Integral sliding mode based optimal composite nonlinear feedback control for a class of systems

This paper presents an optimization method of designing the integral sliding mode （ISM） based composite nonlinear feedback （CNF） controller for a class of low order linear systems with input saturation. The optimal CNF control is first designed as a nominal control to yield high tracking speed and low overshoot. The selection of all the tuning parameters for the CNF control law is turned into a minimization problem and solved automatically by particle swarm optimization （PSO） algorithm. Subsequently, the discontinuous control law is introduced to reject matched disturbances. Then, the optimal ISM-CNF control law is achieved as the sum of the optimal CNF control law and the discontinuous control law. The effectiveness of the optimal ISM-CNF controller is verified by comparing with a step by step designed one. High tracking performance is achieved by applying the optimal ISM-CNF controller to the tracking control of the micromirror.     

基于控制参数化的注塑工业过程最优反馈控制方法

本文针对一类典型的注塑工业过程系统, 研究了注塑填充过程中产生的熔体流动速度最优跟踪控制问题, 提出了一种基于控制参数化的计算最优反馈控制器设计方法以实现注塑过程中熔融聚合物流动前沿位移的最优跟 踪控制, 进而达到改善注塑零件性能的高效生产目标. 首先, 面向注塑工艺复杂生产过程建立了动态过程系统数学 模型, 提出了注塑机内部熔融聚合物流动前沿位置的动态最优跟踪控制问题; 其次, 设计了一种多级反馈控制律, 通 过控制参数化方法将控制反馈核进行了参数化表示, 将控制器设计问题转化为一序列最优参数决策问题; 然后, 通 过状态灵敏度方程分析方法, 求解出了目标函数及约束条件关于决策变量参数梯度信息的显式表达式, 并基于所提 供的梯度信息结合序列二次规划算法进行了高效优化迭代求解; 最后, 通过实验仿真验证了本文所提出的最优反 馈控制器设计方法的可行性和有效性.     

基于动态规划的约束优化问题多参数规划求解方法及应用

结合动态规划和单步多参数二次规划, 提出一种新的约束优化控制问题多参数规划求解方法. 一方面能得到约束线性二次优化控制问题最优控制序列与状态之间的显式函数关系, 减少多参数规划问题求解的工作量; 另一方面能够同时求解得到状态反馈最优控制律. 应用本文提出的多参数二次规划求解方法, 建立无限时间约束优化问题状态反馈显式最优控制律. 针对电梯机械系统振动控制模型做了数值仿真计算.     

An ODE Comparison Theorem With Application in the Optimal Exit Time Control Problem

The optimal exit time control (OETC) problem tries to find the feedback control law with a reasonable cost that can keep the system state inside a certain subset of the state space, called the safe set, for the longest time under random perturbations. The symmetry property of its solutions has been proved previously when the state dimension is higher than one. In this note, a comparison theorem is established that compares the solutions to two ODEs arising in the 1-D OETC problem. The symmetry of solutions to the 1-D OETC problem is proved using this comparison theorem. An example is presented to show how the symmetry result can help to solve the OETC problem analytically in certain cases.      

A technique for suboptimal feedback control of nonlinear systems

A simple easily implemented method is developed for obtaining a suboptimal control law for the optimization problem associated with minimizing a quadratic cost functional for nonlinear systems. The suboptimal control law is derived using a Taylor's series representation for the feedback gain matrix after modeling the nonlinear system by a linear system at each instant of time. The resultant control law is of feedback form and is nonlinear in state. The suboptimal control is obtained without using iterative techniques or any true optimal solutions. A second-order numerical example illustrates the effectiveness of the method and gives a comparison to the results of previous methods.     

Optimal control of weakly coupled bilinear systems

The optimization of the time-invariant bilinear weakly coupled system with a quadratic performance criterion is considered. A sequence of linear state and costate equations is constructed such that the open-loop solution of the optimization problem is obtained in terms of the reduced-order subsystems. This leads to a reduction in the size of the required computations and allows parallel processing of information. The near-optimal closed-loop control is obtained in the form of a linear feedback law, with the feedback gains calculated from two reduced-order independent time-varying linear-quadratic optimal control problems.     

