Robust event‐triggered model predictive control for constrained linear continuous system

Model predictive control (MPC) is capable to deal with multiconstraint systems in real control processes; however, the heavy computation makes it difficult to implement. In this paper, a dual‐mode control strategy based on event‐triggered MPC (ETMPC) and state‐feedback control for continuous linear time‐invariant systems including control input constraints and bounded disturbances is developed. First, the deviation between the actual state trajectory and the optimal state trajectory is computed to set an event‐triggered mechanism and reduce the computational load of MPC. Next, the dual‐mode control strategy is designed to stabilize the system. Both recursive feasibility and stability of the strategy are guaranteed by constructing a feasible control sequence and deducing the relationship of parameters, especially the inter‐event time and the upper bound of the disturbances. Finally, the theoretical results are supported by numerical simulation. In addition, the effects of the parameters are discussed by simulation, which gives guidance to balance computational load and control performance.     

Robust constrained predictive control of uncertain norm-bounded linear systems

A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N. The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported.     

Robust practical output regulation for a class of uncertain linear minimum‐phase systems by output‐based event‐triggered control

In this paper, we consider the robust practical output regulation problem for a class of SISO uncertain linear minimum‐phase systems subject to external disturbances by an output‐based event‐triggered control law, where the reference inputs and the external disturbances are both generated by a so‐called exosystem with known dynamics. Our approach consists of two steps. First, on the basis of the internal model principle, we convert the problem into the robust practical stabilization problem of a well‐defined augmented system. Second, we design an output‐based event‐triggered mechanism and an output‐based event‐triggered control law to solve the stabilization problem, which in turn leads to the solvability of the original problem. What is more, we show that the event‐triggered mechanism prevents the Zeno behavior from happening. A numerical example is given to illustrate the design. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1‐gain and L∞‐gain characterization

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply rates are employed here for robustness and performance analysis using L₁‐gain and L_∞‐gain. Robust stability analysis is performed using integral linear constraints for which several classes of uncertainties are discussed. The approach is then extended to robust stabilization and performance optimization. The obtained results are expressed in terms of robust linear programming problems that are equivalently turned into finite dimensional ones using Handelman's theorem. Several examples are provided for illustration. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust explicit model predictive control for linear systems via interpolation techniques

This paper presents a novel interpolation‐based model predictive control (IMPC) for constrained linear systems with bounded disturbances. The idea of so‐called ‘pre‐stabilizing’ MPC is extended by making interpolation among several ‘pre‐stabilizing’ MPC controllers, through which the domain of attraction can be magnificently enlarged. Compared with the standard ‘pre‐stabilizing’ MPC, the proposed approach has the advantage of combining the merits of having a large domain of attraction and a good behavior. Furthermore, such an IMPC problem can be solved off‐line by multi‐parametric programming. The optimal solution is given in an explicitly piecewise affine form. A simple algorithm for the implementation of the explicit MPC control laws is also proposed. Copyright © 2009 John Wiley & Sons, Ltd.     

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.     

线性参变过驱动系统鲁棒控制分配策略

针对一类具有不确定时变参量的线性参变(linear parameter-varying,LPV)过驱动系统的控制分配问题,考虑系统的不确定参量扰动和执行器物理约束,利用伪控指令分配误差和控制量误差的1--范数,建立了含有时变不确定因子的控制分配优化模型.根据鲁棒优化思想,采用矢量变换技术处理时变不确定因子,得到了一种基于有约束锥二次凸优化模型的鲁棒控制分配算法,实现对LPV过驱动系统伪控指令的在线优化分配.最后,对某4轮电动汽车时变二自由度转向过驱动控制系统的对比仿真实验表明,相比常规4WS和伪逆控制分配方法,本文的鲁棒控制分配算法有效地降低了系统参变量不确定扰动的影响,得到更合理的控制分配解,有效改善了车辆的操纵稳定性.     

