Uncertain Interconnected Systems Research Articles

Decentralized low-complexity tracking of uncertain interconnected high-order nonlinear systems with unknown high powers

A global decentralized low-complexity tracker design methodology is proposed for uncertain interconnected high-order nonlinear systems with unknown high powers. It is assumed that interconnected nonlinearities are bounded by completely unknown nonlinearities, rather than, a linear combination of high-ordered state variables. Compared with the existing decentralized results for interconnected nonlinear systems with known high powers, the decentralized robust controller, which achieves the pre-designable transient and steady-state tracking performance for each subsystem, is designed by employing nonlinear error surfaces with time-varying performance functions, regardless of unknown nonlinear interactions and high powers related to virtual and actual control variables. The proposed decentralized continuous robust low-complexity tracker is realized without the use of any adaptive or function approximation techniques for estimating unknown parameters and nonlinearities. The stability and preassigned tracking performance of the resulting decentralized low-complexity control system are thoroughly analyzed in the Lyapunov sense. Finally, simulation results on coupled underactuated mechanical systems are provided to show the effectiveness of the proposed theoretical result.

Stochastic and adaptive optimal control of uncertain interconnected systems: A data-driven approach

This paper provides a novel non-model-based, data-driven stochastic H∞ control design for linear continuous-time stochastic interconnected systems with unknown dynamics. Our contributions are three-fold. First, we develop a tool to show how to assign an arbitrarily small input-to-output stochastic L2 gain of the closed-loop system, by combining the gain assignment technique with the zero-sum dynamic game-based H∞ control design. Second, robustness to dynamic uncertainties is tackled using the small-gain theory. Third, we develop a non-model-based stochastic robust adaptive dynamic programming (RADP) algorithm for adaptive optimal controller design. In sharp contrast to the existing methods, the obtained algorithm is based on value iteration (VI), and the knowledge of an initial stabilizing control policy is no longer needed. An example of a power electronic system is adopted to illustrate the obtained results.

Bivariate Optimization for Control Design of Interconnected Uncertain Nonlinear Systems: A Fuzzy Set-Theoretic Approach

A new fuzzy set-theoretic approach to the control design of interconnected uncertain nonlinear system is proposed. The uncertainty of the system is nonlinear and (possible) fast time-varying, which may be due to unknown parameter and input disturbance. The uncertainty bound can be described via a fuzzy set. In this paper, the control design consists of the control scheme design and control gain optimization. Under a state transformation, a new robust control scheme in deterministic form is proposed for the interconnected system, which is not fuzzy if-then rule-based. The optimal design of the control gain is then proposed via the fuzzy description of the uncertainty bound, which is formulated as a bivariate constrained optimization problem by minimizing a fuzzy-based performance index. We show that the globally unique solution to this optimization problem always exists. The closed-form (i.e., analytic) solution and the corresponding minimum value of the performance index are also presented. The resulting control is able to render the system performance in twofold. First, it guarantees uniform boundedness and uniform ultimate boundedness of the system regardless of the actual value of uncertainty. Second, it minimizes the fuzzy-based performance index associated with both the fuzzy system performance and the control cost.

Decentralized adaptive output-feedback control of interconnected nonlinear time-delay systems using minimal neural networks

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.

Distributed modifier-adaptation schemes for the real-time optimisation of uncertain interconnected systems

ABSTRACTThis paper proposes a set of distributed real-time optimisation schemes for the steady-state optimisation of parametrically and structurally uncertain systems that are composed of multiple interconnected subsystems. These schemes are derived in the framework of modifier adaptation and use uncertain system models of varying complexity. Consequently, each distributed modifier-adaptation scheme imposes different requirements on the available plant measurements, the communication network, and the control architecture. We prove that every scheme can converge to the plant optimum despite model uncertainty and compare the main features of each approach. Finally, we illustrate our findings via a numerical example.

