基于伪谱法的自由采样实时最优反馈控制及应用

利用高斯伪谱法收敛速率快、精度高的特点,基于通用伪谱优化软件包在线求解非线性系统的最优控制问题.将伪谱反馈控制理论与非线性最优控制理论结合起来,给出了一种自由采样实时最优反馈控制算法,该算法通过连续在线生成开环最优控制的方式提供闭环反馈.考虑计算误差、模型参数不确定性和干扰的作用,假定系统状态方程右侧的非线性向量函数关于状态、控制和系统参数是Lipschitz连续的,利用Bellman最优性原理对闭环控制系统的有界稳定性进行了分析和理论证明.最后,以高超声速再入飞行器为应用对象,研究了其再入制导问题,仿真结果验证了该算法的可行性和有效性.     

Optimal Deterministic and Stochastic Macroeconomic Policies for Slovenia: An Application of the OPTCON Algorithm

This paper reports about applications of optimal control theory to the analysis of macroeconomic policies for Slovenia during its way into the Euro Area. For this purpose, the model SLOPOL4, a macroeconometric model for Slovenia, is used. Optimal policies are calculated using the OPTCON algorithm, an algorithm for determining (approximately) optimal solutions to deterministic and stochastic control problems. We determine optimal exchange rate and fiscal policies for Slovenia as solutions to optimum control problems with a quadratic objective function and the model SLOPOL4 as constraint. Several optimization experiments under different assumptions about the exchange rate regime are carried out. The sensitivity of the results with respect to several assumptions is investigated; in particular, the reaction of the optimal paths on varying the stochastic character of the model parameters is examined. If the stochastic nature of more parameters is taken into consideration, the resulting policies are closer to the deterministic solution than with only a few stochastic parameters.     

Optimal fixed rules and simple feedback laws in the design of economic policy

The constancy parameter of fixed-rate-of-growth rules and the parameters of simple feedback laws, linking policy instruments to specified endogenous variables, can be determined optimally within a policy optimization framework. An approach for doing this is described along with results using the National Institute of Economic and Social Research nonlinear econometric model of the U.K. The framework is also extended to rational expectations. The effect of an optimal fixed-rate-of-growth monetarist rule is illustrated in an example incorporating the credible announcement of monetary targets. This is evaluated against a strategy derived without the assumption of announcement effects. The use of indicators is also discussed to provide an empirical example for parametrized optimal feedback laws. Exchange rate indicators are derived and compared with open-loop policies. Robust control extensions are suggested and Monte Carlo simulations are used to test the behaviour of the policies in the presence of stochastic disturbances.     

基于保辛算法的绳系卫星系统闭环反馈控制问题求解

应用非线性系统滚动时域控制的保辛算法求解绳系卫星系统子星释放和回收过程的闭环反馈控制问题.通过第二类Lagrange方程推导出二体绳系卫星系统的动力学方程;通过拟线性化方法将绳系卫星系统闭环反馈控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代求解;通过保辛算法将线性非齐次Hamilton两端边值问题转化为线性方程组的求解;通过递进更新时间步的状态变量和控制变量,完成绳系卫星系统的闭环反馈控制.数值仿真表明:相对于Legendre伪谱方法,用保辛算法求解绳系卫星系统的闭环反馈控制问题的计算速度和收敛速度较快.绳系卫星系统的开环控制和闭环反馈控制问题数值仿真结果表明:在绳系卫星的初始状态存在偏差的情况下,使用开环控制会导致系统在终端无法达到稳定状态,而使用闭环反馈控制则能在一段时间内抵消初始状态向量偏差对系统产生的影响,最终达到稳定状态.     

Design of Optimal Feedbacks in the Class of Inertial Controls

Two optimal control problems in the class of inertial controls (continuous controls of bounded values and rates) are investigated: the first is the optimal excitation of dynamic systems and the related design of attainability sets and the second is a linear optimal control problem with terminal constraints. They are solved by a dynamic adaptive linear programming method. First, open-loop solutions are constructed and then an algorithm for the optimal controller for the linear optimal control problem is designed, which in real time generates current optimal feedback. Examples are given to illustrate the results.     

Least-squares identification for ARMAX models without the positivereal condition

Recursive identification problems of linear stochastic feedback control systems described by ARMAX models are studied without imposing the strictly positive real condition on the noise model. An increasing lag least squares is used in the first step to estimate the noise process, while the parameter estimate is formed in the second step by an extended least squares. In the algorithm, there is an increase in computational cost in comparison to traditional algorithms. However the results of this note do not need any a priori information or conditions on the noise model except that of stability, and they are applicable to the identification of general feedback control systems     

Stochastic suboptimal pointwise regulation control for linear discrete-time distributed parameter systems

Based on an examination of the concept of open-loop-optimal feedback control of Dreyfus (1964), a suboptimal stochastic pointwise regulation control scheme for linear distributed parameter systems with unknown plant and measurement noise covariances is presented. By enforcing the term coupling the control and estimation costs in the open-loop cost functional to zero, the suboptimal control scheme retains the controller-estimator in a cascade structure. An on-line algorithm is presented to adaptively select the filter parametrized by a scalar gain so as to minimize the equivalent cost functional derived from the open-loop case. Bounds on the filter gain that ensure filter tracking of the state are obtained. The control scheme is efficient and reasonably simple to use. A numerical example is presented.     