Self‐triggered state‐feedback control of linear plants under bounded disturbances

This paper addresses the problem of self‐triggered state‐feedback control for linear plants under bounded disturbances. In a self‐triggered scenario, the controller is allowed to choose when the next sampling time should occur and does so based on the current sampled state and on a priori knowledge about the plant. Besides comparing some existing approaches to self‐triggered control available in the literature, we propose a new self‐triggered control strategy that allows for the consideration of model‐based controllers, a class of controllers that includes as a special case static controllers with a zero‐order hold of the last state measurement. We show that our proposed control strategy renders the solutions of the closed‐loop system globally uniformly ultimately bounded. We further show that there exists a minimum time interval between sampling times and provide a method for computing a lower bound for it. An illustrative example with numerical results is included in order to compare the existing strategies and the proposed one. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust Kalman filtering for uncertain discrete‐time linear systems

This paper presents a steady‐state robust state estimator for a class of uncertain discrete‐time linear systems with norm‐bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd.     

Robust and non‐linear control of marine system

Robust and non‐linear control theories useful for real marine system are developed and applied to a variety of marine vehicles and equipments. In the thesis, the basic principle of marine control system development is described and advanced robust control algorithm and non‐linear control algorithm applicable for real system are shown. It's effectiveness is confirmed by numerical simulations, tank tests, and sea trial tests. Copyright © 2001 John Wiley & Sons, Ltd.     

Integrated fault detection system design for linear discrete time‐varying systems with bounded power disturbances

This paper investigates the problem of an integrated fault detection system design for linear discrete time‐varying systems with bounded power disturbances. In the integrated design of residual generator and evaluator, an approximated energy constraint is first imposed on the bounded power disturbances, and then selected by solving a min–max problem to achieve minimal‐size set of undetectable faults under the condition of zero false alarms. To tackle the problem that the computational burden involved in solving the min–max optimization grows with time, the moving horizon method is proposed. The proposed approach in this paper has two advantages: (i) the approximated energy constraint on bounded power disturbances is explicitly selected as a min–max solution in the integrated design to improve fault detection rate; by contrast, when directly applying any existing fault detection method to the case of bounded power disturbances, a predefined approximated energy constraint is implicitly introduced without considering fault detection performance; (ii) the design objective of the proposed approach can choose to consider faults only in the recent time horizon rather than faults in the complete time horizon; this strategy enhances detection performance of recent faults and benefits early fault detection, but has not been considered by existing fault detection methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Semiglobal stabilization of linear systems using constrained controls: a parametric optimization approach

A bounded feedback control for asymptotic stabilization of linear systems is derived. The designed control law increases the feedback gain as the controlled trajectory converges towards the origin. A sequence of invariant sets of decreasing size, associated with a (quadratic) Lyapunov function, are defined and related to each of them, the corresponding possible highest gain is chosen, while maintaining the input bounded. Gains as functions of the position are designed by explicitly solving a c-parameterized programming problem. The proposed method allows global asymptotic stabilization of open-loop stable systems, with inputs subject to magnitude bounds and globally bounded rates. In the general case of linear systems that are asymptotic null controllable with bounded input, the semiglobal stabilization is also addressed taking into account the problem of semiglobal rate-limited actuators. The method is illustrated with the global stabilization of an inertial navigator, and the stabilization of a nonlinear model of a crane with hanging load. Copyright © 1999 John Wiley & Sons, Ltd.     

采用鲁棒容许集对有约束的不确定系统作鲁棒模型预测控制

针对输入和状态受约束的干扰有界多胞不确定线性系统,提出了基于鲁棒容许集的扩大吸引域鲁棒模型预测控制(RMPC)方法.首先给出了多面体不变集的鲁棒容许集计算方法,并推导了鲁棒容许集存在的充分必要条件.其次,为了拓展Tube不变集鲁棒模型预测控制算法的适用范围,讨论了干扰有界多胞不确定线性系统的Tube不变集控制策略.之后为了扩大约束系统吸引域,提出了干扰有界多胞不确定系统的鲁棒容许集模型预测控制策略.通过采用鲁棒容许集和Tube不变集RMPC,该方法不仅扩大了吸引域,而且降低了在线计算量;同时,采用基于最小鲁棒正不变集的Tube不变集策略保证了算法的鲁棒性.最后仿真结果验证了算法的有效性.     

