Tube‐based robust nonlinear model predictive control

This paper extends tube‐based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube‐based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Reduced order model predictive control for constrained discrete‐time linear systems

A reduced order model predictive control (MPC) is discussed for constrained discrete‐time linear systems. By employing a decomposition method for finite‐horizon linear systems, an MPC law is obtained from a reduced order optimization problem. The decomposition enables us to construct pairs of initial state and control sequence which have large influence on system responses, and it also characterizes the standard LQ control. The MPC law is obtained based on a combination of the LQ control and dominant input sequences over the prediction horizon. The proposed MPC method is illustrated with numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

面向FPGA便捷部署的智能模型预测控制

现场可编程逻辑门阵列(FPGA)具有可编程、易并行化的独特优势, 是实现一体化感知、决策、控制最具前景的人工智能芯片之一, 但其硬件描述语言(HDL)不易掌握. 本文提出了一种基于神经网络的智能MPC及其FPGA便捷部署方法, 使用高层次综合(HLS)生成HDL代码, 并通过MATLAB-Modelsim联合仿真验证代码功能, 可克服人工编写HDL代码的困难, 提高控制算法的部署效率. 该方法利用了深度神经网络的结构特点和FPGA的并行计算优势, 离线训练神经网络在线仅需硬件化正向传播, 在低资源占用的同时具有严格计算时间保证. 将所提方法分别应用于高速、高维控制系统中, FPGA在环测试验证了其有效性.     

Multirate sliding mode disturbance compensation for model predictive control

In this paper, a novel hierarchical multirate control scheme for nonlinear discrete‐time systems is presented, consisting of a robust nonlinear model predictive controller (NMPC) and a multirate sliding mode disturbance compensator (MSMDC). The proposed MSMDC acts at a faster rate than the NMPC in order to keep the system as close as possible to the nominal trajectory predicted by NMPC despite model uncertainties and external disturbances. The a priori disturbance compensation turns out to be very useful in order to improve the robustness of the NMPC controller. A dynamic input allocation between MSMDC and NMPC allows to maximize the benefits of the proposed scheme that unites the advantages of sliding mode control (strong reduction of matched disturbances, low computational burden) to those of NMPC (optimality, constraints handling). Sufficient conditions required to guarantee input‐to‐state stability and constraints satisfaction by the overall scheme are also provided. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

A toolkit for nonlinear model predictive control using gradient projection and code generation

Nonlinear model predictive control (NMPC) is a control strategy based on finding an optimal control trajectory that minimizes a given objective function. The optimization is recalculated at each control cycle and only the first control values are actually used. The dynamics of the system can be nonlinear and there can be constraints on states and controls. A new toolkit called VIATOC has been developed that can be used to automatically generate the code needed to implement NMPC. The generated code is self-contained ANSI C and the compiled program has a small footprint. In VIATOC, the gradient projection method is used to solve the nonlinear optimization problem. Barzilai–Borwein type step length selection for the gradient method has also been implemented. The performance of the controllers generated with the toolkit is compared with those solved with the ACADO toolkit and HQP. The performance of the optimization is compared with two different test cases with different numbers of controls and states. The first one is based on a model of a pendulum hanging freely on a movable platform. The second one is a more complex model of a chain of three masses connected by springs. Seven different prediction horizons between 10 and 100 steps are used. When the time to achieve a near optimum solution is measured, VIATOC is in most cases the fastest one when the length of the prediction horizon is shorter than 70 steps.     

Linearized min‐max robust model predictive control: Application to the control of a bioprocess

This work deals with the problem of trajectory tracking for a nonlinear system with unknown but bounded model parameter uncertainties. First, this work focuses on the design of a robust nonlinear model predictive control (RNMPC) law subject to model parameter uncertainties implying solving a min‐max optimization problem. Secondly, a new approach is proposed, consisting in relating the min‐max problem to a more tractable optimization problem based on the use of linearization techniques to ensure a good trade‐off between tracking accuracy and computation time. The developed strategy is applied in simulation to a simplified macroscopic continuous photobioreactor model and is compared to the RNMPC and nonlinear model predictive controllers. Its efficiency and its robustness against parameter uncertainties and/or perturbations are illustrated through numerical results.     

Self‐triggered model predictive control for networked control systems based on first‐order hold

In this work, a new self‐triggered model predictive control (STMPC) algorithm is proposed for continuous‐time networked control systems. Compared with existing STMPC algorithms, the proposed STMPC is implemented based on linear interpolation (first‐order hold) rather than the standard zero‐order hold, which helps further reduce the difference between the self‐triggered control signal and the original time‐triggered counterpart and thus reduce the rate of triggering. Based on the first‐order hold implementation, a self‐triggering condition is derived and the corresponding theoretical properties of the closed‐loop system are analyzed. Finally, the comparison between the proposed algorithm and the zero‐order hold–based STMPC is carried out through both theoretical analysis and a simulation example to illustrate the effectiveness of the proposed method.     

