Junping Du

Robust Discrete-Time Iterative Learning Control for Nonlinear Systems With Varying Initial State Shifts

This note is concerned with the robust discrete-time iterative learning control (ILC) design for nonlinear systems with varying initial state shifts. A two-gain ILC law is considered using a 2D analysis approach. Sufficient conditions are derived to guarantee both convergence of the learning process for fixed initial condition and boundedness of the tracking error for variable initial condition. It is shown that the error data with anticipation in time can well handle the varying initial state shifts in discrete-time ILC.

Robust Design of a Class of Time-Delay Iterative Learning Control Systems With Initial Shifts

This paper is mainly devoted to the iterative learning control (ILC) design for time-delay systems (TDS) in the presence of initial shifts, especially when the system parameters are subject to polytopic-type uncertainties. The ILC laws using a pure error term and/or an initial rectifying action to address the initial shifts are considered, and the two-dimensional (2-D) system theory is employed to develop necessary and sufficient conditions for the asymptotic stability of ILC. For the monotonic convergence of ILC, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) based on the bounded real lemma (BRL). It is shown that adding the pure error term in the D-type learning law helps to meet certain LMIs to achieve a monotonically convergent ILC law. Specifically, this property is first investigated for linear time-invariant systems (LTIS), which is then discussed for the possible extension to TDS. Two numerical examples are included to illustrate the main results.

Data-Driven Control for Relative Degree Systems via Iterative Learning

Iterative learning control (ILC) is a kind of effective data-driven method that is developed based on online and/or offline input/output data. The main purpose of this paper is to supply a unified 2-D analysis approach for both continuous-time and discrete-time ILC systems with relative degree. It is shown that the 2-D Roesser system framework can be established for general ILC systems regardless of relative degree, under which convergence conditions can be provided to guarantee both asymptotic stability and monotonic convergence of the ILC processes. In particular, conditions for the monotonic convergence of ILC can be given in terms of linear matrix inequalities, and formulas for the updating law can be derived simultaneously. Simulation results are presented to illustrate the effectiveness of ILC determined through the 2-D design approach in dealing with the higher order relative degree problem of ILC systems, as well as the robustness of such ILC against uncertainties.

Finite-Time Synchronous Control for Multiple Manipulators With Sensor Saturations and a Constant Reference

This paper is devoted to the finite-time synchronous control problem for multiple manipulators subject to sensor saturations. An effective framework through defining a class of coordinated saturation functions is introduced, under which the distributed protocols with continuous feedbacks are constructed. By applying the homogeneous theory for stability analysis, it is proven that all the multiple manipulators converge to the target position in finite time without disturbances. In the presence of disturbances, it is shown that the position errors can reach a neighborhood of the origin in finite time. Numerical simulations on four robot manipulators with two degrees of freedom are presented to demonstrate the efficiency of our proposed protocols.

Tracking Algorithms for Multiagent Systems

This paper is devoted to the consensus tracking issue on multiagent systems. Instead of enabling the networked agents to reach an agreement asymptotically as the time tends to infinity, the consensus tracking between agents is considered to be derived on a finite time interval as accurately as possible. We thus propose a learning algorithm with a gain operator to be determined. If the gain operator is designed in the form of a polynomial expression, a necessary and sufficient condition is obtained for the networked agents to accomplish the consensus tracking objective, regardless of the relative degree of the system model of agents. Moreover, the H∞ analysis approach is introduced to help establish conditions in terms of linear matrix inequalities (LMIs) such that the resulting processes of the presented learning algorithm can be guaranteed to monotonically converge in an iterative manner. The established LMI conditions can also enable the iterative learning processes to converge with an exponentially fast speed. In addition, we extend the learning algorithm to address the relative formation problem for multiagent systems. Numerical simulations are performed to demonstrate the effectiveness of learning algorithms in achieving both consensus tracking and relative formation objectives for the networked agents.

