Zhihua Qu

Lyapunov, Adaptive, and Optimal Design Techniques for Cooperative Systems on Directed Communication Graphs

This paper presents three design techniques for cooperative control of multiagent systems on directed graphs, namely, Lyapunov design, neural adaptive design, and linear quadratic regulator (LQR)-based optimal design. Using a carefully constructed Lyapunov equation for digraphs, it is shown that many results of cooperative control on undirected graphs or balanced digraphs can be extended to strongly connected digraphs. Neural adaptive control technique is adopted to solve the cooperative tracking problems of networked nonlinear systems with unknown dynamics and disturbances. Results for both first-order and high-order nonlinear systems are given. Two examples, i.e., cooperative tracking control of coupled Lagrangian systems and modified FitzHugh-Nagumo models, justify the feasibility of the proposed neural adaptive control technique. For cooperative tracking control of the general linear systems, which include integrator dynamics as special cases, it is shown that the control gain design can be decoupled from the topology of the graphs, by using the LQR-based optimal control technique. Moreover, the synchronization region is unbounded, which is a desired property of the controller. The proposed optimal control method is applied to cooperative tracking control of two-mass-spring systems, which are well-known models for vibration in many mechanical systems.

A Self-Organizing Strategy for Power Flow Control of Photovoltaic Generators in a Distribution Network

The focus of this paper is to develop a distributed control algorithm that will regulate the power output of multiple photovoltaic generators (PVs) in a distribution network. To this end, the cooperative control methodology from network control theory is used to make a group of PV generators converge and operate at certain (or the same) ratio of available power, which is determined by the status of the distribution network and the PV generators. The proposed control only requires asynchronous information intermittently from neighboring PV generators, making a communication network among the PV units both simple and necessary. The minimum requirement on communication topologies is also prescribed for the proposed control. It is shown that the proposed analysis and design methodology has the advantages that the corresponding communication networks are local, their topology can be time varying, and their bandwidth may be limited. These features enable PV generators to have both self-organizing and adaptive coordination properties even under adverse conditions. The proposed method is simulated using the IEEE standard 34-bus distribution network.

Robust control of nonlinear uncertain systems under generalized matching conditions

This paper consider the problem of stabilizing nonlinear uncertain systems. First, we define for nonlinear uncertain systems the generalized matching conditions which encompass a larger class of uncertain systems than the existing matching conditions. Then, a systematic procedure of robust control design is developed for the class of systems satisfying the generalized matching conditions. The procedure is recursive and straightforward, and makes the stability results be easily established. The proposed control is a continuous and bounded function of the system state and requires only nonlinear bounding functions on the size of uncertainties. Global stability in terms of either asymptotic, exponential, or uniform ultimate bounded stability is guaranteed under the proposed control. Extension to tracking problem is shown to be trivial.

Tracking control of rigid-link electrically – driven robot manipulators

This paper illustrates a simple, hand-crafted approach which can be used to design tracking controllers for rigid-link electrically-driven (RLED) robot manipulators. The control methodology is intuitively simple since it is based on concepts readily identified by most control engineers. To illustrate the approach, we develop a corrective tracking controller for the RLED robot dynamics which yields global exponential stability for the link tracking error under the assumption of exact model knowledge. To compensate for the uncertainties in the rigid-link electrically-driven robot model, we then design a corrective robust tracking controller which yields global uniform ultimate bounded stability of the link tracking error. The proposed controller is robust with regard to parametric uncertainties and additive bounded disturbances while correcting for the typically ignored electrical actuator dynamics.

Robust tracking control of robots by a linear feedback law

For the trajectory following problem of a robot manipulator, a simple linear robust fedback control law with constant gain matrix is proposed that makes the resulting error system uniformly ultimately bounded. This control law is very easy to implement by simply choosing a feedback gain according to the coefficients of a polynomial function of the tracking errors which is a bounding function for the terms in the Lagrange-Euler formulation. In the limit as the gain approaches infinity the error system becomes globally asymptotically stable. >

A new analytical solution to mobile robot trajectory generation in the presence of moving obstacles

The problem of determining a collision-free path for a mobile robot moving in a dynamically changing environment is addressed in this paper. By explicitly considering a kinematic model of the robot, the family of feasible trajectories and their corresponding steering controls are derived in a closed form and are expressed in terms of one adjustable parameter for the purpose of collision avoidance. Then, a new collision-avoidance condition is developed for the dynamically changing environment, which consists of a time criterion and a geometrical criterion, and it has explicit physical meanings in both the transformed space and the original working space. By imposing the avoidance condition, one can determine one (or a class of) collision-free path(s) in a closed form. Such a path meets all boundary conditions, is twice differentiable, and can be updated in real time once a change in the environment is detected. The solvability condition of the problem is explicitly found, and simulations show that the proposed method is effective.

Robust Iterative Learning Control for a Class of Nonlinear Systems

A novel nonlinear control scheme-robust iterative learning control (RILC) is developed in this paper. The new robust ILC system provides a general framework targeting at synthesizing learning control and robust control methods with the help of Lyapunovs direct method, thereafter being able to handle more general classes of nonlinear uncertain systems. In the proposed control scheme, learning control and variable structure control are made to function in a complementary manner. The nonlinear learning control strategy is applied directly to the structured system uncertainties which can be separated and expressed as products of unknown state-independent functions and known state-dependent functions. For non-structured system uncertainties associated with known bounding functions as the only a priori knowledge, variable structure control (VSC) strategy is applied to ensure the global asymptotic stability. In addition, important issues regarding the objective trajectory categories, resetting condition, derivative signal requirement and their relationships have been made clear in this paper.

On the state observation and output feedback problems for nonlinear uncertain dynamic systems

Abstract In this paper, we examine the problems of state observation and state trajectory control by output feedback for the class of non-linear systems in [3,11]. We begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is Globally Exponentially Stable (GES). We then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the GES sense. Specific time-varying bounds on the observation error and the state trajectory are also developed; revealing how the corresponding observer or control parameters can be adjusted to improve the system performance.

Brief Robust fault-tolerant self-recovering control of nonlinear uncertain systems

In this paper, the problem of devising a fault-tolerant robust control for a class of nonlinear uncertain systems is investigated. Possible failures of the sensor measuring the state variables are considered, and a robust measure is developed to identify the stability- and performance-vulnerable failures. Based on evaluation of the robust measure, a fault-tolerant robust control will switch itself between one robust control strategy designed under normal operation and another under the faulty condition. It is shown that, under two input-to-state stability conditions, the proposed scheme guarantees not only the desired performance under normal operations but also robust stability and best achievable performance when there is a sensor failure of any kind.

Toward a globally robust decentralized control for large-scale power systems

A robust control scheme is presented that stabilizes a nonlinear model of a power system to a very large class of disturbances that includes any disturbances causing the system to exhibit sustained oscillation. The disturbance can be anywhere in the power system. The fact that the improvement in stability is significant and system wide leads to the name globally robust control. The control is local or decentralized in the sense that the control of each generator depends only on information available at that generator, and is derived using Lyapunovs direct method. The derivation is quite general, permitting a second-order representation of the turbine/governor and any generator model. Simulation results are presented which show the effectiveness of the proposed control against instabilities of current importance including sustained oscillations following a major system disturbance such as a fault or major line outage. The control is also effective for steady-state operation.