Optimization of large-scale systems using gradient-type interaction prediction approach

The optimal output tracking control problem for nonlinear large-scale dynamic systems is considered. A series-based approximate approach for designing the optimal controller is proposed with respect to quadratic performance indexes. By using the approach, the high order, coupling, nonlinear two-point boundary value problem is transformed into a sequence of linear decoupling two-point boundary value problems. By intercepting the frontal finite terms of the solution series, we obtained a suboptimal tracking control law. A simulation example illustrates the efficiency of the optimal output tracking control law designed.

In this article, finite-time control is investigated for multiple time-delayed large-scale nonlinear systems against state and input constraints. There are multiple time-varying delays, intermittent actuator faults, and intermittent sensor faults in this model. Takagi–Sugeno fuzzy model is used to describe the nonlinear system. There are few tries to studying finite-time control for large-scale nonlinear systems. First, a dynamic output feedback controller is designed in this article to make the system finite-time bounded. Then, an augmented closed-loop model is constructed. Sufficient conditions of finite-time control are given by the fuzzy Lyapunov function. Finally, the feasibility of the approach is verified by two simulation examples.

Partitioned Based Cooperative Distributed Model Predictive Control for Large-Scale Nonlinear Systems

This paper proposes a novel adaptive synchronization approach for a class of nonlinear large-scale systems via T-S fuzzy model. It is known that the practical large-scale systems are very complicated with nonlinear coupling strength between every two subsystems, thus the classical linear control methods are invalid for them. To overcome this deficiency, we employ the T-S fuzzy model in this paper. Firstly, the local linearization approach is utilized to preprocess the nonlinear large-scale systems, and then, according to the universal approximation property of TS fuzzy model, a new system model is established. Secondly, the fuzzy adaptive synchronization controllers are designed by using Parallel Distributed Compensation technique and the corresponding stability analysis is presented through Lyapunov technique. In addition, a new criterion, under which the proposed control scheme can be transformed into pinning control and save unnecessary costs, is also given. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our proposed approach.

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.

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.

As engineering systems become more complex, the need for 'optimal' designs becomes apparent and very important. A centralised approach can be economically unfeasible, owing to computer limitations, or because it is too complex and cumbersome to be implemented. In this paper, an approach using a suboptimal controller is proposed leading to a structural optimisation problem of large scale systems (LSS). The mathematical formulation of this problem is provided. A new structural controller is developed, and a step-by-step algorithm to design it is provided. An overall cost is defined and can be computed from the proposed algorithm. Two simple examples illustrating the applicability and usefulness of the new structural optimisation approach are included.

Decentralized event-trigger-based predefined-time adaptive control of large-scale nonlinear systems

Adaptive neural decentralized output-feedback control for nonlinear large-scale systems with input time-varying delay and saturation

In this article, a decentralized adaptive fault-tolerant control(FTC) scheme is proposed for a class of large-scale nonlinear systems with unknown time-varying parameters, actuator faults and unknown strong interconnections. Firstaccording to the fundamental traits of Gaussian function for the interconnection terms, the interference of interconnection terms to the system is eliminated effectively. Second, By employing command filter technique and adaptive neural control, the "singular" and "explosion of complex" problems in the backstepping procedure are circumvented. It is shown that all the closed-loop signals are bounded and the tracking errors converge to arbitrarily small residual sets. Finally, the effectiveness of decentralized adaptive fault-tolerant control scheme is demonstrated by simulation results.

In this paper, a novel distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimal tracking control scheme is designed for a class of physically interconnected large-scale nonlinear systems in the presence of strict-feedback form, external disturbance and saturating actuators. First, by designing feedforward control, the distributed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimal tracking control problem of a physically interconnected large-scale system is transformed into equivalent control of a decoupled multiagent system. Subsequently, a feedback control algorithm is designed to learn the optimal control input and the worst-case disturbance policy. The algorithm guarantees that the function approximation error and the distributed tracking error are uniformly ultimately bounded while the cost function converges to the bounded L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain optimal value. Finally, the effectiveness of the proposed scheme is demonstrated by simulation results of distributed control for the mobile multirobot system.

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.

We propose a reduced-space interior-point approach to nonlinear optimization problems with general inequality constraints. It is an extension of the quasi-sequential approach to dynamic optimization of large-scale systems. Inequality constraints are formed by adding slack variables to an equality constrained barrier (interior-point) problem which is solved by a range space step and a null space step in every iteration. Mathematical derivations and computation schemes are presented. We take a highly nonlinear parameter estimation problem as an example to demonstrate the effectiveness of this approach. The result is compared with the full space approach in terms of overall CPU time and number of iterations.

The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.

This paper addresses the development of a dynamic programming decomposition-coordination algorithm for the optimal control of discrete-time large-scale systems with multiple time delays. The systems under study can be converted into the corresponding augmented systems satisfying the Markov processes denning the augmented state vectors. The resulting dynamic programming can then be further decomposed into a series of subproblems which might be solved in parallel by combining the dynamic programming techniques with approaches to matrix partition. The entire system's solution is finally given by the iterative computation between the subproblems being the local control level and the coordinator. The major advantages of the proposed algorithm over others are to avoid two-point boundary-value problems of the systems with multiple time delays and to significantly reduce the computer memory and time required for such large-scale systems optimal control problems.