Consensus control of leader-following nonlinear multi-agent systems with distributed adaptive iterative learning control

This paper addresses the consensus problem of leader-following nonlinear multi-agent systems with iterative learning control. The assumption that only a small portion of following agents can receive the information of leader agent is considered. To approximate the nonlinear dynamics of a given system, the radial basis function neural network is introduced. Then, a distributed adaptive iterative learning control protocol with an auxiliary control term is designed, where the estimates of nonlinear dynamics are applied in control protocol design and three adaptive laws are presented. Furthermore, the convergence of the proposed control protocol is analysed by Lyapunov stability theory. Finally, a simulation example is provided to demonstrate the validity of theoretical results.     

Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking

In this work, we present a new distributed adaptive iterative learning control (AILC) scheme for a class of high-order nonlinear multi-agent systems (MAS) under alignment condition with both parametric and nonparametric system uncertainties, where the actuators may be faulty and the control input gain functions are not fully known. Backstepping design with the composite energy function (CEF) structure is used in the discussion. Through rigorous analysis, we show that under this new AILC scheme, uniform convergence of agents output tracking error over the iteration domain is guaranteed. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed AILC scheme.     

Observer-based distributed adaptive iterative learning control for linear multi-agent systems

This paper investigates the consensus problem for linear multi-agent systems from the viewpoint of two-dimensional systems when the state information of each agent is not available. Observer-based fully distributed adaptive iterative learning protocol is designed in this paper. A local observer is designed for each agent and it is shown that without using any global information about the communication graph, all agents achieve consensus perfectly for all undirected connected communication graph when the number of iterations tends to infinity. The Lyapunov-like energy function is employed to facilitate the learning protocol design and property analysis. Finally, simulation example is given to illustrate the theoretical analysis.     

Adaptive iterative learning control for switched nonlinear continuous-time systems

In this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.     

Networked iterative learning control approach for nonlinear systems with random communication delay

This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.     

Monotonically convergent iterative learning control for linear discrete-time systems

In iterative learning control schemes for linear discrete time systems, conditions to guarantee the monotonic convergence of the tracking error norms are derived. By using the Markov parameters, it is shown in the time-domain that there exists a non-increasing function such that when the properly chosen constant learning gain is multiplied by this function, the convergence of the tracking error norms is monotonic, without resort to high-gain feedback.     

Noise tolerant iterative learning control for a class of continuous-time systems

The paper proposes a noise tolerant iterative learning control (ILC) for a class of linear continuous-time systems, which achieves high-precision tracking for uncertain plants by iteration of trials in the presence of heavy measurement noise. The robustness against measurement noise is achieved through (i) projection of continuous-time I/O signals onto a finite-dimensional parameter space, (ii) using error data of all past iterations via an integral operation in the learning law and (iii) noise reduction by H² optimization subject to a specified convergence speed of the ILC.     

Broadcast stochastic receding horizon control of multi-agent systems

Optimal regulation of stochastically behaving agents is essential to achieve a robust aggregate behavior in a swarm of agents. How optimally these behaviors are controlled leads to the problem of designing optimal control architectures. In this paper, we propose a novel broadcast stochastic receding horizon control architecture as an optimal strategy for stabilizing a swarm of stochastically behaving agents. The goal is to design, at each time step, an optimal control law in the receding horizon control framework using collective system behavior as the only available feedback information and broadcast it to all agents to achieve the desired system behavior. Using probabilistic tools, a conditional expectation based predictive model is derived to represent the ensemble behavior of a swarm of independently behaving agents with multi-state transitions. A stochastic finite receding horizon control problem is formulated to stabilize the aggregate behavior of agents. Analytical and simulation results are presented for a two-state multi-agent system. Stability of the closed-loop system is guaranteed using the supermartingale theory. Almost sure (with probability 1) convergence of the closed-loop system to the desired target is ensured. Finally, conclusions are presented.