Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints

Robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative. This paper overcomes these issues through an augmented autonomous prediction formulation, and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance, namely invariance with probability p.     

Scenario Violation in Nursing Activities: Nursing Risk Management from the Viewpoint of Chance Discovery

This paper introduces scenarios that from a time series of events under a coherent context of performing nursing risk management. First, we describe general nursing risk management procedures. Then we review our previous nursing accident or incident protection model based on abduction. This paper extends the nursing accident or incident protection model by using the concept of scenario. That is, the model introduces chronological information in knowledge presentation. Then this paper regards a set of nursing activities as a scenario and characterizes a (nursing) accident or incident as a scenario violation. The main purpose of this paper is to present nursing risk management from the viewpoint of scenario violation in the context of chance discovery.     

Maximal controllability of input constrained unstable systems by the addition of implicit constraints

The null controllable set of a system is the largest set of states that can be controlled to the origin. Control systems that have a region of attraction equal to the null controllable set are said to be maximally controllable closed-loop systems. In the case of open-loop unstable plants with amplitude constrained control it is well known that the null controllable set does not cover the entire state-space. Further the combination of input constraints and unstable system dynamics results in a set of state constraints which we call implicit constraints. It is shown that the simple inclusion of implicit constraints in a controller formulation results in a controller that achieves maximal controllability for a class of open-loop unstable systems.     

The value of side information in network flow optimization

Consider a group of agents who seek to simultaneously traverse a graph. Each edge of the graph has an associated weight (e.g., a delay), and the agents seek to minimize the cumulative weight incurred by all agents as each traverses a path of the graph. An edge’s weight is a function of the number of agents that use that edge as well as an inherent random weight. If the agents have no side information about the random component, they will (deterministically) organize themselves so as to optimize their average performance. We consider a generalization of this framework whereby the agents have access to a limited amount of shared side information about the edge weights, and we study the relationship between information quantity and performance.     

Explicit use of probabilistic distributions in linear predictive control

The guarantee of feasibility given feasibility at initial time is an issue that has been overlooked by many of the recent papers on stochastic model predictive control. Effective solutions have recently been proposed, but these carry considerable online computational load and a degree of conservativism. For the case that the elements of the random additive disturbance vector are independent, the current paper ensures that probabilistic constraints are met and that a quadratic stability condition is satisfied. A numerical example illustrates the efficacy of the proposed algorithm, which achieves tight satisfaction of constraints and thereby attains near-optimal performance.     

一种网络控制系统的随机通信逻辑设计与分析

针对网络控制系统的带宽约束问题,提出一种基于系统状态的状态依赖泊松过程决定的随机通信逻辑,并将其应用于一般结构的状态反馈网络控制系统．介绍了具有通信逻辑的网络控制系统的结构,建立了具有随机通信逻辑的网络控制系统模型．利用随机稳定性理论和带时倚强度泊松过程相关原理,进一步证明了系统保持均方渐近稳定的充分条件．最后通过仿真算例验证了结论的有效性．     

Scenario construction and reduction applied to stochastic power generation expansion planning

A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.     

Stochastic simulation-based genetic algorithm for chance constraint programming problems with continuous random variables

In this article, we present a stochastic simulation-based genetic algorithm for solving chance constraint programming problems, where the random variables involved in the parameters follow any continuous distribution. Generally, deriving the deterministic equivalent of a chance constraint is very difficult due to complicated multivariate integration and is only possible if the random variables involved in the chance constraint follow some specific distribution such as normal, uniform, exponential and lognormal distribution. In the proposed method, the stochastic model is directly used. The feasibility of the chance constraints are checked using stochastic simulation, and the genetic algorithm is used to obtain the optimal solution. A numerical example is presented to prove the efficiency of the proposed method.     

Controller design for a class of nonlinear systems with input saturation using convex optimization

In this paper, we propose a new design strategy for nonlinear systems with input saturation. The resulting nonlinear controllers are locally asymptotically stabilizing the origin. The proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state-dependent input saturation. Linear saturating state feedback controllers and soft variable-structure controllers are developed based on this system formulation. The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist. Polynomial approximation based on Legendre polynomials is used to extend the methodology to a more general class of nonlinear systems. To demonstrate the benefit of this design method, a stabilizing controller for a single link manipulator with flexible joint is developed.     

Real-time optimization under parametric uncertainty: a probability constrained approach

Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.     

Innovation support system for creative product design based on chance discovery

Under a turbulently changing and highly competitive market, discovery of a chance is always significant for many companies to launch new and creative products or services in time, fulfilling consumers demands for occupying more market share. Many available methods on market research for designing new products are more focused on the analysis process, so that product designers run short of ideas discovery. In this paper, we present a novel innovation support system (ISS) based on chance discovery with data crystallization to assist human innovation in designing new products, especially creative products. The ISS is a human-centric system to enable value cognition and follows the following process: (1) visualized scenario graph generation, (2) human value cognition, (3) value co-creation based on shared knowledge, and (4) emerging chances evaluation. The result of a case study validates the effectiveness of ISS.     

On the computational complexity and generalization properties of multi-stage and stage-wise coupled scenario programs

We discuss the computational complexity and feasibility properties of scenario sampling techniques for uncertain optimization programs. We propose an alternative way of dealing with a special class of stage-wise coupled programs and compare it with existing methods in the literature in terms of feasibility and computational complexity. We identify trade-offs between different methods depending on the problem structure and the desired probability of constraint satisfaction. To illustrate our results, an example from the area of approximate dynamic programming is considered.     

Observer matrix gain optimization for stochastic continuous time nonlinear systems

It is shown that for a class of stationary stochastic nonlinear systems (satisfying a global Lipschitz condition) the high-gain observer with a constant gain matrix may guarantee an upper bound for the averaged quadratic error of state estimation. The nonlinearity is assumed to be a priory known. The main contribution of this paper consists in designing of a numerical procedure for the optimal gain matrix minimizing this upper bound. The convergence analysis of this procedure is presented as well as an example illustrating its finite steps workability: it is shown that within a neighborhood of the optimal matrix gain the others provide lower estimation performance.     

基于终端凸集约束的新MPC 控制器

针对一类离散系统,研究了带有终端约束凸集的MPC控制问题.通过离线设计一组椭圆不变集,并将其组合成一个终端约束凸集,其中凸集参数作为在线优化变量.在线运算时,根据实际的终端状态即时地选择合适的终端不变集,从而有效地扩大了系统的可行域.分别给出了设计MPC控制器的离线和在线算法,仿真实例说明了该方法的有效性.