constrained nonlinear processes with offset-free input-to-state stable fuzzy predictive control

This paper develops an efficient offset-free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model. The estimated disturbance signals account for all the plant-model mismatch and unmodeled plant disturbances. An augmented piecewise observer, constructed by solving some linear matrix inequalities, is used to estimate the system states and the lumped disturbances. Based on the reference from an online constrained target generator, the fuzzy model predictive control law can be easily obtained by solving a convex semi-definite programming optimization problem subject to several linear matrix inequalities. The resulting closed-loop system is guaranteed to be input-to-state stable even in the presence of observer estimation error. The zero offset output tracking property of the proposed control approach is proved, and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant.     

Dissipative control for a class of uncertain nonlinear control systems

A general dissipative controller is proposed to achieve robust tracking control performance for a class of uncertain single‐input single‐output (SISO) nonlinear systems. The feedback linearization technique is employed to transform the nonlinear system into an assignable inner linear system with a differential control input so that the relationship of the external (input) power and the stored energy of system can be shown clearly. Then, a dissipative controller with an assignable attenuation level is proposed to make the system energy dynamics fit a required dissipative inequality. The unstable factors of the system can then be attenuated accordingly. The system stability is guaranteed even if the system has permanent unavoidable uncertainties. The proposed design can be achieved without the use of traditional means, i.e. optimal control, which requires solution of a Hamilton inequality (or Riccati equation). The Lyapunov stable condition is assured in our approach when the system uncertainties belong to L _∞. Moreover, due to the compatibility of the proposed controller, the controller can be embedded into the designs of other controllers. In those designs, knowledge of the system functions is not required. Basically, the proposed dissipative controller is independent of the system functions. The use of the bounds of the system function is considered to prove the system stability only. Two simulations are given to illustrate the effectiveness of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On mean‐square H∞ control for discrete‐time nonlinear stochastic systems with (x,u, v)‐dependent noises

In this paper, the H_∞ control problem is investigated for a general class of discrete‐time nonlinear stochastic systems with state‐, control‐, and disturbance‐dependent noises (also called (x, u, v)‐dependent noises). In the system under study, the system state, the control input, and the disturbance input are all coupled with white noises, and this gives rise to considerable difficulties in the stability and H_∞ performance analysis. By using the inequality techniques, a sufficient condition is established for the existence of the desired controller such that the closed‐loop system is mean‐square asymptotically stable and also satisfies H_∞ performance constraint for all nonzero exogenous disturbances under the zero‐initial condition. The completing square technique is used to design the H_∞ controller with hope to reduce the resulting conservatism, and a special algebraic identity is employed to deal with the cross‐terms induced by (x, u, v)‐dependent noises. Several corollaries with simplified conditions are presented to facilitate the controller design. The effectiveness of the developed methods is demonstrated by two numerical examples with one concerning the multiplier‐accelerator macroeconomic system.     

Event‐triggered H∞ control for a class of nonlinear networked control systems using novel integral inequalities

This paper is concerned with event‐triggered H_∞ control for a class of nonlinear networked control systems. An event‐triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event‐triggered transmission scheme, the closed‐loop system is modeled as a system with an interval time‐varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov–Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event‐triggered H_∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to the robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality‐based conditions are formulated to design both event‐triggered and time‐triggered H_∞ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.