Output feedback control for interconnected time-delay systems with prescribed performance

Adaptive Decentralized Control for Interconnected Time-Delay Uncertain Nonlinear Systems With Different Unknown Control Directions and Deferred Full-State Constraints

In this article, the problem of adaptive decentralized control is investigated for a class of interconnected time-delay uncertain nonlinear systems with different unknown control directions and deferred asymmetric time-varying (DTV) full-state constraints. By constructing the novel time-varying asymmetric integral barrier Lyapunov function (TVAIBLF), the conservative limitation of constant integral barrier Lyapunov function (IBLF) or symmetric IBLF is reduced and the need on the prior knowledge of control gains is also avoided, while the deferred constraints directly imposed on the states of system are achieved by introducing the shifting function into the controller design. Furthermore, based on the Nussbaum-type functions, a new adaptive decentralized control strategy for interconnected time-delay nonlinear systems with subsystems having different control directions is proposed via backstepping method. And it is proven that the proposed control method can guarantee that all signals in closed-loop system are bounded and the transform errors asymptotically converge to zero. Finally, the effectiveness of the proposed control strategy is illustrated through the simulation results.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control of Nonlinear Interconnected Systems With Unmodeled Dynamics and Prescribed Performance

This article proposes two adaptive asymptotic tracking control schemes for a class of interconnected systems with unmodeled dynamics and prescribed performance. By applying an inherent property of radial basis function (RBF) neural networks (NNs), the design difficulties aroused from the unknown interactions among subsystems and unmodeled dynamics are overcome. Then, in order to ensure that the tracking errors can be suppressed in the specified range, the constrained control problem is transformed into the stabilization problem by using an auxiliary function. Based on the adaptive backstepping method, a time-triggered controller is constructed. It is proven that under the framework of Barbalat's lemma, all the variables in the closed-loop system are bounded and the tracking errors are further ensured to converge to zero asymptotically. Furthermore, the event-triggered strategy with a variable threshold is adopted to make more precise control such that the better system performance can be obtained, which reduces the system communication burden under the condition of limited communication resources. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

Reduced-Order Observer-Based Output-Feedback Tracking Control for Nonlinear Time-Delay Systems With Global Prescribed Performance

In this article, the output-feedback tracking control problem is considered for a class of nonlinear time-delay systems in a strict-feedback form. Based on a state observer with reduced order, a novel output-feedback control scheme is proposed using the backstepping approach, which is able to guarantee the system transient and steady-state performance within a prescribed region. Different from existing works on prescribed performance control (PPC), the present method can relax the restriction that the initial value must be given within a predefined region, say, PPC semiglobally. In the case that the upper bound functions for nonlinear time-delay functions are unknown, based on the approximate capacity of fuzzy-logic systems, an adaptive fuzzy approximation control strategy is proposed. When the upper bound functions are known in prior, or in a product form with unknown parameters and known functions, an output-feedback tracking controller is designed, under which the closed-loop signals are globally ultimately uniformly bounded, and tracking control with global prescribed performance can be achieved. Simulation results are given to substantiate our method.

Neural Networks-Based Distributed Adaptive Control of Nonlinear Multiagent Systems

The cooperative control problem of nonlinear multiagent systems is studied in this paper. The followers in the communication network are subject to unmodeled dynamics. A fully distributed neural-networks-based adaptive control strategy is designed to guarantee that all the followers are asymptotically synchronized to the leader, and the synchronization errors are within a prescribed level, where some global information, such as minimum and maximum singular value of graph adjacency matrix, is not necessarily to be known. Based on the Lyapunov stability theory and algebraic graph theory, the stability analysis of the resulting closed-loop system is provided. Finally, an numerical example illustrates the effectiveness and potential of the proposed new design techniques.

Decentralized Adaptive Output Feedback Fault Detection and Control for Uncertain Nonlinear Interconnected Systems

This paper studies the problem of decentralized adaptive output feedback fault detection and control for a class of uncertain nonlinear interconnected systems. The K-filters are designed to estimate the unmeasured state variables of the system. Moreover, the built-in noise dampening filters are introduced to attenuate the influence caused by the measurement noises. Then the fault detection scheme is proposed by designing the residual and threshold signals. Subsequently, by using the backstepping design method, the decentralized switched control strategies are proposed with the help of the neural network approximation technique. Based on the Lyapunov stability theory, it is proved strictly that all signals of the resulting closed-loop system are bounded. Finally, a simulation example is presented to verify the effectiveness of the theoretical result.

Adaptive Neural Tracking Control for Interconnected Switched Systems With Non-ISS Unmodeled Dynamics

The adaptive neural network tracking control problem is investigated for a class of interconnected switched systems. The considered systems are with unmodeled dynamics, some of which do not satisfy the input-to-state stable (ISS) condition. By utilizing the neural network to approximate the composite unknown nonlinear functions, the corresponding decentralized tracking controller is designed for each subsystem with the help of dynamic surface control method. Some subsystems are stable with the designed controller, while other subsystems may not be stable because of non-ISS unmodeled dynamics, but they have some special properties with the designed controller. Then, a novel switching signal scheme is established such that the interconnected switched system is stable in the sense of semi-global boundedness, and the tracking errors can converge to predefined residual sets with prescribed performance index. Moreover, the switching scheme allows the number of switches to grow faster than traditional average dwell time method. Finally, a numerical example is provided to demonstrate the effectiveness of the presented results.

Minimal-Approximation-Based Decentralized Backstepping Control of Interconnected Time-Delay Systems

A decentralized adaptive backstepping control design using minimal function approximators is proposed for nonlinear large-scale systems with unknown unmatched time-varying delayed interactions and unknown backlash-like hysteresis nonlinearities. Compared with existing decentralized backstepping methods, the contribution of this paper is to design a simple local control law for each subsystem, consisting of an actual control with one adaptive function approximator, without requiring the use of multiple function approximators and regardless of the order of each subsystem. The virtual controllers for each subsystem are used as intermediate signals for designing a local actual control at the last step. For each subsystem, a lumped unknown function including the unknown nonlinear terms and the hysteresis nonlinearities is derived at the last step and is estimated by one function approximator. Thus, the proposed approach only uses one function approximator to implement each local controller, while existing decentralized backstepping control methods require the number of function approximators equal to the order of each subsystem and a calculation of virtual controllers to implement each local actual controller. The stability of the total controlled closed-loop system is analyzed using the Lyapunov stability theorem.