Hierarchical Robust Performance Analysis of Uncertain Large Scale Systems

In this paper, the problem of robust performance analysis of interconnected uncertain systems with hierarchical structure is investigated. The computational load associated with such problems does not allow a direct application of robustness analysis usual tools. To overcome this difficulty, we exploit the hierarchical structure of the problem and propose an algorithm to perform robustness analysis using integral quadratic constraint “propagation” along the hierarchical structure. This algorithm allows us to establish a tradeoff between computation time required to perform the analysis and the conservatism of the obtained results. Furthermore, it is possible to perform parallel computation using the proposed algorithm.

Decentralised disturbance-observer-based adaptive tracking in the presence of unmatched nonlinear time-delayed interactions and disturbances

ABSTRACTThis paper proposes an approximation-based nonlinear disturbance observer (NDO) approach for decentralised adaptive tracking of uncertain interconnected pure-feedback nonlinear systems with unmatched time-delayed nonlinear interactions and external disturbances. Compared with the existing approximation-based NDO approach for uncertain interconnected nonlinear systems where the centralised design framework was proposed, the main contribution of this paper is to develop a decentralised and memoryless NDO-based adaptive control scheme in the presence of unknown time-varying delayed interactions and disturbances unmatched in the control inputs. The recursive design methodology is derived to construct the decentralised NDO and controller where the function approximators used in the decentralised NDO are employed to design the decentralised adaptive controller. From the Lyapunov stability theorem using Lyapunov--Krasovskii functionals, it is shown that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors converge to an adjustable neighbourhood of the origin.

Decentralised adaptive robust control schemes of uncertain large‐scale time‐delay systems with multiple unknown dead‐zone inputs

A simple design method is presented such that the decentralised adaptive robust control schemes with a relatively simple structure can be synthesised for a class of uncertain large-scale interconnected time-delay systems with multiple dead-zone inputs. It is supposed that any information on dead-zone input non-linearities is completely unknown. On the basis of adaptive technique, a self-tuning control gain function is introduced for each subsystem to construct a simple local state feedback controller which is structurally linear in the local state variables. The simple design method presented in this study might be well understood by engineering designers, and the resulting simple control schemes can be easily implemented in a number of practical engineering control problems. By combining the presented design method with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain interconnected dynamical systems with completely unknown dead-zone in the actuators. Finally, the simulations of some numerical examples are provided to show the design procedure of the presented method and to demonstrate the validity of the theoretical results.

Output-Feedback Fault Detection and Accommodation of Uncertain Interconnected Systems With Time-Delayed Nonlinear Faults

This paper addresses a distributed fault detection and accommodation (DFDA) problem for uncertain nonlinear interconnected systems with faults in time-delayed nonlinearities. In contrast to existing DFDA works, we consider uncertain time-delayed interactions among subsystems and their faults, and additionally delays are assumed to be unknown. Under these conditions, a distributed memoryless local fault detection scheme consisting of a local detection estimator and its corresponding time-varying detection threshold is presented for each subsystem by using only output measurements. Then, a decentralized output-feedback control scheme for a local fault accommodation is designed based on this detection estimator and the adaptive approximation technique. The fault detectability and the stability of the proposed output-feedback DFDA scheme are thoroughly investigated in the Lyapunov sense. A simulation example is provided to illustrate the effectiveness of the proposed methodology.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

In this paper, an adaptive neural net- works (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

Neural-Network-Based Adaptive Decentralized Fault-Tolerant 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.

Super-twisting-based continuous neural networks modelling of second-order interconnected systems

ABSTRACTThe aim of this work was to design a non-parametric model of interconnected systems represented by uncertain second-order systems with incomplete information (only the generalized position vector is measurable). Artificial neural networks appeared to be a plausible alternative to get a non-parametric representation of the aforementioned interconnected systems. The modelling strategy used a set of spatial distributed second-order continuous neural networks (CNN). Each node in the interconnected system was represented as a second-order continuous neural network added by the super-twisting discontinuous sliding mode algorithm. The non-parametric modelling problem was reduced to design a feasible expression for the CNN weights in order to reproduce the states (including the generalized derivative of position vector) of all the nodes dynamics together and simultaneously. The adaptive laws for the CNN weights ensured the convergence of the CNN trajectories to the states of the uncertain interconnected system. To investigate the qualitative behaviour of the suggested methodology, two numerical examples were proposed. The first one represents the interconnection of three mass–spring–damper mechanical systems. The second example considers the problem of the non-parametric modelling problem for a wave partial differential equation. A set of three-dimensional graphic representations were used to demonstrate the identification abilities achieved by the CNN designed in this study for the second case.

