Decentralized Guaranteed Cost Control Research Articles

Overlapping Decentralized Guaranteed Cost Control Method for Discrete-Time Systems of Building Structures with Uncertain Parameters under Earthquake Action

This paper proposes a discrete-time overlapping decentralized guaranteed cost control algorithm via state feedback. Based on the inclusion principle, a structure system is decoupled into multiple subsystems, and the discretized subsystems’ controllers are designed by using the guaranteed cost control algorithm. Finally, the subsystems’ controllers are contracted into overlapping controllers of the original system, and the design of the control system is completed. This control method is introduced to the civil engineering field to solve the seismic control problem for discrete-time systems of building structures with uncertain parameters. The numerical analysis of the nine-story building structure model with uncertain parameters is carried out. The results show that the proposed control method can still effectively reduce the seismic response of discrete-time system when the structural parameters are uncertain, and the control effect is similar to the centralized control strategy; at the same time, the sampling rate and data transmission speed of the system are improved to ensure the reliability of the system. It illustrates the feasibility and effectiveness of the presented approach.

Decentralized guaranteed cost control with H∞ performance for large‐scale web‐winding system

AbstractIn this paper, a decentralized guaranteed cost H∞ control strategy is proposed for large‐scale web‐winding systems with uncertain and time‐varying parameters. First, the large‐scale web‐winding system is viewed as a synthetic system composed of several dynamic subsystems, and interval matrix is used to deal with parameter uncertainties and the changes of set point. Second, a decentralized guaranteed cost control (DGCC) is developed to achieve the track goal, and guarantees that a cost function defined for the control system has an upper bound. Furthermore, an optimal DGCC (ODGCC) is designed to minimize the upper bound. Third, H∞ control strategy is incorporated in the DGCC to increase closed‐loop system robustness to parameter uncertainties and external disturbances. Finally, some simulation and experiments are performed on a three‐motor web‐winding system to verify the effectiveness of the presented control methods.

Adaptive Dynamic Programming-Based Decentralized Guaranteed Cost Control for Reconfigurable Manipulators with Uncertain Environments

In this paper, a novel decentralized guaranteed cost control method is designed for reconfigurable manipulators with uncertain environments based on the adaptive dynamic programming (ADP) approach. Each joint module, which is the basic unit for constructing the reconfigurable manipulators, is regarded as a subsystem with model uncertainties that include the error of frictional modeling and the interconnection dynamic coupling (IDC) effect. Then, by employing a robust controller and a neural network (NN) identifier-based compensation controller, the decentralized guaranteed cost control issue with uncertain environments can be changed into the optimal control issue of reconfigurable manipulators. Based on ADP algorithm, the critic neural network is introduced to approximate the modified cost function, and then the Hamilton–Jacobi–Bellman equation is addressed by the policy iterative algorithm, thus making the obtention of approximate optimal control policy doable. The stability of the robotic system under the proposed control policy is demonstrated by employing the Lyapunov theory. Finally, the effectiveness of the proposed control policy for reconfigurable manipulators with different configurations is verified by simulation experiments.

Dynamic output feedback control for nonlinear large-scale interconnected systems

Purpose This paper aims to focus on the design of a decentralized observation and control method for a class of large-scale systems characterized by nonlinear interconnected functions that are assumed to be uncertain but quadratically bounded. Design/methodology/approach Sufficient conditions, under which the designed control scheme can achieve the asymptotic stabilization of the augmented system, are developed within the Lyapunov theory in the framework of linear matrix inequalities (LMIs). Findings The derived LMIs are formulated under the form of an optimization problem whose resolution allows the concurrent computation of the decentralized control and observation gains and the maximization of the nonlinearity coverage tolerated by the system without becoming unstable. The reliable performances of the designed control scheme, compared to a distinguished decentralized guaranteed cost control strategy issued from the literature, are demonstrated by numerical simulations on an extensive application of a three-generator infinite bus power system. Originality/value The developed optimization problem subject to LMI constraints is efficiently solved by a one-step procedure to analyze the asymptotic stability and to synthesize all the control and observation parameters. Therefore, such a procedure enables to cope with the conservatism and suboptimal solutions procreated by optimization problems based on iterative algorithms with multi-step procedures usually used in the problem of dynamic output feedback decentralized control of nonlinear interconnected systems.

Optimal Control of Iron-Removal Systems Based on Off-Policy Reinforcement Learning

The goethite iron-removal process is an important procedure to remove the iron ions from the zinc hydrometallurgy. However, as a coherent system with complex reaction mechanism, associated uncertainties, and interconnected adjacent reactors, it is difficult for the process to accurately control the ion concentration. Because a large amount of historical data can be obtained during the process, an optimal control algorithm based on off-policy reinforcement learning is proposed in this paper to overcome these difficulties. According to the historical data, the weights of neural network are learned offline, and the optimal control strategy is solved online. Firstly, a bounded function is introduced to define the maximum effect of the coherent system on the subsystem cost function and to extend the cost function of the nominal system, so that the decentralized guaranteed cost control problem can be expressed as the optimal control problem of the nominal system. Then, an approximate iterative control algorithm based on actor-critic structure is proposed. The actor and critic neural networks are used to approximate control strategies and cost functions respectively. To achieve complete off-line, a new neural network is added to the actor-critic structure to approximate a part of the unknown system structure, and the three neural network parameters are optimized by the state transition algorithm. Finally, the strategy update and strategy iteration operations are performed alternately to learn optimal control strategies. The effectiveness and flexibility of the proposed off-policy optimal control method is validated by data from a real industrial goethite iron-removal process.

