Uncertain Interconnected Systems Research Articles

Finite-time event-triggered output-feedback adaptive decentralized echo-state network fault-tolerant control for interconnected pure-feedback nonlinear systems with input saturation and external disturbances: A fuzzy control-error approach

In this paper, we introduce a decentralized Event-Triggered fault-tolerant echo-state network (ESN) direct adaptive controller for uncertain interconnected nonlinear systems in pure-feedback form. The proposed controller addresses input saturation, actuator faults, external disturbances, and unavailable states for measurement. Unlike the existing works in the literature that adapts the ESN weights using the tracking error, our method employs the control error that is estimated using a fuzzy inference system, to derive the adaptation laws. The complexity explosion typically seen with recursive back-stepping and Dynamic Surface Control (DSC) designs is completely avoided. Our control scheme addresses four types of state-dependent actuator faults: bias, drift, loss of accuracy, as well as loss of effectiveness. The ESNs approximate unknown ideal control laws, while robust terms are added to enhance the stability of the closed-loop system. Stability analysis ensures that tracking errors converge, in finite time, to a small compact set near the origin due to the strictly positive real (SPR) property. Simulation results of a quadrotor UAV and a mathematical system are presented. A comparative analysis is performed with another approach to emphasize the effectiveness of the proposed method.

Robust Policy Iteration of Uncertain Interconnected Systems With Imperfect Data

This paper investigates the robust optimal control problem of a class of continuous-time, partially linear, interconnected systems. In addition to the dynamic uncertainties resulted from the interconnected dynamic system, unknown bounded disturbances are taken into account throughout the learning process, wherein the system’s dynamics and the disturbances are assumed unknown. These challenges lead the collected online data to be imperfect. In this scenario, traditional data-driven control techniques, such as adaptive dynamic programming (ADP) and robust ADP, encounter a challenge in approximating the optimal control policy precisely due to imperfect data and computational errors. In this paper, a novel data-driven robust policy iteration method is proposed to simultaneously solve the robust optimal control problems. Without relying on the knowledge of the system’s dynamics, the external disturbances or the complete state, the implementation of the proposed method only needs to access the input and partial state information. Based on the small-gain theorem, the notions of strong unboundedness observability and input-to-output stability, it is guaranteed that the learned robust optimal control gain is stabilizing and that the solution of the closed-loop system is uniformly ultimately bounded despite the existence of dynamic uncertainties and unknown external disturbances. The simulation results reveal the efficiency and practicality of the proposed data-driven control method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the use of reinforcement learning to improve the quality of designing adaptive optimal controllers for engineering applications. Adaptive dynamic programming methods, in particular policy iteration (PI), are widely used in solving optimal control problems. However, due to the iterative nature of PI, the approximated optimal control policy may be inaccurate and imprecise. Especially, when using imperfect system’s measurements instead of the modelling information. This can result in causing the learned control policy to deviate from the actual optimal policy. This becomes more challenging in the existence of dynamic uncertainties and unknown external disturbances which corrupt the measurements and result in imperfect data. This work investigates the conditions on the uncertainties such that the proposed novel data-driven PI algorithm is robust to system’s uncertainties, unknown external disturbances and imperfect measurements. The approximated robust optimal control policy performs robustly in the existences of imperfect data and uncertainties, and at the same time is close enough to the optimal control policy.

Quantized-output-feedback practical prescribed-time design strategy for decentralized tracking of a class of interconnected nonlinear systems with unknown interaction delays

This paper proposes a decentralized practical prescribed-time (PT) tracking design using quantized output feedback (QOF) for uncertain interconnected lower-triangular systems with unknown time-delay interconnections. The local output signals are assumed to be only measured and quantized for the PT tracker design under a band-limited network. By employing a PT-dependent scaling function, a decentralized memoryless PT observer based on quantized local outputs is developed to estimate local unmeasurable state variables. Owing to output quantization, the available output feedback signals become discontinuous. As a result, the tracking error between the actual (i.e., unquantized) local output and the local desired signal cannot be utilized in the local virtual controller. To address this issue, a novel adaptive compensation mechanism is derived to design the local PT neural network tracking laws using only quantized local outputs and estimated states. The proposed PT tracking controller does not require information on the interconnected nonlinear functions and interaction delays. During the Lyapunov stability analysis, the boundary layer error decomposition approach is employed to address the issue of non-differentiability in the local virtual control laws. The proposed QOF control system achieves practical PT stability. It is shown that the settling time of local tracking errors can be predetermined, regardless of the design parameters and initial conditions. Finally, the proposed QOF decentralization strategy is supported with illustrative examples and a comparison to demonstrate its benefits.