Optimal ensemble control of stochastic time-varying linear systems

We consider the optimal guidance of an ensemble of independent, structurally identical, finite-dimensional stochastic linear systems with variation in system parameters between initial and target states of interest by applying a common control function without the use of feedback. Our exploration of such ensemble control systems is motivated by practical control design problems in which variation in system parameters and stochastic effects must be compensated for when state feedback is unavailable, such as in pulse design for nuclear magnetic resonance spectroscopy and imaging. In this paper, we extend the notion of ensemble control to stochastic linear systems with additive noise and jumps, which we model using white Gaussian noise and Poisson counters, respectively, and investigate the optimal steering problem. In our main result, we prove that the minimum norm solution to a Fredholm integral equation of the first kind provides the optimal control that simultaneously minimizes the mean square error (MSE) and the error in the mean of the terminal state. The optimal controls are generated numerically for several example ensemble control problems, and Monte Carlo simulations are used to illustrate their performance. This work has immediate applications to the control of dynamical systems with parameter dispersion or uncertainty that are subject to additive noise, which are of interest in quantum control, neuroscience, and sensorless robotic manipulation.     

Stochastic observability in network state estimation and control

A hidden Markov model for the traffic congestion control problem in transmission control protocol (TCP) networks is developed, and the question of observability of this system is posed. Of specific interest are the dependence of observability on the congestion control law and the interaction between observability ideas and the effectiveness of feedback control. Analysis proceeds with a survey of observability concepts and an extension of some available definitions for linear and nonlinear stochastic systems. The key idea is to link the improvement of state estimator performance to the conditioning on the output data sequence. The observability development proceeds from linear deterministic systems to linear Gaussian systems, nonlinear systems, etc., with backwards compatibility to deterministic ideas. The principal concepts relate to the entropy decrease of scalar functions of the state, which in the linear case are describable in terms of covariance matrices. A feature of nonlinear systems is that the estimator properties may affect the closed-loop control performance. Results are derived linking stochastic reconstructibility to strict improvement of the optimal closed-loop control performance over open-loop control for the hidden Markov model. The entropy provides a means to quantify and thus order simulation results for a simplified TCP network. Motivated by the link between feedback control and reconstructibility, the entropy formulation is also explored as a means to discriminate between different control strategies for improving estimator performance. This approach has connections to dual-adaptive control ideas, where the control has the simultaneous and opposing goals of regulating the system and of exciting the system to prevent estimator divergence.     

Adaptive receding horizon control for constrained MIMO systems

An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented.     

Stochastic stabilization of hybrid differential equations

This paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system. New methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided. These results are then used to examine stochastic stabilization by stochastic feedback controls. Two types of structure controls, namely state feedback and output injection, are discussed. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. A couple of examples and computer simulations are worked out to illustrate our theory.     

Global parameter optimization for biokinetic modeling of simple batch experiments

Environmental process modeling is challenged by the lack of high quality data, stochastic variations, and nonlinear behavior. Conventionally, parameter optimization is based on stochastic sampling techniques to deal with the nonlinear behavior of the proposed models. Despite widespread use, such tools cannot guarantee globally optimal parameter estimates. It can be especially difficult in practice to differentiate between lack of algorithm convergence, convergence to a non-global local optimum, and model structure deficits. For this reason, we use a deterministic global optimization algorithm for kinetic model identification and demonstrate it with a model describing a typical batch experiment. A combination of interval arithmetic, reformulations, and relaxations allows globally optimal identification of all (six) model parameters. In addition, the results suggest that further improvements may be obtained by modification of the optimization problem or by proof of the hypothesized pseudo-convex nature of the problem suggested by our results.     

Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives

Intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which many important details cannot be included in the model. Owing the influence of the combination of heat coefficient, unknown discharge coefficient, and change of temperature, it was supposed that parameters of the pneumatic cylinder are random (stochastic parameters). On the other side, it has been well known that the nonlinear model can be approximated by a linear model with time‐varying parameters. Due to the aforementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. In practical conditions, in measurements, there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. In this paper, the robust recursive algorithm for output error models with time‐varying parameters is proposed. The convergence property of the proposed robust algorithm is analyzed using the methodology of an associated ordinary differential equation system. Because ad hoc selection of model orders leads to overparameterization or parsimony problem, the robust Akaike's criterion is proposed to overcome these problems. By determining the least favorable probability density for a given class of probability distribution represents a base for design of the robust version of Akaike's criterion. The behavior of the proposed robust identification algorithm is considered through intensive simulations that demonstrate the superiority of the robust algorithm in relation to the linear algorithms (derived under an assumption that the stochastic disturbance has a Gaussian distribution). The good practical values of the proposed robust algorithm to identification of the pneumatic cylinder are illustrated by experimental results. Copyright © 2016 John Wiley & Sons, Ltd.     

