Integral representations of solutions for linear stochastic equations with multiplicative perturbances

We consider the problem of explicitly representing the solutions of multiplicatively perturbed stochastic equations. We represent the solution as an integral Cauchy formula whose transition matrix is random in the case of multiplicative perturbations. Similar to deterministic theory, the transition matrix can be expressed in terms of the fundamental matrix or given by a stochastic Peano series. We give equations for statistical moments of the state vector and explicit integral representations of their solutions. For computing transition matrices of equations on moments, we use some group-theoretical notions and results whose usefulness is illustrated with simple examples.     

A robust control for a linear inertial object

The idea of compulsory separation of object motions is the ground of the procedure for synthesizing a robust system with the subsequent solution of the problem of analytical design of optimal controllers for designing a controller that makes it possible to perform partial mutual compensation of these motions.     

Robust linear object control by indirect measurements

We study the problem of designing a robust surveillance system for a linear object whose input and output is subject to various external uncontrolled disturbing influences, and regulating variables cannot be measured. We offer a control algorithm that provides satisfaction of target surveillance conditions by reference signals and compensating parametric and exogenous disturbances with the necessary precision. We show numerical examples and results of computer modeling.     

Robust control of a linear object under parametric uncertainty

A robust control problem for a linear nonstationary system under condition of incomplete information about its parameters is considered. Problems of robust and d-robust stabilization are formulated, and conditions of existence of their solutions are found. To construct robust control, minimax technique is used. Conditions of equivalence of solutions to the classical control problem and to that in the minimax formulation are determined.     

Periodic and event-based impulse control for linear stochastic systems with multiplicative noise

This paper studies the performance comparison of periodic and event-based sampling for a class of linear stochastic systems with multiplicative noise, where the impulse control is adopted. By solving boundary value problems, we obtain the analytic expressions of the mean sampling time and the average state variance under the event-based sampling. It is shown that the event-based impulse control has substantially smaller average state variance than the periodic control under the same sampling frequency. Particularly, for the integrator case, the performance ratio of the two sampling methods is given explicitly. By simulation, it is demonstrated that the advantage of event-based sampling over periodic sampling is most obvious for unstable systems, followed by critical stable systems, and least obvious for stable systems.     

Optimal control of linear systems with time-delay and observation noise

The problem of controlling a linear system to minimize a quadratic cost criterion is investigated when the system output is a delayed linear combination of system states corrupted by additive observation noise. It is shown that the optimal control is generated by the cascade combination of a Kalman filter and a least mean-squared predictor. Expressions are derived for the minimum cost and for the state variances.     

Minimax control of linear stochastic systems with noise uncertainty

The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.     

Preview control for a class of linear stochastic systems with multiplicative noise

ABSTRACT

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective.     

Optimal stationary control of linear systems with control-dependent noise

Optimal stochastic control is investigated for linear systems in which the intensity of the driving noise is proportional to control input. Conditions are given under which an optimal control always exists. It is shown that the optimal control is linear in the system state. A convergent algorithm is developed for computing the optimal feedback gains.     

Optimal control of discrete-time linear fractional-order systems with multiplicative noise

A finite horizon linear quadratic (LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique, two methods are proposed for solving this problem. The first one seems to be new and uses a linear, expanded-state model of the LFS. The LQ optimal control problem reduces to a similar one for stochastic linear systems and the solution is obtained by solving Riccati equations. The second method appeals to the principle of optimality and provides an algorithm for the computation of the optimal control and cost by using directly the fractional system. As expected, in both cases, the optimal control is a linear function in the state and can be computed by a computer program. A numerical example and comparative simulations of the optimal trajectory prove the effectiveness of the two methods. Some other simulations are obtained for different values of the fractional order.     

Compensating for computational delay in digital equivalent ofcontinuous control systems

A computer-aided method to compensate for the computational delay in the digital equivalent of continuous control systems is presented. The objective is to obtain the transfer function of the digital controller so that the performance of the equivalent digital control system is as close to that of the existing continuous system as possible. This is done by matching the frequency response of the digital control system to that of the existing system with a minimum weighted mean-square error. A formula for computing the parameters of the digital controller is obtained as a result. The design method is illustrated with an example     

网络控制系统的时延在线估计与时延补偿策略研究

针对网络控制系统中的网络时延问题,引入了一种时延在线估计算法,并根据动态矩阵控制的特点,提出了一种基于分段动态矩阵控制算法的网络时延补偿策略,利用分段动态矩阵控制算法对网络控制系统中的时延信号进行预测,以补偿其在网络传输中的时延.     

Optimal linear representations of images for object recognition

Although linear representations are frequently used in image analysis, their performances are seldom optimal in specific applications. This paper proposes a stochastic gradient algorithm for finding optimal linear representations of images for use in appearance-based object recognition. Using the nearest neighbor classifier, a recognition performance function is specified and linear representations that maximize this performance are sought. For solving this optimization problem on a Grassmann manifold, a stochastic gradient algorithm utilizing intrinsic flows is introduced. Several experimental results are presented to demonstrate this algorithm.     