Control-error-based output-feedback adaptive decentralized neural network controller for interconnected uncertain strict-feedback nonlinear systems with input saturation

In this paper, a control-error-based decentralized neural network (NN) direct adaptive controller is presented for uncertain interconnected nonlinear systems, in strict-feedback form, subject to input saturation and external disturbances with unavailable states for measurement. Different from the existing results in the literature, the proposed approach is based on the control error instead of the tracking error resulting in a separation-like principle. Furthermore, the explosion of complexity due to back-stepping recursive design is completely avoided along with discarding all restrictive assumptions imposed on the unmatched interconnections. Actually, NNs are used to approximate the unknown ideal control laws, and auxiliary control terms are appended to deal with approximation errors and enhance the stability of the closed-loop system. Besides, fuzzy inference systems are introduced to estimate the unknown control errors, leading to simplified derivation of adaptive laws. Thanks to the strictly positive real (SPR) property, the tracking errors are proved to converge asymptotically to zero using Lyapunov theory, which is superior to bounded stability results usually found in the literature. Simulation results show the effectiveness of the proposed approach.

An improved robust distributed [formula omitted] control method for uncertain interconnected large-scale time-delayed systems

In modern industries, systems have become increasingly large-scale and complex, comprising multiple interconnected subsystems where the performance of each subsystem impacts the others. Ensuring stability and performance under uncertainties, external disturbances, and time delays is crucial for such systems. This paper proposes a new distributed control method that stabilizes a specific type of time-varying input-delayed large-scale system in the presence of uncertainties and external disturbances. The proposed method employs Jensen’s inequality to reduce the number of decision variables and uses reciprocally convex and descriptive methods to minimize conservatism and decrease computation time. The performance of the proposed method is evaluated on a full-car model with an active suspension system as a novel approach to controlling large-scale systems. This paper describes how to divide a large-scale full-car system into several interconnected subsystems, for the first time. The results indicate the potential of the proposed controller in enhancing the performance of the system in comparison with other previous control methods.

Quantized-state-based decentralized neural network control of a class of uncertain interconnected nonlinear systems with input and interaction time delays

This paper presents a quantized-state-based decentralized control strategy for uncertain interconnected nonlinear systems with time-varying delays under a networked control environment. Full state variables quantized via a uniform-hysteretic quantizer are available only for a decentralized adaptive control design. Unlike the existing decentralized adaptive recursive control designs, this study is focused on establishing a quantized-state-based decentralized learning mechanism for neural networks using discontinuously quantized states. Moreover, the stability of a decentralized neural network tracking system in the presence of time delays is analyzed. For each subsystem, a neural-network-based local adaptive tracker using a delay compensator is designed based on the local quantized state feedback. Technical lemmas pertaining to quantization errors and adaptive laws are presented to ensure the boundedness of all closed-loop signals and the convergence of local tracking errors to an adjustable neighborhood of the origin. Finally, illustrative simulations clarify and verify the decentralization strategy of the developed state-quantized adaptive tracking system. The control performance is evaluated using the root mean square control errors, where the values are 0.0293 and 0.0134 for each subsystem in Example 1 and 0.0467 and 0.0384 for each subsystem in Example 2.

Distributed adaptive control for H∞ tracking of uncertain interconnected dynamical systems

SummaryA distributed adaptive control is proposed for tracking of an interconnected dynamical system in the presence of disturbances and system/interconnection uncertainties. A reference model which achieves a robust tracking against disturbances is introduced by using control with transients. Then a distributed adaptive control law is developed for an uncertain interconnected dynamical system, where it employs the specified reference model. It is shown that the boundedness of the error dynamics behaviors as well as zero tracking error in the steady state is guaranteed by the proposed distributed adaptive control in the presence of disturbances and uncertainties. An explicit error bound related to tracking is also established.

Decentralized Backstepping Control for Interconnected Systems With Non-Triangular Structural Uncertainties

In this article, a decentralized adaptive control scheme is proposed based on backstepping techniques for a class of uncertain interconnected systems with unknown modeling errors and interactions. Unlike existing results, the functions bounding modeling errors and interactions are not required to meet the triangular condition. Namely, such functions are allowed to depend on all the states of the interconnected system. It is shown that the proposed adaptive control scheme can ensure all signals in the closed-loop system bounded. Simulation studies verify the effectiveness of the proposed scheme.