Real-time optimal control and observation

A survey of the results obtained by authors and their coworkers (mainly in 2000–2003) on realization of modern principles of optimal control and observations in real time was made. Optimal control problems and the problems of observation of deterministic systems, problems under the conditions of set-membership uncertainty; perfect and imperfect measurements, feedforward, feedback, and combined loop cases, inertial and inertialess controls; and special and dynamical regulators for indirect control, linear piecewise linear, and nonlinear models are considered consecutively. The presentation focuses mainly on linear models, since the optimal control of nonlinear systems is based on linear or piecewise linear approximations of the initial model. For the realization of the positional solutions of the optimal control and observation problems, fast dual methods taking into account the dynamical nature of the problems being investigated are justified. The application of the results on optimal control in real time for the solution of classical control problems (problems of regulating, stabilizing, tracking, etc.) is discussed. The presentation is accompanied by computational examples.     

Gain-scheduled control of an electrostatic levitator

A simple gain-scheduling approach to the position control of electrostatically levitated materials is presented. An electrostatic levitator is currently being constructed at the German Aerospace Center (DLR). It can be used for containerless processing of metals and nonconducting materials. Time-varying sample charges and the fact that the plant is open-loop unstable make this a difficult and challenging control problem. The nonlinear parameter-dependent system is approximated by two local linear models. Based on these models, two local linear controllers are designed. LMI-based pole region assignment is used to reduce the design procedure to the tuning of three parameters with intuitive meaning. The sample charge is estimated with a discrete-time extended Kalman filter and used as scheduling parameter. Experimental results demonstrate that gain-scheduled control achieves a significantly better performance than fixed-gain, observer-based state feedback control.     

Stochastic optimal open-loop feedback control: Approximate solution of the Hamiltonian system

Considering a dynamic control system with random model parameters and using the stochastic Hamilton approach stochastic open-loop feedback controls can be determined by solving a two-point boundary value problem (BVP) that describes the optimal state and costate trajectory. In general an analytical solution of the BVP cannot be found. This paper presents two approaches for approximate solutions, each consisting of two independent approximation stages. One stage consists of an iteration process with linearized BVPs that will terminate when the optimal trajectories are represented. These linearized BVPs are then solved by either approximation fixed-point equations (first approach) or Taylor-Expansions in the underlying stochastic model parameters (second approach). This approximation results in a deterministic linear BVP, which can be handled by solving a matrix Riccati differential equation.     

反馈非线性系统随机梯度辨识算法及其收敛性

反馈非线性受控自回归系统是由前向通道的受控自回归模型和反馈通道的静态非线性构成, 这类系统经过参数化后得到双线性参数辨识模型. 本文通过对辨识模型中双线性参数乘积项进行分解, 基于梯度搜索原理, 提 出了反馈非线性系统的随机梯度辨识算法. 为了改善随机梯度算法的收敛速度, 引入遗忘因子, 文章给出了遗忘因子随机梯度算法, 利用随机过程理论, 建立了随机梯度算法的参数估计收敛定理, 证明了算法的收敛性. 最后, 通过数值仿真验证了算法的有效性.     

Development of a stochastic optimization for multireservoir scheduling

Seasonal reservoir scheduling for multireservoir hydrothermal power systems is a practical, nonlinear, stochastic problem of high dimension. Extension of an existing deterministic algorithm to handle stochastic aspects is desirable. A linear feedback rule, but with chance constraints on lower limits only, gives some promising results. Exact solution by stochastic dynamic programming is possible only for a one-reservoir model. This result is compared to the deterministic and linear feedback solutions.     

Multistage stochastic linear differential game with decision-time constraint

In this work, we consider a class of multistage stochastic linear differential game with quadratic cost function subject to a post initial measurement decision constraint, Secure strategies, in the sense of minimax and maximin, are derived for each player by applying dynamic programming. Both of the minimax and maximin controls are shown to be of linear feedback form. It is demonstrated that both the certainty equivalence principle and the separation theorem from stochastic control theory hold. The derived algorithm, even for the multistage and stochastic nature of the problem, is of closed form and can be employed in real-time applications     

跳变双线性随机离散组合系统的保成本分散控制

研究一类跳变双线性随机离散组合系统的保成本分散控制问题．首先给出问题可解的充分条件,然后基于线性矩阵不等式方法设计保成本分散状态反馈控制律．理想的保成本分散状态反馈控制器可通过应用现有的软件,求解一组线性矩阵不等式而得到．仿真例子说明了该方法的有效性.