Adaptive Control Of Interconnected Systems Research Articles

Decentralized model reference adaptive control for interconnected systems with time‐varying delays and unknown dead‐zone inputs

AbstractIn this study, the decentralized model reference adaptive control (DMRAC) problem is tackled for a class of time‐varying delay interconnect systems that comprise unknown system matrices and unknown dead‐zone inputs. Two robust adaptive control methods are proposed for state tracking based on the moderate matching time‐varying delay nonlinear assumptions and the matching between the controlled system and reference model matrices, respectively. The control gain function is explicitly expressed, and it is applied to the adaptive law gains simultaneously. Moreover, a Lyapunov–Krasovskii functional with two integral functions is developed. Besides the properties of the type‐B Nussbaum function, the circumstance where the system parameters are fully unknown is considered. As indicated by the results, all signals in the closed‐loop system are bounded while fulfilling asymptotically tracked control objectives. The simulation example of this study verifies the effectiveness and feasibility of the proposed design method.

Small-Gain Approach to Fuzzy Adaptive Control for Interconnected Systems With Unmodeled Dynamics

This article presents a new stabilizing control scheme for a class of interconnected nonlinear systems subjected to unmodeled dynamics and immeasurable states. Fuzzy logic systems are applied to approximate the unknown functions, and a fuzzy-based state observer is constructed. The interconnection of the overall system is completely compensated via the cyclic-small-gain condition theorem, and the small-gain theorem is introduced to overcome the unmodeled dynamics in each subsystem. Furthermore, assumptions from prior literature are relaxed, and computing burden is reduced through the design of less adaptive laws. This article proves that under the designed control scheme, the closed-loop systems are controlled to be input-to-state practically stable and that all signals are guaranteed to be semiglobally uniformly ultimately bounded. Finally, this article’s simulation section illustrates the effectiveness of the proposed approach through an example derived from a practical system model.

Nonlinear Adaptive Control of Interconnected Systems Using Neural Networks

In this letter, we solve the problem of decentralized adaptive asymptotic tracking for a class of large scale systems with significant nonlinearities and uncertainties. Neural networks (NNs) are used as a control part to cancel the effect of the unknown nonlinearity. Semiglobal asymptotic stability results are obtained and the tracking error converges to zero.

Robust Decentralized Adaptive Control for Interconnected Systems With Time Delays

The problem of robust stabilization for a class of time-varying nonlinear large-scale systems subject to multiple time-varying delays in the interconnections is considered. The interconnections satisfy the match condition, and are bounded by nonlinear functions that may contain a high-order polynomial with a time delay. Without the knowledge of these bounds, we present adaptive state feedback controllers that are continuous and independent of time delays. Based on the Lyapunov stability theorem, we prove that the controllers can render the closed loop systems uniformly ultimately bounded stable. We also apply the result to constructing adaptive feedback controllers to stabilize a class of interconnected systems whose nominal systems are linear. Finally, several examples are given to show the potential of the proposed techniques.

Decentralized variable structure model-following adaptive control for interconnected systems with series nonlinearities

The problem of model-referenced control for interconnected systems with series non-linearities is investigated. By applying variable structure control theory, we propose a controller which is able to drive the error subsystem between the model state and the plant state to zero. The presented variable structure controller ensures the global reaching condition of the sliding mode of the error system. It shows that the uncertain nonlinear dynamic system also possesses the property of insensitivity to uncertainties and disturbances as a linear system does. Furthermore, the sliding mode can be designed to converge within a specified exponential speed.

Partially decentralized adaptive control of interconnected systems with improved performance

A partially decentralized model reference adaptive controller proposed earlier is modified for improving the bad zero-state performance that may result from the poor knowledge of the subsystem parameters. The improvement in performance is achieved by treating the parameter mismatch in each local subsystem as an external disturbance and then designing an auxiliary local feedback to reject the effect of this mismatch on the local tracking error. The resulting closed loop system is analysed in the presence of unmodelled interconnections and it is shown that, whenever the uncertainty in the high frequency gain of the transfer function of each isolated subsystem is less than 100%, the modified scheme results in improved zero-state performance provided that the unmodelled interconnections are ‘small enough’. Furthermore, the performance improvement, achievable using the proposed scheme depends on the size of the unmodelled interconnections in such a way that, as the unmodelled interconnections disappear, the improvement in zero-state performance can be made arbitrary. The proposed scheme uses high gain compensators in each local control law and so sensor noise amplification is a potential trouble-spot.

Singularity–Free Decentralized Adaptive Control of Interconnected Systems

A new indirect decentralized adaptive control algorithm for discrete-time system is presented in this paper. The key idea in the algorithm is to design local controller such that each subsystem is independently controlled in some extent and to have no any singularities. Global boundedness of all signals for the whole closed loop system is guaranteed in the presence of interconnections, unmodelled dynamics and bounded disturbances of the subsystems. The algorithm needs neither the restrictions on plant parameters, and zeros nor the introduction of persistent excitation.

