Robust LQR design for systems with probabilistic uncertainty

In this paper, we consider the design of robust quadratic regulators for linear systems with probabilistic uncertainty in system parameters. The synthesis algorithms are presented in a convex optimization framework, which optimize with respect to an integral cost. The optimization problem is formulated as a lower‐bound maximization problem and developed in the polynomial chaos framework. Two approaches are considered here. In the first approach, an exact optimization problem is formulated in the infinite‐dimensional space, which is solved approximately using polynomial‐chaos expansions. In the second approach, an approximate problem is formulated using a reduced‐order model and solved exactly. The robustness of the controllers from these two approaches are compared using a realistic flight control problem based on an F16 aircraft model. Linear and nonlinear simulations reveal that the first approach results in a more robust controller.     

Robust stabilisation of time-varying delay systems with probabilistic uncertainties

For robust stabilisation of time-varying delay systems, only sufficient conditions are available to date. A natural question is as follows: if the existing sufficient conditions are not satisfied, and hence no controllers can be found, what can one do to improve the stability performance of time-varying delay systems? This question is addressed in this paper when there is a probabilistic structure on the parameter uncertainty set. A randomised algorithm is proposed to design a state-feedback controller, which stabilises the system over the uncertainty domain in a probabilistic sense. The capability of the designed controller is quantified by the probability of stability of the resulting closed-loop system. The accuracy of the solution obtained from the randomised algorithm is also analysed. Finally, numerical examples are used to illustrate the effectiveness and advantages of the developed controller design approach.     

概率规划的研究与发展

概率规划是智能规划研究的一个重要方面, 首先给出概率规划领域定义语言, 并介绍其语法及语义, 随后重点介绍了求解概率规划的各种方法, 如动态规划、启发式动态规划和基于规划图的方法等, 并分析了各种方法的特点. 最后对国际概率规划比赛进行了介绍.     

Visibility-based probabilistic roadmaps for motion planning

This paper presents a variant of probabilistic roadmap methods (PRM) that recently appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps, called visibility roadmaps. Our algorithm integrates an original termination condition related to the volume of the free space covered by the roadmap. The planner has been implemented within a software platform allowing us to address a large class of mechanical systems. Experiments show the efficiency of the approach, in particular for capturing narrow passages of collision-free configuration spaces.     

Computation of a multi-objective production planning model with probabilistic constraints

In this paper, a multi-objective production planning model has been presented for a captive plant. The model includes multi-products, multi-plants, and multi-objective with some probabilistic constraints. The probabilistic constraints have been transformed into deterministic constraints assuming the parameters as independent normal random variables. The deterministic problem has been computed with two different methods, namely weighting method and fuzzy programming method. Finally, the integral solution obtained by these two methods have been compared.     

Narrow passage sampling for probabilistic roadmap planning

Probabilistic roadmap (PRM) planners have been successful in path planning of robots with many degrees of freedom, but sampling narrow passages in a robot's configuration space remains a challenge for PRM planners. This paper presents a hybrid sampling strategy in the PRM framework for finding paths through narrow passages. A key ingredient of the new strategy is the bridge test, which reduces sample density in many unimportant parts of a configuration space, resulting in increased sample density in narrow passages. The bridge test can be implemented efficiently in high-dimensional configuration spaces using only simple tests of local geometry. The strengths of the bridge test and uniform sampling complement each other naturally. The two sampling strategies are combined to construct the hybrid sampling strategy for our planner. We implemented the planner and tested it on rigid and articulated robots in 2-D and 3-D environments. Experiments show that the hybrid sampling strategy enables relatively small roadmaps to reliably capture the connectivity of configuration spaces with difficult narrow passages.     

Robust probabilistic PCA with missing data and contribution analysis for outlier detection

Principal component analysis (PCA) is a widely adopted multivariate data analysis technique, with interpretation being established on the basis of both classical linear projection and a probability model (i.e. probabilistic PCA (PPCA)). Recently robust PPCA models, by using the multivariate t-distribution, have been proposed to consider the situation where there may be outliers within the data set. This paper presents an overview of the robust PPCA technique, and further discusses the issue of missing data. An expectation-maximization (EM) algorithm is presented for the maximum likelihood estimation of the model parameters in the presence of missing data. When applying robust PPCA for outlier detection, a contribution analysis method is proposed to identify which variables contribute the most to the occurrence of outliers, providing valuable information regarding the source of outlying data. The proposed technique is demonstrated on numerical examples, and the application to outlier detection and diagnosis in an industrial fermentation process.     