Decentralized guaranteed cost control of interconnected systems with uncertainties: A learning-based optimal control strategy

A novel learning-based optimal control approach is constructed to attain the decentralized guaranteed cost controller design for a class of continuous-time complex nonlinear systems with dynamical uncertainties and interconnections. This is performed by combining robust decentralized control formulation with adaptive critic learning technique. By expressing the interconnected subsystems as a whole system and introducing a new cost function for the overall plant, the decentralized guaranteed cost control problem is formulated as an optimal control problem for the nominal overall system. Then, a policy iteration based learning control algorithm is employed to solve the modified Hamilton–Jacobi–Bellman equation with respect to the nominal plant iteratively. A critic neural network is constructed to approximate the optimal state feedback control law and then the uniform ultimate boundedness stability issue is analyzed. Meanwhile, a simulation experiment is conducted to verify the good performance of the control approach.

Decentralized guaranteed cost stabilization of time-delay large-scale systems based on reduced-order observers

This paper addresses the problem of decentralized guaranteed cost stabilization (DGCS) of large-scale systems with delays both in the isolated subsystems and interconnections based on reduced-order observers. Sufficient conditions for the existence of delay-independent decentralized guaranteed cost controller (DGCC) are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMIs constraints is formulated to design the optimal DGCC which minimizes the guaranteed cost of the closed-loop large-scale systems. Finally, a simulation is performed to show the effectiveness of the proposed control scheme.

Study of delay-independent decentralized guaranteed cost control for large scale systems

This study introduces delay independent decentralized guaranteed cost control design method based on two controller structures for nonlinear uncertain interconnected large scale systems with time delays. First, a set of equivalent Takagi-Sugeno (T-S) fuzzy models are extended to represent the systems. Then a decentralized state-feedback guaranteed cost performance controller is proposed for the fuzzy systems. Based on delay independent Lyapunov functional approach, some sufficient conditions for the existence of the controller can be cast into the feasible problem of LMIs irrespective of the sizes of the time delays so that the system can be asymptotically stabilized for all considered uncertainties whose sizes are not larger than their bounds. Finally, the minimizing approach is proposed to search the suboptimal upper bound value of guaranteed cost function. Moreover, the corresponding conditions are extended into the generalized dynamic output-feedback close-loop system. Finally, the better control performances of the proposed methods are shown by the simulation examples.

Non-fragile guaranteed cost control for uncertain neutral large-scale interconnected systems

Thcis paper focuses on the problem of non-fragile decentralized guaranteed cost control for uncertain neutral large-scale interconnected systems with time-varying delays in state, control input and interconnections. A novel scheme, viewing the interconnections with time-varying delays as effective information but not disturbances, is developed. Based on Lyapunov stability theory, using various techniques of decomposing and magnifying matrices, a design method of the non-fragile decentralized guaranteed cost controller for unperturbed neutral large-scale interconnected systems is proposed and the guaranteed cost is presented. The further results are derived for the uncertain case from the criterion of unperturbed neutral large-scale interconnected systems. Finally, an illustrative example shows that the results are significantly better than the existing results in the literatures.

DECENTRALIZED ROBUST CONTROL WITH GUARANTEED COST FOR HYBRID COMPLEX NETWORKS

In this paper, robust control of the decentralized guaranteed cost was studied for a class of complex network with impulsive effects and nonlinear perturbation. Based on the Lyapunov stability theorem, sufficient conditions for the decentralized guaranteed cost controllers were obtained. The design method of the decentralized guaranteed cost control law was given by solving a parameter-dependent Riccati matrix equation. An example is given to illustrate the effectiveness of the presented scheme.

Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Additive Control Gain

This paper investigates an application of additive control gain to the guaranteed cost control problem of decentralized robust control for a class of discrete-time uncertain large-scale systems. Based on Linear Matrix Inequality (LMI) design approach, a class of decentralized local fixed state feedback controllers with the additive control gain is established. The novel contribution of this paper is that the multi objective control is attained by using the additive control gain. Although the additive control gain is included in the uncertain large-scale systems, the closed-loop system is asymptotically stable. In order to demonstrate the efficiency of our proposed controller, using the fuzzy logic control as the additive control gain, the simple numerical example is given.

Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach

In this paper, we propose a design method of guaranteed cost controllers for uncertain large-scale systems with time delays in subsystem interconnections using delayed feedback. Using the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.

An LMI approach to decentralized guaranteed cost control for a class of uncertain nonlinear large-scale delay systems

The guaranteed cost control problem via the decentralized robust control for nonlinear uncertain large-scale systems that have delay in both state and control input is considered. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality (LMI). It is shown that the decentralized local state feedback controllers can be obtained by solving the LMI.