Predictive Consensus for Networked Multi‐Agent Systems with Switching Topology and Variable Delay

This paper investigates consensus problems of networked linear time invariant (LTI) multi‐agent systems, subject to variable network delays and switching topology. A new protocol is proposed for such systems with matrix B that has full row rank, based on stochastic, indecomposable, aperiodic (SIA) matrix and the predictive control scheme. With the predictive scheme the network delay is compensated. Consensus analysis based on the seminorm is provided. The conditions are obtained for such systems with periodic switching topology to reach consensus. The proposed protocol can deal with time‐varying delays, switching topology, and an unstable mode. The numerical examples demonstrate the effectiveness of the theoretical results.     

Efficient non-linear model based predictive control

For a large number of degrees of freedom and/or large dimension systems, non-linear model based predictive control algorithms based on dual mode control can become intractable. This paper proposes an alternative which deploys the closed-loop paradigm that has proved to be very effective for the case of linear time-varying or uncertain systems. The various attributes and computational advantages of the approach are shown to carry over to the non-linear case.     

A robust constrained model predictive control scheme for norm‐bounded uncertain systems with partial state measurements

A robust model predictive control scheme for a class of constrained norm‐bounded uncertain discrete‐time linear systems is developed under the hypothesis that only partial state measurements are available for feedback. The proposed strategy involves a two‐phase procedure. Initialization phase is devoted to determining an admissible, though not optimal, linear memoryless controller capable to formally address the input rate constraint; then, during on‐line phase, predictive capabilities complement the designed controller by means of N steps free control actions in a receding horizon fashion. These additive control actions are obtained by solving semidefinite programming problems subject to linear matrix inequalities constraints. As computational burden grows linearly with the control horizon length, an example is developed to show the effectiveness of the proposed approach for realistic control problems: the design of a flight control law for a flexible unmanned over‐actuated aircraft, where the states of the flexibility dynamics are not measurable, is discussed, and a numerical implementation of the controller within a nonlinear simulation environment testifies the validity of the proposed approach and the possibility to implement the algorithm on an onboard computer.     

Event‐driven model predictive control of timed hybrid Petri nets

Hybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating, in a natural way, continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete‐time and continuous‐time approaches. Continuous‐time approaches are usually more precise, but can be computationally prohibitive. Discrete‐time approaches are less complex, but can entail mode‐mismatch errors due to fixed time discretization. This work proposes an optimization‐based event‐driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode‐mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed‐loop strategy based on event‐driven model predictive control. Copyright © 2013 John Wiley & Sons, Ltd.     

A sliding mode control approach for systems subjected to a norm‐bounded uncertainty

This paper proposes a design approach of continuous sliding mode control of uncertain systems, the uncertainty being norm bounded. The two steps of the design methodology are investigated. The existence step, in which we choose the sliding surface that gives good behaviour during the sliding mode, is formulated as a pole assignment of linear uncertain system in a sector through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization. In the reaching step, we propose a continuous nonlinear control strategy ensuring a bounded motion about the ideal sliding mode, thus approximating the ideal dynamic behaviour in the presence of uncertainty. Finally, the validity and the applicability of this approach are illustrated by a flight stabilization benchmark example. Copyright © 2006 John Wiley & Sons, Ltd.     

Multi-objective control for stochastic model reference systems based on LMI approach and sliding mode control concept

In this article, a multi-objective control u(t) is designed for stochastic model reference systems to achieve the following three objectives simultaneously: the pole placement constraint, H _∞-norm constraint and individual error state variance constraint. Using the invariance property of sliding mode control, the reference model input and the plant error term will disappear on the sliding mode of the error system. By combining the upper bound covariance control theory, pole placement skill and H _∞-norm control theory, a controller, in which the control feedback gain matrix is synthesised utilising linear matrix inequality (LMI) approach, is derived to achieve the above multiple objectives. Furthermore, a practical example for the problem of ship yaw-motion systems is adopted to illustrate the proposed method.     

Model predictive control for uncertain max–min-plus-scaling systems

In this paper we extend the classical min–max model predictive control framework to a class of uncertain discrete event systems that can be modelled using the operations maximization, minimization, addition and scalar multiplication, and that we call max–min-plus-scaling (MMPS) systems. Provided that the stage cost is an MMPS expression and considering only linear input constraints then the open-loop min–max model predictive control problem for MMPS systems can be transformed into a sequence of linear programming problems. Hence, the min–max model predictive control problem for MMPS systems can be solved efficiently, despite the fact that the system is non-linear. A min–max feedback model predictive control approach using disturbance feedback policies is also presented, which leads to improved performance compared to the open-loop approach.     

Robust explicit model predictive control via regular piecewise-affine approximation

This paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. First, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforced a priori, rather than checked a posteriori via Lyapunov analysis.     

State-space approach to nonlinear predictive generalised minimum variance control

A nonlinear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process, but because of the assumed structure of the system, the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well-known GPC controller.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Max-plus-linear model-based predictive control for constrained hybrid systems：linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

基于神经网络与多模型的非线性自适应广义预测解耦控制

针对一类非线性多变量离散时间动态系统,提出了基于神经网络与多模型的非线性自适应广义预测解耦控制方法.该控制方法由线性鲁棒广义预测解耦控制器和神经网络非线性广义预测解耦控制器以及切换机构组成.线性鲁棒广义预测解耦控制器用于保证闭环系统输入输出信号有界,神经网络非线性广义预测解耦控制器能够改善系统性能.切换策略通过对上述两种控制器的切换,保证系统稳定的同时,改善系统性能.同时本文给出了所提自适应解耦控制方法的稳定性和收敛性分析.最后,通过仿真实例验证了该方法的有效性.     

一类不确定模糊模型的输出反馈鲁棒预测控制

针对一类满足扇形界条件的不确定模糊模型描述的非线性系统,提出一种输出反馈鲁棒预测控制方法．该方法将鲁棒预测控制的Min-Max优化问题转化为具有LMI约束的线性目标最小化问题,并且不需系统状态完全可测,仅仅利用系统测量输出和不可测状态的界限值来确定保证闭环系统鲁棒稳定的输出反馈控制器．仿真实验证明了该方法的有效性．     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

H∞ control of continuous-time Markov jump linear systems with detector-based mode information†

This paper features new results on H_∞ analysis and control of linear systems with Markov jump disturbances, in a scenario of partial observations of the jump process. We consider the situations in which the jump process can only be measured through a suitable detector. A distinctive feature of the approach here is that it is general enough to encompass particular scenarios such as that of perfect information, no information (mode independent) and cluster observations of the Markov jump process. The main results, comprising a new bounded real lemma and a condition for state feedback synthesis, are expressed via linear matrix inequality-based optimisation problems. The method devised for the design of H_∞ controllers is applied to the control of an unmanned aerial vehicle model.     

A model predictive control framework for constrained uncertain positive systems

In this paper, a new model predictive control framework is proposed for positive systems subject to input/state constraints and interval/polytopic uncertainty. Instead of traditional quadratic performance index, simple linear performance index, linear Lyapunov function, cone invariant set with linear form and linear computation tool are first adopted. Then, a control law that can handle the constraints and robustly stabilise the systems is proposed. The advantages of the new framework lie in the following facts: (1) an equivalent linear problem is formulated that can be easily solved than other problems including the quadratic ones, (2) simple linear index and linear tool can be used based on the essential property of positive systems to achieve the desired control performance and (3) a general model predictive control law without sign restriction is designed. Finally, an attempt of application on mitigating viral escape is provided to verify the effectiveness of the proposed approach.