Dynamic output feedback robust model predictive control

The synthesis approach for dynamic output feedback robust model predictive control is considered. The notion of quadratic boundedness is utilised to characterise the stability properties of the augmented closed-loop system. A finite horizon performance cost, which corresponds to the worst case of both the polytopic uncertainty and the bounded disturbance/noise, is utilised. It is not required to specify the horizon length. A numerical example is given to illustrate the effectiveness of the proposed controller.     

具有可参数化不确定性系统的对偶自适应模型预测控制

控制系统中存在的不确定性为其性能优化带来诸多问题.自适应控制和鲁棒控制是针对系统存在的不确定性而采取的不同设计策略;前者没有充分考虑系统的未建模动态,而后者往往是针对不确定的最大界而设计,具有较强的保守性.本文试图将自适应控制和鲁棒控制的策略相结合,提出了一种在模型预测控制中利用未来不确定信息的对偶自适应模型预测控制策略.该策略将系统中由未建模动态引起的不确定性参数化表达,并为其设定边界约束,作为优化问题中新的约束,在优化控制目标的同时减小系统不确定性对控制的影响.仿真结果表明,本文提出的算法较传统自适应模型预测控制算法,对于系统存在的不确定性由于在迭代过程中采用参数化描述,得到了更好的系统性能,且具有更好的收敛性.     

Observer‐based cooperative distributed fault‐tolerant model predictive control with imperfect network communication and asynchronous measurements

Intermittent actuator and sensor faults tolerant are simultaneously considered in a distributed control system with imperfect communication network. The asynchronous measurements of different output variables in one sampling period are synchronized through a novel two‐stage model‐based projection method. Different from centralized control network, in both layer‐to‐layer and in‐layer communication, the packet delay, loss and disordering are corrected by the predicted data from model predictive control. Moreover, a completely distributed state observer is established for both system states and sensor faults problem with bounded noise uncertainties. For the intermittent actuator faults, actuator plug‐and‐play design methods based on model predictive control has been introduced, making the actuator faults estimation omitted. The distributed stability conditions are derived for the proposed fault‐tolerant controller, and the online feasibility is explained in detail. Numerical simulation is given to verify the design procedure.     

Enhanced information reconfiguration for distributed model predictive control for cyber‐physical networked systems

This paper considers a class of cyber‐physical networked systems, which are composed of many interacted subsystems, and are controlled in a distributed framework. The operating point of each subsystem changes with the varying of working conditions or productions, which may cause the change of the interactions among subsystems correspondingly. How to adapt to this change with good closed‐loop optimization performance and appropriate information connections is a problem. To solve this problem, the impaction of a subsystem's control action on the performance of related closed‐loop subsystems is first deduced for measuring the coupling among subsystems. Then, a distributed model predictive control (MPC) for tracking, whose subsystems online reconfigure their information structures, is proposed based on this impaction index. When the operating points changed, each local MPC calculates the impaction indices related to its structural downstream subsystems. If and only if the impaction index exceeds a defined bound, its behavior is considered by its downstream subsystem's MPC. The aim is to improve the optimization performance of entire closed‐loop systems and avoid the unnecessary information connections among local MPCs. Besides, contraction constraints are designed to guarantee that the overall system converges to the set points. The stability analysis is also provided. Simulation results show that the proposed impaction index is reasonable along with the efficiency of the proposed distributed MPC.     

Distributed nonlinear model predictive control based on contraction theory

A novel distributed model predictive control algorithm for continuous‐time nonlinear systems is proposed in this paper. Contraction theory is used to estimate the prediction error in the algorithm, leading to new feasibility and stability conditions. Compared to existing analysis based on Lipschitz continuity, the proposed approach gives a distributed model predictive control algorithm under less conservative conditions, allowing stronger couplings between subsystems and a larger sampling interval when the subsystems satisfy the specified contraction conditions. A numerical example is given to illustrate the effectiveness and advantage of the proposed approach.     

Stochastic model predictive control: Insights and performance comparisons for linear systems

In this paper, we define several instances of model predictive control (MPC) for linear systems, including both deterministic and stochastic formulations. We show by explicit computation of the associated control laws that, under certain conditions, different formulations lead to identical results. This paper provides insights into the performance of stochastic MPC. Amongst other things, it shows that stochastic MPC and traditional MPC can give identical results in special cases. In cases where the solutions are different, we show that the explicit formulation of the problem can give insight into the performance gap.     

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.     

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.