基于BMI的一类不确定分段线性系统的最优控制设计

将不确定分段线性系统的最优控制问题转化成最优控制性能界的优化问题．其中性能上界的优化是以反馈增益为寻优参数的一组双线性矩阵不等式(BMI)问题，对此将遗传算法和内点法结合， 设计了一种混合算法进行求解．最后的算例表明控制律的设计及其求解算法的有效性．     

受扰线性离散系统的前馈2反馈最优控制

研究具有已知动态特性但未知初始条件的持续外界扰动的线性离散系统最优控制问题。给出了前馈一反馈最优控制律的存在唯一性条件，并提出了最优控制律的设计算法．通过降维扰动观测器解决了前馈一反馈最优控制律的物理不可实现问题．对近海结构物振动控制的实例仿真表明，该设计算法易于实现，在抑制外部持续扰动和鲁棒性方面优于经典的状态反馈最优控制。     

2D system approach based output feedback repetitive control for uncertain discrete-time systems

This paper presents a two-dimensional (2D)-based approach to the problem of output feedback repetitive control for uncertain discrete-time systems. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2D system. Then sufficient conditions for the existence of output feedback control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal output feedback control law by minimizing the upper bound of a given cost function. Compared with the commonly used 1D-based method, the proposed approach increases the degree of freedom of controller design by not only including in the scheme an output feedback gain but also a feed forward one which can be simultaneously solved using the 2D-based procedures presented in the paper. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

具有正弦扰动的时滞系统前馈-反馈次优控制:灵敏度法

研究线性时滞系统在外部正弦扰动作用下的前馈-反馈最优减振问题,提出了一种最优控制律的灵敏度设计方法．通过引入灵敏度参数并围绕它展开幂级数,将系统的最优控制问题简化为不含超前项和时滞项的两点边值问题族．通过截取最优控制级数的有限和获得原系统的前馈-反馈次优控制律．仿真结果表明,与经典状态反馈最优控制相比,本文的算法更加鲁棒,能更加有效地抑制正弦扰动．     

带有持续扰动非线性系统的前馈-反馈最优控制

研究具有外界持续扰动作用下非线性系统的最优控制问题,提出了一种设计前馈一反馈最优控制器的逐次逼近算法．利用该算法可将在扰动作用下的非线性系统的最优控制问题转化为求解线性非齐次两点边值序列的问题．得到的最优控制律由解析的线性前馈-反馈项和伴随向量序列极限形式的非线性补偿项组成．通过截取非线性补偿序列的有限项,可得到前馈-反馈次优控制律．仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制．     

An algorithm for simultaneous stabilization using decentralizedconstant gain output feedback

An algorithm which solves, numerically, the simultaneous stabilization problem using a constant gain decentralized control law is presented. The algorithm is determined from the necessary conditions for minimizing an optimal control problem. The optimal control problem consists of n plant models each with its own cost function. The costs are summed to create an average cost function and equality constraints are added to yield the decentralized control structure. The algorithm can start with any stabilizing full state feedback gain for each model and will converge to the optimal constant feedback gain for all models assuming a solution exists. Examples of the algorithm are given for Kharitonov synthesis and optimal gain scheduled control law synthesis using output feedback     

An algorithm for synthesis of the suboptimal control law for quasi-linear stochastic dynamical systems

We consider the information constrained optimization problem for stochastic dynamical systems governed by quasi-linear Ito equations. Let us describe the information constraints. We suppose that each control vector component depends on a prespecified set of precisely measured state vector components. In this article we present an algorithm for synthesis of the suboptimal control law. This control law is the linear feedback regulator. The linear parameter and the constant term of the regulator are polynomial functions of time. The algorithm is successfully applied to the problem of two-link robotic arm optimal control. These manipulators may be effectively used at space stations, e.g. for moving cargo in outer space.     