State agnostic planning graphs: deterministic,non-deterministic,and probabilistic planning

Planning graphs have been shown to be a rich source of heuristic information for many kinds of planners. In many cases, planners must compute a planning graph for each element of a set of states, and the naive technique enumerates the graphs individually. This is equivalent to solving a multiple-source shortest path problem by iterating a single-source algorithm over each source.We introduce a data-structure, the state agnostic planning graph, that directly solves the multiple-source problem for the relaxation introduced by planning graphs. The technique can also be characterized as exploiting the overlap present in sets of planning graphs. For the purpose of exposition, we first present the technique in deterministic (classical) planning to capture a set of planning graphs used in forward chaining search. A more prominent application of this technique is in conformant and conditional planning (i.e., search in belief state space), where each search node utilizes a set of planning graphs; an optimization to exploit state overlap between belief states collapses the set of sets of planning graphs to a single set. We describe another extension in conformant probabilistic planning that reuses planning graph samples of probabilistic action outcomes across search nodes to otherwise curb the inherent prediction cost associated with handling probabilistic actions. Finally, we show how to extract a state agnostic relaxed plan that implicitly solves the relaxed planning problem in each of the planning graphs represented by the state agnostic planning graph and reduces each heuristic evaluation to counting the relevant actions in the state agnostic relaxed plan. Our experimental evaluation (using many existing International Planning Competition problems from classical and non-deterministic conformant tracks) quantifies each of these performance boosts, and demonstrates that heuristic belief state space progression planning using our technique is competitive with the state of the art.     

Robust design optimization of electro-thermal microactuator using probabilistic methods

Micromachining of microelectromechanical systems which is similar to other fabrication processes has inherent variation that leads to uncertain dimensional and material properties. Methods for optimization under uncertainty analysis can be used to reduce microdevice sensitivity to these uncertainties in order to create a more robust design, thereby increasing reliability and yield. In this paper, approaches for uncertainty and sensitivity analysis, and robust optimization of an electro-thermal microactuator are applied to take into account the influence of dimensional and material property uncertainties on microactuator tip deflection. These uncertainties include variation of thickness, length and width of cold and hot arms, gap, Young modulus and thermal expansion coefficient. A simple and efficient uncertainty analysis method is performed by creating second-order metamodel through Box-Behnken design and Monte Carlo simulation. Also, the influence of uncertainties has been examined using direct Monte Carlo Simulation method. The results show that the standard deviations of tip deflection generated by these uncertainty analysis methods are very close to each other. Simulation results of tip deflection have been validated by a comparison with experimental results in literature. The analysis is performed at multiple input voltages to estimate uncertainty bands around the deflection curve. Experimental data fall within 95 % confidence boundary obtained by simulation results. Also, the sensitivity analysis results demonstrate that microactuator performance has been affected more by thermal expansion coefficient and microactuator gap uncertainties. Finally, approaches for robust optimization to achieve the optimal designs for microactuator are used. The proposed robust microactuators are less sensitive to uncertainties. For this goal, two methods including Genetic Algorithm and Non-dominated Sorting Genetic Algorithm are employed to find the robust designs for microactuator.     

Robust Pareto active suspension design for vehicle vibration model with probabilistic uncertain parameters

Using the robust design of a vehicle vibration model considering uncertainties can elaborately show the effects of those unsure values on the performance of such a model. In this paper, probabilistic metrics, instead of deterministic metrics, are used for a robust Pareto multi-objective optimum design of five-degree of freedom vehicle vibration model having parameters with probabilistic uncertainties. In order to achieve an optimum robust design against probabilistic uncertainties existing in reality, a multi-objective uniform-diversity genetic algorithm (MUGA) in conjunction with Monte Carlo simulation is used for Pareto optimum robust design of a vehicle vibration model with ten conflicting objective functions. The robustness of the design obtained using such a probabilistic approach is shown and compared with that of the design obtained using deterministic approach.     

Robust planning of airport platform buses

Most airports have two types of gates: gates with an air bridge to the terminal and remote stands. For flights at a remote stand, passengers are transported to and from the aircraft by platform buses. In this paper we investigate the problem of planning platform buses as it appears at Amsterdam Airport Schiphol. We focus on robust planning, i.e. we want to avoid that the bus planning is affected by flight delays and in this way invokes delays in other flights and ground-handling processes. We present a column generation algorithm for planning of platform buses that maximizes robustness. We also present a discrete-event simulation model to compare our algorithm to a first-come-first-served heuristic as is used in current practice. Our computational results with real-life data indicate that our algorithm significantly reduces the number of replanning steps and special recovery measures during the day of operation.     