Robust decentralized optimal stabilizability of continuous time uncertain interconnected systems: Application to large scale power system

This article introduces a new design of a decentralized robust optimal feedback controller for a class of large-scale systems using the modified algebraic Riccati equations. The studied class of large-scale systems is characterized by structured uncertainties that are bounded. Our main contribution in this work is the use of the Lyapunov direct method for the stability analysis, associated with a quadratic function, in order to determine a new sufficient condition to guarantee the global asymptotic stability of the class of the studied uncertain interconnected systems. The proposed control approach is then implemented on a large-scale power systems composed of three interconnected generators. Simulation results show that the proposed robust optimal controller is quite effective and has an outstanding performance.

Distributed adaptive control for optimal tracking of uncertain interconnected dynamical systems

Distributed adaptive control for optimal tracking of uncertain interconnected dynamical systems

Decentralized robust preview control for uncertain continuous-time interconnected systems

This paper investigates the problem of robust preview tracking control for uncertain continuous-time interconnected systems. We adopt the technology of decentralized control. The tracking controller for each uncertain isolated subsystem is first designed. With the help of an uncertain error system, the considered tracking problem is converted into a regulation problem. The preview tracking controller for the nominal system is obtained by utilizing existing results. A novel method is proposed to tackle the uncertainty in the systems. In this method, the uncertainty bound is incorporated into the cost function. As a result, the preview tracking controller of the nominal system can be treated as a robust preview controller of the uncertain isolated subsystem. Then, the controllers of the uncertain isolated subsystems are assembled as a robust preview controller of uncertain interconnected systems. Finally, an academic numerical example is presented to show the effectiveness and superiority of the proposed controller.

Decentralized adaptive control of uncertain interconnected systems with triggering state signals

Backstepping is a powerful technique of control design for uncertain systems and has been well received. As it involves differentiating virtual control signals recursively, the involved signals must be differentiable. However, when the measured states are only transmitted based on event-triggered conditions, such requirement will not be met, making the recursive backstepping design procedure inapplicable. Thus it is still an open problem to study how an event-triggered scheme is employed to transmit state signals in decentralized control of uncertain interconnected systems with dynamic interactions. In this paper, we present a solution by constructing a new decentralized adaptive backstepping-based control algorithm capable of coping with discontinuity caused by state-triggering. With aid of appropriately chosen Lyapunov functions, all signals in the closed-loop system are ensured globally uniformly bounded. Simulation results are presented to demonstrate the effectiveness of the proposed methodology.

Dynamic event-triggered distributed guaranteed cost FTC scheme for nonlinear interconnected systems via ADP approach

A novel dynamic event-triggered distributed fault tolerant control (FTC) scheme with guaranteed cost is proposed for uncertain nonlinear interconnected systems suffering from time-varying actuator faults. The event-triggered FTC problem of uncertain interconnected system is first converted to a series of equivalent event-triggered optimal control designs of isolated fault-free auxiliary subsystems by defining a modified cost function for each auxiliary subsystem. The equivalence of problem transformation is demonstrated meanwhile the upper bound of cost function of overall interconnected system is analyzed. Subsequently, for the isolated auxiliary subsystem, a dynamic event-triggered adaptive dynamic programming (DET-ADP) algorithm is proposed to obtain the optimal control policy, which can remove the restriction of initial admissible control, eliminate the actor network, and save more communication resources. Furthermore, we prove that the closed-loop auxiliary subsystems are ensured to be uniform ultimate bounded based on Lyapunov approach. Finally, simulation results are presented to validate the developed dynamic event-triggered distributed guaranteed cost FTC scheme.

Robust finite-time PID control for discrete-time large-scale interconnected uncertain system with discrete-delay

In this paper, we investigate the decentralized proportional–integral–derivative (PID) output-feedback control problem for a class of discrete-time uncertain large-scale systems with delayed interconnections. The robust finite time stabilization of the addressed uncertain large-scale system is attained via the feedback control with the prescribed extended passive performance index. Specifically, by using an appropriate Lyapunov–Krasovskii functional, a new set of sufficient conditions is derived on the basis of linear matrix inequality which ensures the finite-time boundedness of the augmented closed-loop uncertain large-scale systems. Furthermore, cone complementarity linearization (CCL) algorithm is developed to obtain the control gain parameters. Finally, a numerical example is provided to illustrate the effectiveness of proposed control design.

Decentralised robust tracking and model following for uncertain large-scale interconnected systems with time-varying delays and dead-zone inputs

The problem of decentralised robust tracking and model following is investigated for a class of uncertain large-scale interconnected systems with both any time-varying delays and any dead-zone input constraints. By combining an adaptive approach with a multiply integral inequality proposed recently in the control literature, a new design method is developed so that (i) the designed decentralised robust tracking control schemes are direct, i.e. not the complicated ones composed of two parts, which can overwhelm the dead-zone input constraints; (ii) it is unnecessary to know any information on the characteristic parameters of dead-zone functions and the time-varying delays, which makes the decentralised robust tracking control rather simple. It is also proved that the local tracking error between the output of each actual subsystem with delays and input constraints and the dynamical signals of the corresponding local reference model is uniformly exponentially bounded. Finally, a numerical example is also given to describe the design procedure and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.