New Formulation of Dynamic Output Feedback Robust Model Predictive Control with Guaranteed Quadratic Boundedness

The dynamic output feedback robust model predictive controller for a system with both polytopic uncertainty and bounded disturbance is addressed in this paper. This controller utilizes a main optimization problem to find the control law and a simple auxiliary optimization problem to refresh the bounds on the true state. The main optimization problem, which is not necessarily solved at each sampling instant, achieves the near‐optimal solution. The auxiliary optimization, which is solved at each sampling instant, is followed with a simple criterion which determines whether or not to solve the main optimization problem at the next sampling time. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point.     

Optimization over state feedback policies for robust control with constraints

This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.     

State estimation and inferential control for a reactive batch distillation column

An optimal reflux ratio profile is obtained for a reactive batch distillation system utilizing the capacity factor as the objective function in a nonlinear optimization problem. Then, an Artificial Neural Network (ANN) estimator system, which utilizes the use of several ANN estimators, is designed to predict the product composition values of the distillation column from temperature measurements inferentially. The network used is an Elman network with two hidden layers. The designed estimator system is used in the feedback inferential control algorithm, where the estimated compositions and the reflux ratio information are given as inputs to the controller to see the performance of the ANN. In the control law, a scheduling policy is used and the optimal reflux ratio profile is considered as pre-defined set-points. It is found that, it is possible to control the compositions in this dynamically complex system by using the designed ANN estimator system with error refinement whenever necessary.     

非线性系统的输入多采样率模糊优化控制

基于多采样率数字控制理论,讨论了非线性连续被控对象和输入多采样率模糊控制器的设计问题.提出用线性矩阵不等式凸优化技术构建非线性系统的输入多采样率T-S模糊模型,并相应地研究了基于优化区域极点配置的PDC状态反馈控制.通过解代数Riccati方程得到控制器的参数,给出了优化数字控制器的设计算法和闭环系统的稳定性条件.计算机仿真表明了所提出方法的有效性.     

Efficient symmetric Hessian propagation for direct optimal control

Direct optimal control algorithms first discretize the continuous-time optimal control problem and then solve the resulting finite dimensional optimization problem. If Newton type optimization algorithms are used for solving the discretized problem, accurate first as well as second order sensitivity information needs to be computed. This article develops a novel approach for computing Hessian matrices which is tailored for optimal control. Algorithmic differentiation based schemes are proposed for both discrete- and continuous-time sensitivity propagation, including explicit as well as implicit systems of equations. The presented method exploits the symmetry of Hessian matrices, which typically results in a computational speedup of about factor 2 over standard differentiation techniques. These symmetric sensitivity equations additionally allow for a three-sweep propagation technique that can significantly reduce the memory requirements, by avoiding the need to store a trajectory of forward sensitivities. The performance of this symmetric sensitivity propagation is demonstrated for the benchmark case study of the economic optimal control of a nonlinear biochemical reactor, based on the open-source software implementation in the ACADO Toolkit.     

An iterative method for suboptimal control of a class of nonlinear time-delayed systems

This work presents an approximate solution method for the infinite-horizon nonlinear time-delay optimal control problem. A variational iteration method (VIM) is applied to design feedforward and feedback optimal controllers. By using the VIM, the original optimal control is transformed into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The existence and uniqueness of the optimal control law are proved. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation results demonstrate the validity and applicability of the VIM.     

带阶跃扰动的线性时滞系统最优无静差控制

研究线性时滞系统在阶跃扰动作用下的最优控制问题．首先基于内模原理构造扰动补偿器,以完全消除阶跃扰动对系统的影响。并将原系统的最优无静差扰动抑制问题转化为无扰动最优控制问题;然后利用灵敏度方法,求得由精确的解析项和伴随向量级数形式补偿项组成的最优控制律,通过截取伴随向量级数的有限项和．可得到次优无静差控制律．仿真实例验证了该方法的有效性．