Preview-based leader-following consensus control of distributed multi-agent systems

This paper investigates the infinite-horizon linear quadratic regulator (LQR) problem of continuous-time LTI systems with random gains imposed on the input channels. The main novelty of this work originates from the point of view that in networked control, designing the channels and controller jointly often leads to an easier problem and meanwhile achieves better performance than designing them separately. Specifically, we formulate the LQR problem with random input gains as a channel/controller co-design problem. Such co-design can be realized by the twist of channel resource allocation, i.e., the channel capacities can be allocated among the input channels subject to an overall capacity constraint. The LQR problem is shown to be attainable under such co-design if and only if a modified algebraic Riccati equation (MARE) has a mean-square (MS) stabilizing solution. The optimal controller is given by a linear state feedback associated with the MS stabilizing solution. Moreover, a Newton's type iteration is developed for the computation of the MS stabilizing solution to the MARE.

This paper considers the linear quadratic regulator (LQR) problem for two-dimensional (2D) systems. The general 2D system is assumed to be represented by the Givone-Roesser model. In attempting to solve the standard 2D LQR problem, it is shown that the notion of diagonal causality arises naturally. The system under consideration is redefined accordingly and it is demonstrated that the new 2D system can be cast as a one-dimensional (1D) non-square descriptor system. Existing results in 1D non-square descriptor system theory are then called upon to solve the modified 2D LQR problem.

Robust leader-following consensus control of one-sided Lipschitz multi-agent systems over heterogeneous matching uncertainties

The authors present a genetic approach to the optimal linear quadratic regulator (LQR) problem. Design of the optimal LQR depends on choosing weighting matrices. One must carry out a trial-and-error process to choose the proper weighting matrices in general. It is not a trivial problem. They show a new possibility using a genetic algorithm (GA) to find the proper weighting matrices and hence to obtain the optimal control gain. They apply the approach to the attitude control of an inverted pendulum system, which is known as the LQR problem. They perform computer simulations on the system with a 50 cm long inverted pendulum and obtain good results.

In this paper, the Linear Quadratic Regulator Problem with a positivity constraint on the admissible control set is addressed. Necessary and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets, Pontryagin's maximum principle and dynamic programming. The main results are concerned with smoothness of the optimal control and the value function. The maximum principle will be extended to the infinite horizon case. Based on these analytical methods, we propose a numerical algorithm for the computation of the optimal controls for the finite and infinite horizon problem. The numerical methods will be justified by convergence properties between the finite and infinite horizon case on one side and discretized optimal controls and the true optimal control on the other.

In this paper, the Linear Quadratic Regulator Problem with a positively constraint on the admissible control set is addressed. Necessary and sufficient conditions for optimality are presented in terms of inner products, projections on closed convex sets. Pontryagin's maximum principle and dynamic programming. Sufficient and sometimes necessary conditions for the existence of positive stabilizing controls are incorporated. Convergence properties between the finite and infinite horizon case are presented. Besides these analytical methods, we describe briefly a method for the approximation of the optimal controls for the finite and infinite horizon problem.

In this article, the issue of leader-following consensus control is addressed for nonlinear multiagent systems with unknown dynamics under switching topologies. The packaged unknown nonlinear dynamics is approximated by neural networks, and the approximate error is compensated by an adaptive robust term. A novel neuro-adaptive consensus controller is derived by incorporating the backstepping recursive design and the average dwell-time method. It is demonstrated that the boundness of the closed-loop multiagent systems is ensured under switching topologies, and the follower agents have the competence to chase the leader agent with the tracking errors asymptotically converging to zero. Simulation investigations have verified the availability of the given leader-following consensus control algorithm.

The event-based leader-following consensus problem for multi-agent systems with input saturation is studied in this paper. The control input update is event-driven, and the triggering function is linear, under the given trigger function and trigger condition. At first, a sufficient condition of the leader-following consensus for multi-agent systems without input saturation is presented. Furthermore, under the constraint of input saturation and communication time delay, the leader-following consensus control is achieved through designing control protocol and choosing suitable parameters of control input. Lyapunov function in combination with S-procedure method is adopted to prove the consensus stability for multi-agent systems with input saturation and communication time delay. Moreover, the Zeno-behavior is excluded for the triggering time sequence. Finally, simulations are present to illustrate the effectiveness of the proposed consensus control protocols.

