A computational method for solving time-delay optimal control problems with free terminal time

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system (which influences the variable time delays in the new system). We develop a gradient-based optimization approach for solving this approximate problem. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.     

带有持续扰动的时滞非线性大系统的最优跟踪控制

研究具有外界持续扰动的时滞非线性大系统的无静差最优跟踪控制问题.将时滞非线性大系统分解为带有互联项的N个时滞非线性子系统,基于内模原理对子系统构造扰动补偿器,将带有外部持续扰动的子系统化为无扰动的增广系统.通过灵敏度法求解不含时滞的两点边值问题,得到子系统的最优跟踪控制律,截取最优跟踪控制律的前N项作为次优控制律来近似系统的最优控制律.仿真实例表明了该设计方法的有效性.     

Optimal control of a nonlinear fed-batch fermentation process using model predictive approach

Bioprocesses are involved in producing different pharmaceutical products. Complicated dynamics, nonlinearity and non-stationarity make controlling them a very delicate task. The main control goal is to get a pure product with a high concentration, which commonly is achieved by regulating temperature or pH at certain levels. This paper discusses model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor. The novel approach used here is to use the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. The result of applying the obtained controller has been displayed and compared with the results of an auto-tuned PID controller used in previous works. Moreover, to avoid high computational cost, the nonlinear model is substituted with neuro-fuzzy piecewise linear models obtained from a method called locally linear model tree (LoLiMoT).     

一类非自衡对象的最优控制

对模型不确定性和控制能量约束并存时一类非自衡对象的最优控制问题作了探讨．首先基于一类随机模型误差的描述,定义了一个平均意义上的包含跟踪误差和控制能量在内的性能指标;然后通过谱分解极小化该性能指标,导出一个最优的控制律,从而为模型不确定性和控制能量约束并存条件下一类非自衡对象的最优控制问题提供了一种实用的控制方法．仿真结果证明了该方法的有效性．     

Optimal control problems with a continuous inequality constraint on the state and the control

We consider an optimal control problem with a nonlinear continuous inequality constraint. Both the state and the control are allowed to appear explicitly in this constraint. By discretizing the control space and applying a novel transformation, a corresponding class of semi-infinite programming problems is derived. A solution of each problem in this class furnishes a suboptimal control for the original problem. Furthermore, we show that such a solution can be computed efficiently using a penalty function method. On the basis of these two ideas, an algorithm that computes a sequence of suboptimal controls for the original problem is proposed. Our main result shows that the cost of these suboptimal controls converges to the minimum cost. For illustration, an example problem is solved.     

Approximation-based control of nonlinear MIMO time-delay systems

Approximation-based control is presented for a class of multi-input multi-output (MIMO) nonlinear systems in block-triangular form with unknown state delays. Neural networks (NNs) are utilized to approximate and compensate for unknown functions in the system dynamics, including the unknown bounds of the functions of delayed states. The use of a separation technique removes the need for any assumption on the function of delayed states, and allows the handling of multiple delays in each function of delayed states. By combining the use of Lyapunov-Krasovskii functionals and adaptive NN backstepping, the proposed control guarantees that all closed-loop signals remain bounded, while the outputs converge to a neighborhood of the desired trajectories. Simulation results demonstrate the effectiveness of the proposed scheme.     

一类不稳定时滞过程的最优控制

本文对控制能量存在约束条件下一类不稳定时滞过程的最优控制问题进行了探讨. 首先基于不稳定过程的互质分解, 由敏感度函数和控制敏感度函数定义了一个包含跟踪误差和控制能量在内的性能指标, 然后应用谱分解最小化该性能指标, 从而为一类不稳定时滞过程导出了一种最优的控制器设计方法, 可使系统在控制能量存在约束时获得最优的控制性能. 仿真研究进一步说明了该方法的有效性.     

状态时滞系统的输入多采样最优控制

本文针对离散状态时滞系统，首先将其变形为无时滞形式，设计出最优控制器；然后运用离散提升技术对输入进行多采样，得到扩展的离散系统模型，再运用最优控制技术对扩展系统进行最优设计。最后对系统进行仿真，结果表明，该算法具有较好的控制效果。具有较好的稳定性。     

Efficient robust constrained model predictive control with a time varying terminal constraint set

An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N=0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.     