Synthesis of Distributed Robust H-Infinity Controllers for Interconnected Discrete Time Systems

This paper presents an algorithm for the synthesis of robust distributed controllers for interconnected linear discrete-time systems. For a network of interconnected uncertain linear time-invariant systems, the distributed controller achieves robust stability and a guaranteed level of robust performance in a well-defined H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. The setting of this paper is in discrete time. Based on the theory of dissipative dynamical systems, conditions for the analysis of robust stability and robust performance of networks are derived in terms of feasibility tests of linear matrix inequalities. From these conditions, computationally tractable synthesis conditions are derived. An iterative D-K type of synthesis algorithm is proposed that yields a robust distributed controller. Convergence properties of the algorithm are inferred.

Hierarchical Decomposition Based Consensus Tracking for Uncertain Interconnected Systems via Distributed Adaptive Output Feedback Control

In this note, distributed adaptive controllers are developed for output consensus tracking of multiple linear systems with unknown parameters, uncertain subsystem interconnections and external disturbances. The subsystems are allowed to have non-identical dynamics and the same yet arbitrary order. It is assumed that only part of subsystems can have direct access to the time-varying trajectory information and the subsystem states are unmeasurable for local feedback control. In our design, the directed graph representing the information transmission status among subsystems is preprocessed by splitting it into a hierarchical structure. Then local adaptive controllers of subsystems in different layers can be computed in a sequential order and the difficulty on deriving mutually dependent local controls in previous consensus works are successfully overcome. In each subsystem, additional estimates are introduced to account for the unknown parameters and states in its neighbors' dynamics. Besides, only the information of local outputs and inputs need be collected from the neighboring subsystems. Certain robust terms are added in distributed adaptive laws to mitigate the effects of uncertain subsystem interactions and disturbances. It is proved that with our scheme, all closed-loop signals can be ensured bounded when the strengths of uncertain subsystem interconnections are sufficiently weak. The tracking errors for the entire group of subsystems will converge to a compact set and the transient tracking error performance can be adjusted by appropriately choosing design parameters.

New results in global stabilization for stochastic nonlinear systems

This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.

Decentralized Variable Gain Robust Controllers with Guaranteed L2 Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems with State Delays

In this paper, we propose a decentralized variable gain robust controller with guaranteed L 2 gain performance for a class of uncertain large-scale interconnected systems with state delays. The proposed decentralized robust controller consists of a fixed gain and a variable gain tuned by parameter adjustment laws. In this paper, it is shown that sufficient conditions for the existence of the proposed decentralized variable gain robust control system are given in terms of LMIs. Finally, a simple illustrative example is shown.

A New Iterative Modeling Approaches for Robustness Analysis of Distributed Generation MGs

Abstract The first challenge in robustness analysis of micro-grid as a large-scale interconnected uncertain system is to provide a model of such systems in a standard form. This is required within different analysis frameworks. This becomes particularly important for network of micro-grids, as analysis tools that can handle such systems heavily rely on the special structure within such model descriptions. Here we propose a model for network of micro-grids as large-scale interconnected uncertain systems that are used in the Integral Quadratic Constraint (IQC) analysis.

Dedcentralized output feedback H-infinity control for uncertain interconnected systems with quantization

Dedcentralized output feedback H-infinity control for uncertain interconnected systems with quantization

Decentralised robust stabilisation of uncertain large-scale interconnected time-delay systems with unknown upper bounds of uncertainties

The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.

Synthesis of Decentralized Variable Gain Robust Controllers with GuaranteedL2Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems

We consider a design problem of a decentralized variable gain robust controller with guaranteedL2gain performance for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller with guaranteedL2gain performance are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.