Quantized Decentralized Adaptive Neural Network PI Tracking Control for Uncertain Interconnected Nonlinear Systems With Dynamic Uncertainties

In this paper, a decentralized adaptive neural network proportional-integral (PI) tracking control scheme is proposed for interconnected nonlinear systems with input quantization and dynamic uncertainties. This algorithm is underpinned by the use of the dynamic signal, graph theory, and function recombination to deal with the difficulties existing in the nontriangular form, unmodeled dynamics, and unknown interconnected terms. Recalling the backstepping method and neural network approximation technology, a new PI tracking controller characterized by simple structure and easy implementation is developed which ensures that all the closed-loop signals are uniformly ultimately bounded. The effectiveness of the obtained controller is exemplified via a numerical example and an application to an inverted pendulum.

Design of Prescribed Performance Controller for Load Disturbance Interconnected Power System Based on Fuzzy Adaptive Backstepping

The complex structure of interconnected power system and the existence of external load disturbance make it difficult to establish accurate system model and realize stability control with preset performance. In this paper, a fuzzy adaptive controller design method with preset performance is proposed for uncertain interconnected power systems. Firstly, the system approximation model is obtained by using the fuzzy approximation principle, then the preset performance control strategy is introduced to transform the steady-state preset performance of the system into an error performance function. Finally, the adaptive controller design with preset performance is realized based on the Backstepping method. For the validity of the algorithm, the Simulink simulation is carried out. The results show that the controller can make the output of the system uniformly bounded, that is, the tracking error can always be controlled within the specified performance range.

Adaptive decentralized finite‐time tracking control for uncertain interconnected nonlinear systems with input quantization

AbstractCompared with the previous references, very few results are available to study control scheme directly for interconnected nonlinear systems (INSs) with strongly interconnected terms described by unknown state‐dependent‐nonlinear functions and input quantization in the finite‐time control literature. In this article, an adaptive decentralized finite‐time tracking control (ADFTTC) algorithm is developed to address the system output tracking problem for a class of INSs with input quantization and strongly interconnected terms. To reduce the computation complexity, the neural network technique is employed to reconstruct the derivative of virtual control laws in each step. By employing adding a power integrator technique, an adaptive decentralized finite‐time tracking controller is constructed, which guarantees all signals in the closed‐loop systems converge to a neighborhood of the origin. Moreover, the developed controller avoids the “singularity” and “explosion of complexity” problems in the recursive design scheme. An example of an inverted pendulum confirms the ADFTTC scheme.

Decentralized event-triggered adaptive control of a class of uncertain interconnected nonlinear systems using local state feedback corrupted by unknown injection data

This paper investigates a decentralized event-triggered adaptive control problem of uncertain interconnected lower-triangular nonlinear systems using corrupted local state feedback. The unknown injection data such as sensor faults or cyber attacks are assumed to be added to full state feedback measurements of each subsystem with unknown nonlinearities. Under this assumption, exactly measured local state variables are unknown during Lyapunov-stability-based recursive control design steps. The primary contributions of this study are (i) to develop a recursive adaptive control design strategy for achieving decentralization of unmatched interconnected nonlinearities using corrupted local state feedback information and (ii) to design a decentralized asynchronous event-triggering mechanism using the corrupted local state variables. To this end, local injection data compensators using neural networks and adaptive tuning laws are designed to compensate for unknown injection data and nonlinear interaction effects. It is shown that the proposed decentralized control system via the corrupted local state feedback ensures the practical stability of the total closed-loop system and the exclusion of Zeno behavior.

Network‐based robust performance analysis for uncertain systems interconnected over an undirected graph

SummaryThis article aims at providing tractable conditions of robust performance (RP) analysis for interconnected uncertain system with networked communication, which is composed of heterogeneous uncertain subsystems connected over an undirected graph. Each subsystem communicates with its neighbors through local packet‐based communication network asynchronously and independently. First, the interconnected uncertain system with networked communication is modeled as a hybrid system. Then sufficient conditions in terms of linear matrix inequalities (LMIs), which are related to the interconnection structure and the maximum allowable transmission interval (MATI) of each local network, are derived such that the interconnected uncertain system is robustly asymptotically stable and achieves the desired RP. These conditions only depend on the parameters of individual subsystem and local network. Finally, an example of power system is given to demonstrate the applicability and effectiveness of our results.