Simultaneous linear-quadratic optimal control design via static output feedback

In this paper, the problem of designing a fixed static output feedback control law which minimizes an upper bound on linear quadratic (LQ) performance measures for r distinct MIMO plants is addressed using linear matrix inequality (LMI) technique. An iterative LMI algorithm is proposed to obtain the solution. Examples are used to demonstrate its effectiveness. Copyright ©1999 John Wiley & Sons, Ltd.     

Numerical solutions for constrained time-delayed optimal control problems

In this paper, time-delayed optimal control problems governed by delayed differential equation are solved. Two different techniques based on integration and differentiation matrices are considered. The time-delayed term of the problem has been approximated by Chebyshev interpolating polynomials. On this basis, the optimal control problem can be solved as a mathematical programming problem. The example illustrates the robustness, accuracy and efficiency of the proposed numerical techniques.     

航天器全状态约束输出反馈控制

针对无角速度测量的刚性航天器姿态跟踪问题,提出一种全状态约束输出反馈控制方法.建立修正罗德里格参数描述的系统模型,提出能够适用于约束与非约束情况的改进型障碍李雅普诺夫函数(MBLF),拓展传统对数型障碍李雅普诺夫函数的适用范围.构造二阶辅助系统,将控制输入和饱和输入之间的差作为构造系统的输入,进而产生信号以补偿饱和的影响.设计状态观测器估计未知状态量,并结合反步法设计输出反馈控制律,保证系统全状态约束性能和姿态跟踪精度.通过李雅普诺夫稳定性分析证明姿态观测误差和跟踪误差能够达到一致最终有界.仿真结果验证所提方法的有效性.     

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.     

A Riccati approach for constrained linear quadratic optimal control

An active-set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. A Riccati-based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure. The solution of each subproblem requires computations that scale linearly with the horizon length. The algorithm is illustrated with numerical examples.     

A constrained optimal control program in APL

This note formulates a dynamic control model which optimizes a quadratic objective functional subject to linear constraints and solves in APL. Besides giving the optimal objective function value, the APL program computes values of the gain matrices, the Riccati equations, the state variables and the control variables. The power, compactness and flexibility of the APL program are undoubted when compared with other software. The most useful result of the exercise is that the APL program can be easily modified to the exact requirements of the individual researcher, faculty member, consultant and student.     

有限时间控制问题综述

有限时间控制系统因具有良好的鲁棒性能和抗扰动性能而受到广泛关注.首先,回顾了有限时间控制方法的起源,并列举了有限时间控制系统的几种常用判据;然后,总结了有限时间控制系统的研究现状;最后,讨论了未来可能的研究方向.     

Butterworth最优控制的逆问题

为了认识Butterworth最优控制的本质,揭开Butterworth最优传递函数与加权矩阵Q,R的相互关系,本文研究Butterworth最优控制的逆问题.首先用Butterworth最优控制确定状态反馈增益阵K,然后给出计算加权矩阵Q的参数化公式,最后用一个例子说明这种确定加权矩阵Q,R的方法的有效性和简便性.     

Time/fuel optimal control of constrained linear discrete systems

A unified approach to solving three common optimal control problems is presented, for linear systems under general constraints. The problems are: (1) the time optimal control problem; (2) the fuel optimal control problem in fixed time; (3) the time optimal control problem with a fuel constraint. A special purpose linear programming algorithm is used. State variable constraints are efficiently handled by a cutting plane algorithm. An example of a sixth order system with two inputs and two state variable constraints illustrates the method as implemented on a personal computer.     

Modified bang‐bang controller for maximal and minimal time optimal control problems

Recently, there have been a series of results regarding two time optimal control problems for a class of linear and nonlinear systems ‐ one is to keep the system states within certain bound for the longest time during feedback disruption and the other is to derive the system states to near the origin as fast as possible after feedback recovery, both under bounded control inputs. These are called maximal and minimal time optimal control problems, respectively. In the existing results, a bang‐bang controller has been commonly suggested as the actual implementation of the optimal controller. In this paper, we suggest a modified version of the bang‐bang controller which can also serve as an approximate optimal controller. Our proposed controller provides the (near) optimal performance with (i) possible reduction of a number of switchings; (ii) possible reduction of control input magnitude.     

Nonlinear optimal control as quantum mechanical eigenvalue problems

A novel approach for approximating the nonlinear optimal feedback control of a system with a terminal cost is proposed. To lessen the difficulty due to nonlinearity, we try to treat the system in a framework of linear theories. For this, we assume a quantum mechanical linear wave associated with the system. Since the control system is constrained by state equations, we handle the system according to quantum mechanics of constrained dynamics. A Hamiltonian is represented as a linear operator acting on a function that describes behavior of waves. Subsequently, nonlinear feedback is calculated without any time integration in the backward direction. Using eigenvalues and eigenfunctions of the linear Hamiltonian operator, an optimal feedback law is given as a combination of analytic functions of time and state variables. We take as an example a system described by two scalar variables for state and control input. Simulation studies on the system by the eigenvalue analysis show that the proposed method reduces calculation time to nearly a tenth that of a numerical calculation of a Hamilton-Jacobi equation by a finite difference method.     