基于PI 控制器的线性系统的鲁棒耗散控制

针对参数具有确定性及不确定性的连续系统,给出两种严格耗散PI控制器的设计方法.首先,系统参数确定时,采用线性矩阵不等式方法,导出了类状态反馈和静态输出反馈严格耗散PI控制器存在的充要条件,并由线性矩阵不等式的可行解构造出严格耗散PI控制器增益的显式表达式;然后,考虑系数矩阵均具有范数有界不确定性时的鲁棒严格耗散控制问题,得到相似的结果;最后,通过数值算例表明了所给方法的有效性.     

Model reference adaptive control of discrete‐time piecewise linear systems

This article presents a switched model reference adaptive controller for discrete‐time piecewise linear systems. In the spirit of the work by Landau in the late seventies, proof of asymptotic stability of the closed‐loop error system is obtained, recasting its dynamics as a feedback system and showing the feedforward and the feedback paths are both passive. The challenge is that both paths can be piecewise linear. Numerical results show excellent performance of the proposed controller even in the face of sudden variations of the plant parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

H∞ model predictive control for constrained discrete‐time piecewise affine systems

This paper investigates stability analysis for piecewise affine (PWA) systems and specifically contributes a new robust model predictive control strategy for PWA systems in the presence of constraints on the states and inputs and with l₂ or norm‐bounded disturbances. The proposed controller is based on piecewise quadratic Lyapunov functions. The problem of minimization of the cost function for model predictive control design is changed to minimization of the worst case of the cost function. Then, this objective is reduced to minimization of a supremum of the cost function subject to a terminal inequality by considering the induced l₂‐norm. Finally, the predictive controller design problem is turned into a linear matrix inequality feasibility exercise with constraints on the input signal and state variables. It is shown that the closed‐loop system is asymptotically stable with guaranteed robust performance. The validity of the proposed method is verified through 3 well‐known examples of PWA systems. Simulation results are provided to show good convergence properties along with capability of the proposed controller to reject disturbances.     

Robust control of linear discrete-time systems

Given a linear discrete-time system with additive disturbances, a general methodology for designing a stable control algorithm is shown. The approach is Lyapunov-based with certain liberty of tailoring the candidate function for a given problem. Comparison to the existing solutions based on a variable structure approach is given.     

Linear matrix inequalities for analysis and control of linear vector second‐order systems

Many dynamical systems are modeled as vector second‐order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second‐order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter‐dependent Lyapunov functions as certificates of stability of uncertain and time‐varying vector second‐order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second‐order form. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust constrained control of piecewise affine systems through set‐based reachability computations

This article addresses finite‐horizon robust control of a piecewise affine system affected by uncertainty and characterized by different affine dynamics (modes) associated with a polyhedral partition of the state space. The goal is to design a static state‐feedback control law that maintains the state of the system within given—possibly time‐varying—sets, subject to actuation constraints. The proposed approach rests on two phases: a reference mode sequence with a sufficiently large robustness level is determined first, and then a tracking state‐feedback control law defined on the reach sets of the controlled system is designed to counteract uncertainty and maintain the reach sets within the reference sequence. If this is not possible and the reach sets split over different modes, then, further reference mode sequences and tracking controllers are computed. The designed state‐feedback control law is represented through a collection of controllers defined on precomputed reach sets of the closed‐loop control system. Performance of the approach is shown on some numerical examples.     

Discrete‐time low‐gain control of linear systems with input/output nonlinearities

Discrete‐time low‐gain control strategies are presented for tracking of constant reference signals for finite‐dimensional, discrete‐time, power‐stable, single‐input, single‐output, linear systems subject to a globally Lipschitz, non‐decreasing input nonlinearity and a locally Lipschitz, non‐decreasing, affinely sector‐bounded output nonlinearity (the conditions on the output nonlinearities may be relaxed if the input nonlinearity is bounded). Both non‐adaptive and adaptive gain sequences are considered. In particular, it is shown that applying error feedback using a discrete‐time ‘integral’ controller ensures asymptotic tracking of constant reference signals, provided that (a) the steady‐state gain of the linear part of the plant is positive, (b) the positive gain sequence is ultimately sufficiently small and (c) the reference value is feasible in a very natural sense. The classes of input and output nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone. The discrete‐time results are applied in the development of sampled‐data low‐gain control strategies for finite‐dimensional, continuous‐ time, exponentially stable, linear systems with input and output nonlinearities. Copyright © 2001 John Wiley & Sons, Ltd.