H∞ sliding mode based scaled consensus control for linear multi-agent systems with disturbances

This paper studies the scaled consensus control problem of networked multi-agent systems with linear coupling dynamics and external disturbances. A state feedback based distributed H∞ sliding mode control (SMC) approach is firstly established by designing integral-type sliding function, and a linear matrix inequality (LMI) based sufficient condition is given, which can guarantee the states of all agents achieving scaled consensus with H∞ disturbance attenuation index on sliding surface. A distributed adaptive SMC law with adaptive updated law is proposed such that the sliding surface is reachable. Then, the output feedback based distributed H∞ SMC is considered by designing distributed observer, and a SMC law is synthesized for the reaching motion based on the state estimates. A LMI based sufficient condition for the scaled consensus with H∞ disturbance attenuation index of the overall closed-loop system is derived. At last, the proposed distributed H∞ SMC is further extended to solve the scaled consensus control problem of networked multi-agent systems under switching topology. An example is included to show the effectiveness of the proposed methods.

Robust H ∞ consensus control of uncertain multi-agent systems with nonlinear dynamics and time-varying delays

This paper is concerned with the H∞ consensus control problem in undirected networks of autonomous agents with nonlinear dynamics, subject to parameter uncertainties and external disturbances. With the consideration of timevarying delays arising from communication among agents, a distributed protocol is proposed using the local delayed state information. Then, by defining an appropriate controlled output function, the consensus problem under the proposed protocol is converted into an H∞ control problem. Based on robust H∞ theory, sufficient conditions are derived to make all agents achieve consensus with desired H∞ performance. Moreover, the feedback matrix in the proposed protocol is determined by solving two linear matrix inequalities (LMIs) with the same dimensions as a single agent. Finally, a numerical simulation is provided to demonstrate the effectiveness of our theoretical results.

Output feedback tracking control for spacecraft relative translation subject to input constraints and partial loss of control effectiveness

In this paper, an adaptive output feedback tracking control scheme is proposed for spacecraft formation flying (SFF) in the presence of external disturbances, uncertain system parameters, input constraints and partial loss of control effectiveness. The proposed controller incorporates a pseudo-velocity filter to account for the unmeasured relative velocity, and the neural network (NN) technique is implemented to approximate the desired nonlinear function and bounded external disturbances. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated nonlinear function, a switch function is employed to generate a switching between the adaptive NN control and the robust controller. Moreover, a fault tolerant part is included in the controller to compensate the partial loss of actuator effectiveness fault. It is shown that the derived controller not only guarantees the tracking error in the closed-loop system to be uniformly ultimately bounded (UUB) but also ensures the control input can rigorously enforce actuator magnitude constraints. Simulation results are provided to demonstrate the effectiveness of the proposed method.

Formation learning algorithms for mobile agents subject to 2-D dynamically changing topologies

In this paper, we consider a two-dimensional (2-D) formation problem for multi-agent systems subject to switching topologies that dynamically change along both a finite time axis and an infinite iteration axis. We present a distributed iterative learning control (ILC) algorithm via the nearest neighbor rules. By employing the 2-D approach, we develop both the asymptotic and exponentially fast convergence of our formation ILC, which can be guaranteed by conditions in terms of the spectral radius and the matrix norms, respectively.

PHD filter for multi-target tracking by variational Bayesian approximation

In this paper, we address the problem of multi-target tracking with unknown measurement noise variance parameters by the probability hypothesis density (PHD) filter. Based on the concept of conjugate prior distributions for noise statistics, the inverse-Gamma distributions are employed to describe the dynamics of the noise variance parameters and a novel implementation to the PHD recursion is developed by representing the predicted and the posterior intensities as mixtures of Gaussian-inverse-Gamma terms. As the target state and the noise variance parameters are coupled in the likelihood functions, the variational Bayesian approximation approach is applied so that the posterior is derived in the same form as the prior and the resulting algorithm is recursive. A numerical example is provided to illustrate the effectiveness of the proposed filter.