094 Completely decentralized indirect adaptive control of interconnected systems

094 Completely decentralized indirect adaptive control of interconnected systems

Global boundedness of discrete-time adaptive control just using estimator projection

In this paper, we study a discrete-time indirect adaptive control algorithm which contains a constrained gradient parameter estimator and a pole assignment control law synthesis module. This adaptive control algorithm does not involve modifications like data normalization, use of deadzones, or injection of persistently excited signals. Also it requires no a priori knowledge of system modelling errors. It is shown that global robustness properties still hold when this simple algorithm is applied to systems with bounded disturbances and arbitrarily small fast parasitic dynamics. The problem of indirect decentralized adaptive control of interconnected systems is also considered. We use the above adaptive algorithm to design completely decentralized local adaptive controllers for each isolated subsystem by ignoring interactions between subsystems. We show that the local controllers designed in this way are robust in the sense that all signals in the closed loop adaptive system are bounded for bounded initial conditions, reference inputs, disturbances and an arbitrarily small amount of interaction between subsystems and unmodelled dynamics of each subsystem.

Completely Decentralized Indirect Adaptive Control of Interconnected Systems

This paper presents a completely decentralized indirect adaptive control scheme for interconnected systems. The general approach based on the interconnections output estimation using the polynomial series offers a general solution for any class of minimum phase interconnected subystems described Input/Output form. The indirect control scheme uses a least squares identification with dead zone and normalization. No structural constraints on the interconnections are necessary to ensure the global system boundedness. It is shown that the stability conditions based on weak interconnections are relaxed. The results are illustrated numerically.

Decentralized indirect adaptive control of interconnected systems

AbstractContinuous time decentralized indirect adaptive controllers are proposed for a large‐scale system composed of N interconnected linear subsystems with unknown parameters. Each local adaptive law utilizes a normalizing signal which is generated using the local input and the outputs of all the subsystems. This requires the exchange of output signals between the different subsystems, so that the scheme is no longer totally decentralized. Nevertheless, the degree of computational complexity is about the same as that of a totally decentralized scheme and this makes the scheme very attractive.

Decentralized stochastic adaptive control of interconnected systems

AbstractThis paper considers the stochastic adaptive control problem for a class of large‐scale systems formed by arbitrary interconnection of subsystems with unknown parameters and non‐linearities. For the estimation of the unknown parameters of the local controllers, stochastic approximation algorithms are used. Conditions sufficient for global stability of the overall system are established. It is shown that the overall tracking error is bounded by a quantity depending on the size of interconnections.

Indirect adaptive control for interconnected systems

An indirect adaptive controller for interconnected systems is introduced. Each subsystem is subject to bounded disturbances and to possibly unbounded interconnections with other subsystems. A variable dead zone is incorporated into a gradient estimation scheme to limit the effects of the interconnections and disturbances. An adaptive state feedback control law is described which stabilizes the interconnected system, forcing the input and output signals of each subsystem to remain bounded.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust Adaptive Control of Interconnected Systems

In this paper we consider the robust adaptive control of interconnected systems whose subsystems contain parasiticses (unmodelled dynamics) and disturbances. Motivated by the idea that restrain the adaptively caculated parameters by the control signals, we give a robust adaptive control law and its generalized form, in which the control weighting has been considered. The new laws are suitable to be used in the cases of decentralized adaptive control of interconnected systems and they are different from the traditional adaptive law (Narendra and Valavani, 1978) and the famous σ-modification (Ioannou and Kokotovic, 1985; Ioannou and Tsakalis, 1986) and e1 modification (Narendr and Annaswamy, 1987). By use of the Lyapunov techniques, the robustness properties of the new laws in respect to parasiticses and disturbances are analyzed. Under the function independence condition or the norm nonzero condition, if the frequences of parasitics are high enough, the control weighting is not too heavy and the coupling between subsystems is moderate, then there must exist a region of convergence Dc and a residual set Dr such that the system variables started from Dc will keep bounded and converge to Dr. Besides, the rates of convergence are exponential.

Decentralized adaptive control of interconnected systems

The adaptive control of a class of large-scale systems formed of an arbitrary interconnection of subsystems with unknown parameters, nonlinearities, and bounded disturbances is investigated. It is first shown that no matter how weak the interconnections are, a decentralized adaptive control scheme can become unstable. Approaches are then developed for stabilization and tracking using new decentralized adaptive controllers. In the case where the relative degree n^{*} of the transfer function of each decoupled subsystem is less than or equal to two, sufficient conditions are established which guarantee boundedness and exponential convergence of the state and parameter errors to bounded residual sets. In the absence of disturbances and interconnections, the decentralized adaptive control schemes guarantee exact convergence of the tracking errors to zero. The effectiveness of the proposed adaptive schemes is demonstrated using a simple example.

Decentralized adaptive control of interconnected systems with reduced-order models

The adaptive control of interconnected systems whose subsystems possess slow and fast modes is investigated in the presence of external disturbances. A simple example is first used to show that a decentralized adaptive controller can become unstable due to the unmodeled interconnections and/or neglected parasitics. An approach is then developed for stabilization and tracking using decentralized adaptive controllers with modified adaptive laws. Sufficient conditions are obtained under which a region of attraction exists for boundedness and exponential convergence of the state/parameter errors to a small residual set. The size of the region of attraction depends on the frequency range of the local parasitics in such a way that if all the local parasitics become infinitely fast, the region of attraction becomes the whole space.