Delay-dependent decentralized control for nonlinear similar interconnected large-scale systems

In this chapter, by using neural network (NN)-based online learning optimal control approach, a decentralized control strategy is developed to stabilize a class of continuous-time large-scale interconnected nonlinear systems . It is proven that the decentralized control strategy of the overall system can be established by adding appropriate feedback gains to the optimal control laws of the isolated subsystems . Then, an online policy iteration (PI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations related to the optimal control problem. By constructing a set of critic NNs, the cost functions can be obtained by NN approximation, followed by the control laws. Furthermore, as a generalization, an NN-based decentralized control law is developed to stabilize the large-scale interconnected nonlinear systems using an online model-free integral PI algorithm. The model-free PI approach can solve the decentralized control problem for large-scale interconnected nonlinear systems with unknown dynamics. Finally, two simulation examples are provided to illustrate the effectiveness of the present decentralized control scheme.

This paper considers the global optimal control for nonlinear interconnected large-scale systems with respect to linear quadratic functional. A successive approximation procedure is proposed to design the feedforward feedback nearly optimal control law. By introducing the Successive Approximation Approach of the nonlinear differential equation theory, a nonhomogeneous linear two-point boundary value problem sequence is constructed to approximate the nonlinear large-scale two-point boundary value problem, which is the necessary condition of the nonlinear control problem. By iteratively solving this nonhomogeneous linear approximating sequence, a global nearly optimal control law that composed of a linear closed-loop feedback compensatory term and an open-loop feedforward compensatory term is designed. An algorithm is presented to design certain qualified nearly optimal control law by truncating an infinite iteration result. An illustrative example shows the validity of the algorithm.

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems’ cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system.

Delay-dependent robust and reliable [formula omitted] fuzzy hyperbolic decentralized control for uncertain nonlinear interconnected systems

This paper studies the problem of global decentralized control by applying time-varying output feedback for large-scale uncertain systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. We show that under a linear growth condition, there is a decentralized output feedback controller rendering the closed-loop systems globally exponentially stable. This is accomplished by extending and output feedback domination design which requires little information about the nonlinear systems. Furthermore, we apply our results to a multi-vehicle system to demonstrate the use of our time-varying output feedback controller.

A globally stabilizing decentralized output-feedback controller is proposed for a general class of nonlinear interconnected large-scale systems. The subsystem interconnections and the dynamics of each subsystem feature both parametric and functional uncertainty. The controller design is based on a general high-gain scaling technique that utilizes arbitrary powers (instead of requiring successive powers) of the high-gain parameter with the powers chosen to satisfy certain inequalities depending on system nonlinearities. The scaling induces a weak-Cascading Upper Diagonal Dominance (w-CUDD) structure on the dynamics and allows relaxation of the cascading dominance assumption on upper diagonal terms. Disturbance attenuation properties of the proposed decentralized controller are also investigated.

Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation

Decentralized optimal controller design for multimachine power systems using successive approximation approach

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of Simulinkand Matlab. These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of SimulinkTM and MatlabTM . These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

An overlapping robust decentralized connective stabilization method based on dynamic state feedback is proposed for a kind of large-scale interconnected systems with loop topological structure. Firstly, the state space of an interconnected system is expanded by using inclusion principle of large-scale systems and the system is divided into a series of pair-wise subsystems in the expanded space. Then, the robust decentralized controllers based on dynamic state feedback for each pair-wise subsystem are designed by using LMI method and Lyapunov theory. Next, the designed repeatedly controllers for every subsystem are contracted back to the original space. Coordination of the control laws can be achieved, so that the original interconnected system is robust connectively stable. Finally, the proposed method is applied to AGC control design of a three-area interconnected power system with loop structure. Simulation results show the feasibility and superiority of the proposed method.

We present a novel decentralized tracking control scheme for a class of large-scale nonlinear systems with partial state constraints. For the first time, backstepping design with the newly proposed BLF is incorporated to effectively deal with the control problem of nonlinear systems with interconnected constraints. To prevent the states of each subsystem from violating the constraints, we employ a special barrier Lyapunov function (BLF), which grows to infinity whenever its argument approaches some finite limits. By ensuring boundedness of the barrier Lyapunov function in the closed loop, we ensure that those limits are not transgressed. Asymptotic tracking is achieved without violation of the constraints, and all closed-loop signals remain bounded. In the end, an illustrative example is presented to demonstrate the performance of the proposed control.

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.

Decentralized PI tracking control for non-Gaussian large-scale interconnected distribution systems

Controllers design for two interconnected systems via unbiased observers