On constrained infinite-time linear quadratic optimal control with stochastic disturbances

In this work, we study the infinite-time linear quadratic optimal control problem for systems with stochastic disturbances and constrained inputs. A number of stochastic problem formulations under the full state information (FSI) structure are considered with a particular focus on the subject of feedback structure and its impact on certainty equivalence. In particular, we clarify results concerning the open-loop hard constrained, closed-loop statistically constrained, and closed-loop hard constrained cases. Extension to the infinite-time framework provides a vehicle for interpreting these controllers and indicates that the last of the three is of most interest to regulation type applications. Additionally, the partial state information problem is considered, and conditions are given for which a separated configuration consisting of the optimal estimator cascaded with the FSI optimal controller remains optimal.     

用输出反馈配置鲁棒极点的李雅普诺夫直接法*

本文讨论了输出反馈配置线性多变量定常系统鲁棒极点的问题,提出了一种设计方法和有关定理,并用实例说明了该法的应用。     

Moving least-squares approximations for linearly-solvable stochastic optimal control problems

Nonlinear stochastic optimal control problems are fundamental in control theory.A general class of such problems can be reduced to computing the principal eigenfunction of a linear operator.Here,we describe a new method for finding this eigenfunction using a moving least-squares function approximation.We use efficient iterative solvers that do not require matrix factorization,thereby allowing us to handle large numbers of basis functions.The bases are evaluated at collocation states that change over iterations of the algorithm,so as to provide higher resolution at the regions of state space that are visited more often.The shape of the bases is automatically defined given the collocation states,in a way that avoids gaps in the coverage.Numerical results on test problems are provided.     

线性离散系统具有闭环极点约束的输出反馈H∞ 控制

对一类线性离散系统, 研究了具有闭环圆盘极点约束的输出反馈H_∞ 控制问题. 基于线性矩阵不等式处理方法, 导出了输出反馈控制器的存在条件和设计方法. 和现有方法相比, 本文的方法具有更小的保守性.     

State-constrained optimal control problems governed by coupled nonlinear wave equations with memory

This work considers the optimal control problems governed by coupled nonlinear wave equations with memory, where the state constraint is a type of integral. First, we investigate the existence of the optimal solution for the optimal control problem, and then we deduce the maximum principle for the optimal solution with state constraint. Moreover, we give a concrete example which is covered by the main result.     

A nonsmooth Newton’s method for control-state constrained optimal control problems

We investigate optimal control problems subject to mixed control-state constraints. The necessary conditions are stated in terms of a local minimum principle. By use of the Fischer–Burmeister function the minimum principle is transformed into an equivalent nonlinear and nonsmooth equation in appropriate Banach spaces. This nonlinear and nonsmooth equation is solved by a nonsmooth Newton’s method. We will show the local quadratic convergence under certain regularity conditions and suggest a globalization strategy based on the minimization of the squared residual norm. A numerical example for the Rayleigh problem concludes the article.     

Numerical treatment of multiobjective optimal control problems

We present a numerical procedure for solving optimal control problems with both linear terminal constraints and multiple criteria. Using a Chebyshev spectral procedure, the problem reduces to a constrained optimization problem which can be solved using hybrid penalty partial quadratic interpolation (HPPQI) technique. The proposed procedure compares quite favorably with other methods on a sample of well-known examples.     

Equivalent optimal compensation problem in the delta domain for systems with white stochastic parameters

The equivalent representation in the delta domain of the digital optimal compensation problem is provided and computed in this article. This problem concerns finding digital optimal full and reduced-order output feedback controllers for linear time-varying and time-invariant systems with white stochastic parameters. It can subsequently be solved in the delta domain using the strengthened optimal projection equations that we recently formulated in this domain as well. If the sampling rate becomes high, stating and solving the problem in the delta domain becomes necessary because the conventional discrete-time problem formulation and solution become ill-conditioned. In this article, by means of several numerical examples and compensator implementations, we demonstrate this phenomenon. To compute and quantify the improved performance when the sampling rate becomes high, a new delta-domain algorithm is developed. This algorithm computes the performance of arbitrary digital compensators for linear systems with white stochastic parameters. The principle application concerns nonconservative robust digital perturbation feedback control of nonlinear systems with high sampling rates.     

Receding horizon output feedback control for constrained uncertain systems using periodic invariance

In this article, we consider a receding horizon output feedback control (RHOC) method for linear discrete-time systems with polytopic model uncertainties and input constraints. First, we derive a set of estimator gains and then we obtain, on the basis of the periodic invariance, a series of state feedback gains stabilising the augmented output feedback system with these estimator gains. These procedures are formulated as linear matrix inequalities. An RHOC strategy is proposed based on these state feedback and state estimator gains in conjunction with their corresponding periodically invariant sets. The proposed RHOC strategy enhances the performance in comparison with the case in which static periodic gains are used, and increases the size of the stabilisable region by introducing a degree of freedom to steer the augmented state into periodically invariant sets.