控制输入受限的准全控制利用率有限时间稳定控制

针对控制输入受限的非线性系统,分6种情况证明有限时间稳定控制器(finite time stable controller, FTSC)作用下的系统状态收敛速度在论域空间中每一点必快于非有限时间稳定控制器(non-FTSC, NFTSC)作用下的系统状态收敛速度,并给出每一类情况下设计参数应满足的充分性约束条件,同时证明这些条件的存在性.在此基础上,提出全控制利用率控制器(CCUC)的定义,证明CCUC必然引起抖振,进而提出准全控制利用率控制器(QCCUC)设计的思想,并证明控制输入受限条件下, FTSC的控制利用率必优于任意快速FTSC(FFTSC),即具有更优的控制性能,从而得到一系列关于参数优化的结论.理论证明的结论通过图表、数例和仿真得到了验证.所得结论对终端滑模控制、加幂积分控制、有限时间稳定backstepping控制等多种FTSC均广泛适用.     

Optimal robust control of nonlinear time-delay systems: Maintaining low operating errors during feedback outages

The problem of maintaining low operating errors during feedback outages is considered for a class of nonlinear systems with time-delays in the input channel. It is shown that there are optimal controllers that keep operating errors below a specified bound for the longest time possible. Furthermore, it is shown that optimal performance can be approximated as closely as desired by using bang-bang controllers – controllers that are relatively easy to calculate and implement.     

On the performance of economic model predictive control with self-tuning terminal cost

In this paper, we analyze the closed-loop performance of a recently introduced economic model predictive control (MPC) scheme with self-tuning terminal cost. To this end, we propose to use a generalized terminal region constraint instead of a generalized terminal equality constraint within the repeatedly solved optimization problem, which allows us to obtain improved closed-loop asymptotic average performance bounds. In particular, these bounds can be obtained a priori. We discuss how the necessary parameters for the generalized terminal region setting can be calculated, and we illustrate our findings with two numerical examples.     

CMOPSO/D算法的发酵过程补料优化控制

为了改善发酵过程补料优化控制的性能指标,提出一种基于改进的分解多目标粒子群优化算法的发酵过程补料优化控制方法。将发酵过程的多目标优化问题分解为若干单目标优化问题,对每个单目标优化问题应用2个粒子群协同搜索最优解,其中一个种群对连接向量进行搜索,改进了连接向量的更新方式,另一个种群将决策空间分解,使用不同种群对不同维度的解向量进行优化,并在进化过程中使用前一个种群的最优解构成完整的解向量评价每个子群的最优解,提高了最优解评价的准确性,保证算法收敛到全局最优解。将该算法用到在工业酵母发酵过程模型中,对补料速率进行优化控制,并同时优化2个性能指标,即菌体浓度最大化和乙醇浓度最小化,并与基本的分解粒子群优化算法的优化结果作对比,该算法获得的Pareto前沿在基本分解粒子群优化算法获得的Pareto前沿下方,并且分布更加完整。实验证明该算法能够获得最优补料速率,使工业酵母发酵过程的菌体浓度提高了约9%,乙醇浓度降低了约为15%,为发酵过程补料优化控制提供了一种有效方法。     

一类不确定模糊动态时滞系统保成本控制

针对一类不确定非线性动态时滞系统，利用模相T—S模型，通过状态反馈对保成本控制问题进行研究。应用线性矩阵不等式给出模糊闭环系统渐近稳定的充分条件，保证了所有允许的不确定闭环系统是稳定的，而且对于一个给定的二次型成本函数，舱保证闭环成本不超过某个界。仿真结果表明所提出的控制方法是有效的。     

基于矩阵测度的非线性广义时滞系统鲁棒模糊控制

研究T-S模糊广义时滞系统的鲁棒控制问题.不同于传统的寻求公共正定矩阵的方法,基于矩阵测度给出保证系统鲁棒稳定的充分条件,并将此条件进一步转化为线性矩阵不等式.通过求解线性矩阵不等式,得到状态反馈控制器和静态输出反馈控制器.最后通过算例仿真验证了方法的有效性.     

Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile.