Robust Design of Stabilizing Controllers for Interconnected Time-delay Systems

doi:10.1016/S0005-1098(97)00229-X

Automatica

Volume 34, Issue 6, June 1998, Pages 795-800

https://doi.org/10.1016/S0005-1098(97)00229-X Get rights and content

Abstract

This paper develops a linear decentralized controller that guarantees the exponential stabilization of a class of interconnected uncertain systems with delays. The uncertainties are mismatched and are composed of three portions: local (within each subsystem), interaction (across the subsystem couplings) and state delay. The stability analysis is based on the constructive use of Lyapunov functional. It has been established that the developed stabilizing controller renders the closed-loop interconnected system globally exponentially stable to a calculable zone around the origin.

References (0)

Cited by (95)

Quantized-output-feedback practical prescribed-time design strategy for decentralized tracking of a class of interconnected nonlinear systems with unknown interaction delays
2024, ISA Transactions
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.
Quantized-state-based decentralized neural network control of a class of uncertain interconnected nonlinear systems with input and interaction time delays
2023, Engineering Applications of Artificial Intelligence
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.
Decentralized adaptive output-feedback control of interconnected nonlinear time-delay systems using minimal neural networks
2018, Journal of the Franklin Institute
This paper presents a minimal-neural-networks-based design approach for the decentralized output-feedback tracking of uncertain interconnected strict-feedback nonlinear systems with unknown time-varying delayed interactions unmatched in control inputs. Compared with existing approximation-based decentralized output-feedback designs using multiple neural networks for each subsystem in lower triangular form, the main contribution of this paper is to provide a new recursive backstepping strategy for a local memoryless output-feedback controller design using only one neural network for each subsystem regardless of the order of subsystems, unmeasurable states, and unknown unmatched and delayed nonlinear interactions. In the proposed strategy, error surfaces are designed using unmeasurable states instead of measurable states and virtual controllers are regarded as intermediate signals for designing a local control law at the last step. Using Lyapunov stability theorem and the performance function technique, it is shown that all signals of the total controlled closed-loop system are bounded and the transient and steady-state performance bounds of local tracking errors can be preselected by adjusting design parameters independent of delayed interactions.
Decentralised Stabilisation of Nonlinear Time Delay Interconnected Systems
2016, IFAC-PapersOnLine
A decentralised state feedback control scheme is proposed to stabilise a class of nonlinear interconnected systems asymptotically based on the characteristics of the system structure. Under the condition that all the nominal isolated subsystems have uniform relative degree, the considered class of interconnected systems is transferred to a new interconnected system formed of single input systems, which facilitates the decentralised control design. A new term, weak mismatched uncertainty, is introduced for the first time to recognise a class of mismatched uncertainties in the isolated subsystems. The study shows that the effects of both matched and weak mismatched uncertainties in the isolated subsystems can be rejected completely by appropriate choice of control, and the effects of matched interconnections can be largely reduced if the control gain is sufficiently high.
Decentralised delay-dependent static output feedback variable structure control
2014, Journal of the Franklin Institute
In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.
Decentralized MRAC for large-scale interconnected systems with time-varying delays and applications to chemical reactor systems
2012, Journal of Process Control
Citation Excerpt :
Ref. [11] investigated a class of interconnected systems and assumed that all delays were equal and constant. In [12], the problem of robust control for a class of interconnected systems with bounded uncertainties was considered. In [13], the sliding mode control method was employed for the decentralized controller design.
The model reference adaptive control problem is investigated for a class of large-scale systems with time-varying delays. The considered systems have mismatched delay functions and matched interconnections. Firstly, a state coordinate transformation is employed to convert the original error system into a cascade system. Secondly, a delay-dependent virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem. By choosing new Lyapunov Krasovskii functional, we show that the designed decentralized continuous adaptive controller renders that the solutions of the closed-loop system converge exponentially to a bounded region. Finally, the theoretic achievements are applied to the control design of a chemical reactor system with two subsystems. The control results show the effectiveness of the proposed method.

View all citing articles on Scopus

^☆: This paper was recommended for publication by Editor Prof. P. Dorato.

View full text

Technical CommuniqueRobust Design of Stabilizing Controllers for Interconnected Time-delay Systems☆

Abstract

Technical Communique
Robust Design of Stabilizing Controllers for Interconnected Time-delay Systems☆