Global H ∞ control for a class of interconnected nonlinear systems

This paper is concerned with the adaptive decentralized fault-tolerant tracking control problem for a class of uncertain interconnected nonlinear systems with unknown strong interconnections. An algebraic graph theory result is introduced to address the considered interconnections. In addition, to achieve the desirable tracking performance, a neural-network-based robust adaptive decentralized fault-tolerant control (FTC) scheme is given to compensate the actuator faults and system uncertainties. Furthermore, via the Lyapunov analysis method, it is proven that all the signals of the resulting closed-loop system are semiglobally bounded, and the tracking errors of each subsystem exponentially converge to a compact set, whose radius is adjustable by choosing different controller design parameters. Finally, the effectiveness and advantages of the proposed FTC approach are illustrated with two simulated examples.

Exponential small-gain theorem and fault tolerant safe control of interconnected nonlinear systems

Neural network learning algorithm for a class of interconnected nonlinear systems

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

In this paper, a generalized decentralized controller design is presented for robust stabilization and achieving certain L 2 gain of a class of nonlinear interconnected systems via dynamic output feedback control within the LMI framework. This large-scale system is composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. The proposed controller design uses the available neighbouring information to design a decentralized controller that operates at each subsystem. An LMI approach is sufficiently proposed as a feasibility problem of a BMI with respect to controller gains via dynamic output feedback structure. The application of power systems shows that the proposed controller can effectively stabilize the nonlinear interconnected systems and achieve desired performance, even in the presence of disturbances and uncertainties.

In this paper, an observer‐based event‐triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event‐triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event‐triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed‐loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.

In this paper, a new distributed fault estimation observer with adjustable parameters is designed for a class of nonlinear interconnected systems. The presented fault estimator consists of proportional and integral terms to improve the accuracy of fault estimation. The observer gain matrices of the proposed fault estimation scheme for the underlying systems are calculated based on robust L2-L2 and L2-L∞ performance. The proposed method achieves a lower performance level in the aspect of quantitative analysis compared with existing fault estimation approaches. A simulation example is provided to demonstrate the effectiveness of the new design method.

This paper investigates the decentralized adaptive fault-tolerant control (FTC) problem of a class of interconnected nonlinear systems in the presence of actuator faults and output constraints. To compensate the effects of unknown nonlinear interactions among subsystems, a tanh-type auxiliary function and the corresponding parameter updating law are proposed. The actuator faults are allowed to be unknown and time-varying, and an adaptive mechanism is designed to estimate the unknown bounds of faults. Meanwhile, the output transformation technique is introduced which transforms the constrained output into an unconstrained one. Stability analysis shows that the proposed scheme can ensure the boundedness of all the closed-loop system signals and the output constraints are not violated. Finally, simulation results are presented to demonstrate the effectiveness of the proposed FTC strategy.

Quantized adaptive decentralized control for interconnected nonlinear systems with actuator faults

In this article, a novel high gain observer (HGO)-based decentralised indirect adaptive fuzzy controller is developed for a class of uncertain affine large-scale nonlinear systems. By the combination of fuzzy logic systems and an HGO, the state variables are not required to be measurable. The proposed feedback and adaptation mechanisms guarantee that each subsystem is able to adaptively compensate for interconnections and disturbances with unknown bounds. It is ascertained using a singular perturbation method that all the signals of the closed-loop large-scale system stand uniformly ultimately bounded and the tracking errors converge to tunable neighbourhoods of the origin. Simulation results of correlated double inverted pendulums substantiate the effectiveness of the proposed controller.

In this paper, a decentralized control strategy based on sliding mode techniques is proposed for a class of nonlinear interconnected systems. Both matched uncertainties in the isolated subsystems and mismatched uncertainties associated with the interconnections are considered. Under mild conditions, sliding mode controllers for each subsystem are designed in a decentralized manner by only employing local information. Conditions are determined which enable information on the interconnections to be employed within the decentralized controller design to reduce conservatism. The developed results are applied to an automated highway system. Simulation results pertaining to a high-speed following system are presented to demonstrate the effectiveness of the approach.

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H ∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H ∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H ∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.

ABSTRACTWe design a decentralised observer-based sampled-data controller with quantised output for a class of interconnected nonlinear systems. Instead of quantising the output directly, we quantise the sampled output to avoid sudden jump. It can be proved that by choosing suitable design parameters, global stability of the system is achieved. An example is given to illustrate the effectiveness of the proposed method.

We present a novel decentralized tracking control scheme for a class of large-scale nonlinear systems with partial state constraints. For the first time, backstepping design with the newly proposed BLF is incorporated to effectively deal with the control problem of nonlinear systems with interconnected constraints. To prevent the states of each subsystem from violating the constraints, we employ a special barrier Lyapunov function (BLF), which grows to infinity whenever its argument approaches some finite limits. By ensuring boundedness of the barrier Lyapunov function in the closed loop, we ensure that those limits are not transgressed. Asymptotic tracking is achieved without violation of the constraints, and all closed-loop signals remain bounded. In the end, an illustrative example is presented to demonstrate the performance of the proposed control.

In this paper, dynamic output feedback control problem is investigated for a class of nonlinear interconnected systems with time delays. Decentralized observer independent of the time delays is first designed. Then, we employ the bounds information of uncertain interconnections to construct the decentralized output feedback controller via backstepping design method. Based on Lyapunov stability theory, we show that the designed controller can render the closed-loop system asymptotically stable with the help of the changing supplying function idea. Furthermore, the corresponding decentralized control problem is considered under the case that the bounds of uncertain interconnections are not precisely known. By employing the neural network approximation theory, we construct the neural network output feedback controller with corresponding adaptive law. The resulting closed-loop system is stable in the sense of semiglobal boundedness. The observers and controllers constructed in this paper are independent of the time delays. Finally, simulations are done to verify the effectiveness of the theoretic results obtained.