Stabilization Parametric Region of Distributed PID Controllers for General First-Order Multi-Agent Systems With Time Delay

The stabilization problem of distributed proportional-integral-derivative(PID)controllers for general first-order multi-agent systems with time delay is investigated in the paper.The closed-loop multi-input multi-output(MIMO)framework in frequency domain is firstly introduced for the multi-agent system.Based on the matrix theory,the whole system is decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix.Considering that the eigenvalues may be complex numbers,the consensus problem of the multi-agent system is transformed into the stabilizing problem of all the subsystems with complex coefficients.For each subsystem with complex coefficients,the range of admissible proportional gains is analytically determined.Then,the stabilizing region in the space of integral gain and derivative gain for a given proportional gain value is also obtained in an analytical form.The entire stabilizing set can be determined by sweeping proportional gain in the allowable range.The proposed method is conducted for general first-order multi-agent systems under arbitrary topology including undirected and directed graph topology.Besides,the results in the paper provide the basis for the design of distributed PID controllers satisfying different performance criteria.The simulation examples are presented to check the validity of the proposed control strategy.

Research on the Low-order Control Strategy of the Power System With Time Delay

In this paper, the design problem of the low-order controller is considered for the power system with a fixed time delay. A linear model of the power system with time delay is firstly established. Then the proportional-integral-differential(PID) controller, which is the typical low-order controller, is designed to improve the stability of the power system. The stabilizing region of the PID controller is obtained. The control parameters chosen arbitrarily in the resultant region can ensure the stability of the power system. Finally, based on the stabilizing result, the PID controller satisfying the H∞performance index is designed, which improves the robustness of the whole power system. The main advantage of the proposed method lies in that there is no need to approximate the model of the power system.The method can be further extended to the power system which is more complex.

Asymmetric time-varying integral barrier Lyapunov function based adaptive optimal control for nonlinear systems with dynamic state constraints

This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints.An asymmetric time-varying integral barrier Lyapunov function(ATIBLF)based integral reinforcement learning(IRL)control algorithm with an actor–critic structure is first proposed.The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated.Thus,optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item.Meanwhile,neural networks are used to approximate the gradient value functions.According to the Lyapunov stability theorem,the boundedness of all signals of the closed-loop system is proved,and the proposed control scheme ensures that the system states are within predefined compact sets.Finally,the effectiveness of the proposed control approach is validated by simulations.