Robust reliable control for systems with random actuator fault and probabilistic nonlinearity with new characters

In this study, the reliable control for time‐varying systems with random actuator faults and probabilistic nonlinearities is investigated. The system under consideration has the following main features: (1) nonlinearities with new characters. The probability information of nonlinearities belonging to different varying bounds is used; (2) its multi‐actuators are subject to various possible faults/failures, and failure rates can vary in some measure; and (3) there are uncertainties in the plant model parameters. Covering these features, a comprehensive model is developed for uncertain time‐varying delay systems. By employing the Lyapunov functional method, free‐weighting matrix method, and the linear matrix inequality technique, we can obtain several delay‐distribution‐dependent sufficient conditions to ensure the exponentially mean square stability of the system. Those conditions are characterized in terms of linear matrix inequalities, and the reliable controller feedback gain can be solved by the standard numerical software. A simulation example is presented to show the effectiveness and applicability of the results. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

基于改进概率地图的无人机实时避障研究

基于空间点采样的概率地图方法能够很好地表示出自由空间的连通性,该方法已在路径规划领域得到了成功的应用。但是,由于在由已得到的采样点基础上构造连通图时,需要检查图的边是否与障碍物发生碰撞,即进行相交检验,限制了概率地图的构造速度,难以满足在实际应用中的实时性要求。针对无人机路径规划问题,以等高线地图作为任务空间,提出了一种新的采样模型,在该模型框架下,依据适当的规则构造临近点集,便可以避免相交检验,提高了路径规划速度。     

Robust Kalman filtering for uncertain discrete-time systems with probabilistic parameters bounded within a polytope

We consider the problem of finite horizon discrete-time Kalman filtering for systems with parametric uncertainties. Specifically, we consider unknown but deterministic uncertainties where the uncertain parameters are assumed to lie in a convex polyhedron with uniform probability density. The condition and a procedure for the construction of a suboptimal filter that minimizes an expected error covariance over-bound are derived.     

Sequential Monte Carlo in reachability heuristics for probabilistic planning

Some of the current best conformant probabilistic planners focus on finding a fixed length plan with maximal probability. While these approaches can find optimal solutions, they often do not scale for large problems or plan lengths. As has been shown in classical planning, heuristic search outperforms bounded length search (especially when an appropriate plan length is not given a priori). The problem with applying heuristic search in probabilistic planning is that effective heuristics are as yet lacking.In this work, we apply heuristic search to conformant probabilistic planning by adapting planning graph heuristics developed for non-deterministic planning. We evaluate a straight-forward application of these planning graph techniques, which amounts to exactly computing a distribution over many relaxed planning graphs (one planning graph for each joint outcome of uncertain actions at each time step). Computing this distribution is costly, so we apply Sequential Monte Carlo (SMC) to approximate it. One important issue that we explore in this work is how to automatically determine the number of samples required for effective heuristic computation. We empirically demonstrate on several domains how our efficient, but sometimes suboptimal, approach enables our planner to solve much larger problems than an existing optimal bounded length probabilistic planner and still find reasonable quality solutions.     

Robust DEA efficiency scores: A probabilistic/combinatorial approach

In this paper we propose robust efficiency scores for the scenario in which the specification of the inputs/outputs to be included in the DEA model is modelled with a probability distribution. This probabilistic approach allows us to obtain three different robust efficiency scores: the Conditional Expected Score, the Unconditional Expected Score and the Expected score under the assumption of Maximum Entropy principle. The calculation of the three efficiency scores involves the resolution of an exponential number of linear problems. The algorithm presented in this paper allows to solve over 200 millions of linear problems in an affordable time when considering up 20 inputs/outputs and 200 DMUs. The approach proposed is illustrated with an application to the assessment of professional tennis players.     

Robust network planning in nonuniform traffic scenarios

Robustness to the environmental variations is an important feature of any reliable communication network. This paper reports on a network theory approach to the design of such networks where the environmental changes are traffic fluctuations, topology modifications, and changes in the source of external traffic. Motivated by the definition of betweenness centrality in network science, we introduce the notion of traffic-aware betweenness (TAB) for data networks, where usually an explicit (or implicit) traffic matrix governs the distribution of external traffic into the network. We use the average normalized traffic-aware betweenness, which is referred to as traffic-aware network criticality (TANC), as our main metric to quantify the robustness of a network. We show that TANC is directly related to some important network performance metrics, such as average network utilization and average network cost. We prove that TANC is a linear function of end-to-end effective resistances of the graph. As a result, TANC is a convex function of link weights and can be minimized using convex optimization techniques. We use semi-definite programming method to study the properties of the optimization problem and derive useful results to be employed for robust network planning purposes.