State-feedback control of systems with multiplicative noise via linear matrix inequalities

We consider LTI systems perturbed by parametric uncertainties, modeled as white noise disturbances. We show how to maximize, via state-feedback control, the smallest norm of the noise intensity vector producing instability in the mean square sense, using convex optimization over linear matrix inequalities. We also show how to maximize performance robustness, where performance is measured by expected output energy, with either bounded initial conditions and zero inputs (classical LQG cost), or zero initial conditions and deterministic inputs of bounded energy (a generalization of the H_∞ norm).     

The nonasymptotic confidence set for parameters of a linear control object under an arbitrary external disturbance

The problem is considered of developing the confidence sets for parameters of the transfer function of a control object (CO) on the basis of observable data. The assumptions as to disturbances (noises), affecting the CO, reduce to a minimum: noises can actually be arbitrary, but instead of them the user must have a chance of adding to the input signal a tentative disturbance independent of them. The procedure of solving this problem is suggested and substantiated, which is developed in the framework of the common diagram “leave-out sign-dominant correlation regions” (LSCR), actively progressed in the modern works of Marko Campi with co-authors, and using the approach, earlier suggested by the author, to the CO reparametrization. The procedure returns the confidence region, which for the finite set of observations with the probability selected by the user contains the parameters of the true transfer function.     

Filtering for discrete-time linear noise delay systems

Optimal state estimation problem for discrete-time systems with delays in noise sequence is investigated. Predictor similar to the traditional Kalman ones is derived based on projection formula in Hilbert space. Filter and fixed-lag smoother are obtained at the same time. The estimators are presented by solving two coupled Riccati-type difference equations. One example shows the effectiveness of the proposed approach.     

Suboptimal stochastic linear feedback control of linear systems with state- and control-dependent noise: The incomplete information case

The stochastic regulation problem for linear systems with state- and control-dependent noise and a noisy linear output equation is considered. The optimal quadratic cost output-feedback control law in a class of linear controllers is found. This problem was first addressed in the early 1970s and solved, in the complete information case, by Wonham. In this paper we give the solution of the problem in the incomplete information case, that is, for a linear output equation corrupted by Gaussian noise. Moreover, a different method is used here, giving the solution in a more direct way even in the complete information case.     

基于多任务混合噪声分布模型表示的视频跟踪

视觉跟踪中,目标信息是不确定的非线性变化过程。随时间和空间而变化的复杂动态数据中学习出较为精确的目标模板并用它来线性表示候选样本外观模型,从而使跟踪器较好地适应跟踪作业中内在或外在因素所引起的目标外观变化是视觉目标跟踪研究的重点。提出一种新颖的多任务混合噪声分布模型表示的视频跟踪算法,将候选样本外观模型假设为由一组目标模板和最小重构误差组成的多任务线性回归问题。利用经典的增量主成分分析法从高维数据中学习出一组低维子空间基向量（模板正样本）,并在线实时采样一些特殊的负样本加以扩充目标模板,再利用扩充后的新模板和独立同分布的高斯-拉普拉斯混合噪声来线性拟合当前时刻的候选目标外观模型,最后计算候选样本和真实目标之间的最大似然度,从而准确捕捉当前时刻的真实目标。在一些公认测试视频上的实验结果表明,该算法将能够在线学习较为精准的目标模板并定期更新目标在不同状态时的特殊信息,使得跟踪器始终保持最佳的状态,从而良好地适应不断发生变化的视觉信息（姿态、光照、遮挡、尺度、背景扰乱及运动模糊等）,表现出更好的鲁棒性能。     

Tracking control for an object in pushing operation

In this paper, we consider the problem of making a manipulator push an object on a flat floor with a point of contact to a desired position. A manipulator control method for the object to follow a planned trajectory is proposed. First, using the given distribution of frictional forces between the object and the floor, we find a particular point, named pseudo center, on which the motion of the pushed object can be approximated by the motion of a wheeled mobile robot on its center. Then, a control rule for the pushing operation is derived by applying a tracking control rule for a nonholonomic mobile robot at the pseudo center. This method makes it possible for the robot to perform the tracking control in the pushing operation. A simulation result shows the effectiveness of the proposed method. Finally, we present an approach for using a mobile manipulator to realize the pushing operation. Experimental verification of the proposed method was performed and the result is described. ©1997 John Wiley & Sons, Inc.     

Optimal control of a linear system subject to partially specified input noise

One of the most basic problems in control theory is that of controlling a discrete‐time linear system subject to uncertain noise with the objective of minimizing the expectation of a quadratic cost. If one assumes the noise to be white, then solving this problem is relatively straightforward. However, white noise is arguably unrealistic: noise is not necessarily independent, and one does not always precisely know its expectation. We first recall the optimal control policy without assuming independence and show that, in this case, computing the optimal control inputs becomes infeasible. In the next step, we assume only the knowledge of lower and upper bounds on the conditional expectation of the noise and prove that this approach leads to tight lower and upper bounds on the optimal control inputs. The analytical expressions that determine these bounds are strikingly similar to the usual expressions for the case of white noise.