Control of time-delay systems represents one important class of control problems. A lot of work has been done in recent years. Much of the research work has been focused on the stability analysis and stabilization of time-delay systems based on the Lyapunov functional and linear matrix inequality (LMI) approaches. While the LMI approach does provide an e±cient tool, the results are mostly only su±cient and only numerical solutions are available. Our research aims to present analytical solutions by some algebraic approaches, which can provide an insightful understanding of control problem of time-delay systems. On the other hand, there has also been significant recent interest in networked multi-agent system (MAS) where unavoidably there exist delays in information acquisition as well as information exchange between agents in addition to possible input/state delays in each agent. This motivates the study of MASs with input and communication delays. The thesis is divided into two parts: Part I is focused on optimal control of single agent systems with multiple input delays; Part II is on distributed consensus control of MAS with communication and input delays. More specifically, in Part I, we shall study the linear quadratic regulation (LQR) and tracking for a single agent with linear dynamics. We first focus on LQR for linear discrete-time systems with multiple delays in a single input channel. By introducing a backward stochastic system, we establish a relationship between the LQR problem for the original system and optimal estimation for a backward stochastic system which can be solved by using projection approach. The explicit optimal controllers are developed for both finite time and infinite time horizon cases. A parallel result for linear continuous-time systems is also established, where the optimal feedback gain is given in terms of the solution of Riccati-type partial differential equations (PDEs).

A continuous time infinite horizon linear quadratic regulator with input constraints is studied. Optimality conditions, both in the open loop and feedback form, and continuity and differentiability properties of the optimal value function and of the optimal feedback are shown. Arguments rely on basic ideas of convex conjugacy, and in particular, use a dual optimal control problem

This paper proposes a polynomial chaos based numerical method providing an optimal controller for the linear-quadratic regulator (LQR) problem when the parameters in the formulation are uncertain, i.e., a controller minimizing the mean value of the LQR cost function obtained for a certain distribution of the uncertainties which is assumed to be known. The LQR problem is written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework, and an iterative algorithm converges to the optimal answer. The algorithm is applied to a simple example for which the answer is already known. Polynomial chaos based methods have the advantage of being computationally much more efficient than Monte Carlo simulations. The Linear-Quadratic Regulator controller is not very well adapted to robust design, and the optimal controller does not guarantee a minimum performance or even stability for the worst case scenario. Stability robustness and performance robustness in the presence of uncertainties are therefore not guaranteed. However, this is a first step aimed at designing more judicious controllers if combined with other techniques in the future. The next logical step would be to extend this numerical method to H2 and then H-infinity problems.

Although a proportional integral derivative type iterative learning control (PIDILC) scheme can achieve good performance, its application is limited by open‐loop structure, parameter tuning, and initial state. In this paper, a novel PIDILC optimized by two‐dimensional infinite horizon linear quadratic regulator (PIDILC‐2D‐IHLQR) is proposed. First, by synthesizing the advantage of the conventional PIDILC method and proportional integral derivative (PID) strategy, a novel closed‐loop PIDILC scheme is obtained. Then, a novel two‐dimensional infinite horizon linear quadratic regulator (2D‐IHLQR) is developed to optimize the parameters of the PIDILC strategy. The limitations of parameter tuning and initial state are solved by this PIDILC‐2D‐IHLQR method. Therefore, the proposed method not only solves the aforementioned limitations but also inherits the advantages of PIDILC algorithm, PID method, and the novel 2D‐IHLQR scheme. Moreover, a stability condition is given based on Lyapunov theory and it can help judge whether the selection of control parameters meets the stability condition. The effectiveness of the proposed method is demonstrated by the case study on an injection modelling process.

In this paper, we consider the leader-following consensus problem for a class of heterogeneous nonlinear discrete-time multi-agent systems (MASs) with unknown dynamics under network deception attacks and sensor faults. The deception attacks considered occur in the communication network between the leader and the followers, compromising the authenticity of the leader's information received by the followers and affecting the cooperative performance. Since not all followers can directly access the leader's information and their measurements may be influenced by deception attacks and sensor faults, a secure distributed estimation algorithm is proposed to allow each follower to obtain accurate information about the leader. To achieve indirect estimation of unknown fault signals, nonlinear autoregressive with exogenous input neural network (NARXNN)-based fault estimators are proposed, combining the open-loop and closed-loop modes of NARXNN. Moreover, considering that followers have unknown dynamics and exhibit heterogeneity, decentralized model-free adaptive controllers are designed based on the estimation of leader information and fault signals. Unlike methods that use consensus error for indirect consensus control, the proposed approach allows each agent to directly acquire a leader estimate and achieve direct leader-following consensus control using only local input/output data. Finally, simulation examples confirm the effectiveness of the proposed data-driven leader-following consensus control method.

Model-free finite-horizon optimal tracking control of discrete-time linear systems

This article investigates adaptive control problems for unknown second-order nonlinear multiagent systems (MASs) via an event-triggered approach. An adaptive event-triggered consensus controller is given to second-order MAS with unknown nonlinear dynamics. We prove that the proposed consensus controller is free from Zeno behavior. Next, an adaptive event-triggered tracking controller is developed for leader-follower MAS with the leader having bounded nonzero control input. Both consensus and tracking controllers are fully distributed, which means that event-triggered controllers only use local cooperative information. Finally, an unknown second-order nonlinear MAS is used to verify the given event-triggered controllers.