/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Introduction to stochastic programming

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Linear And Nonlinear Programming

Model predictive control (MPC) has demonstrated exceptional success for the high-performance control of complex systems [1], [2]. The conceptual simplicity of MPC as well as its ability to effectively cope with the complex dynamics of systems with multiple inputs and outputs, input and state/output constraints, and conflicting control objectives have made it an attractive multivariable constrained control approach [1]. MPC (a.k.a. receding-horizon control) solves an open-loop constrained optimal control problem (OCP) repeatedly in a receding-horizon manner [3]. The OCP is solved over a finite sequence of control actions {u0,u1,f,uN- 1} at every sampling time instant that the current state of the system is measured. The first element of the sequence of optimal control actions is applied to the system, and the computations are then repeated at the next sampling time. Thus, MPC replaces a feedback control law p(m), which can have formidable offline computation, with the repeated solution of an open-loop OCP [2]. In fact, repeated solution of the OCP confers an "implicit" feedback action to MPC to cope with system uncertainties and disturbances. Alternatively, explicit MPC approaches circumvent the need to solve an OCP online by deriving relationships for the optimal control actions in terms of an "explicit" function of the state and reference vectors. However, explicit MPC is not typically intended to replace standard MPC but, rather, to extend its area of application [4]-[6].

/pdf/stochastic-model-predictive-control-an-overview-and-1kyy9166uh.pdf

Stochastic Model Predictive Control: An Overview and Perspectives for Future Research

https://nacto.org/wp-content/uploads/2016/02/2016_Fishman_Bikeshare-A-Review-of-Recent-Literature.pdf

Bikeshare: A Review of Recent Literature

We study the use of kinematic and dynamic vehicle models for model-based control design used in autonomous driving In particular, we analyze the statistics of the forecast error of these two models by using experimental data In addition, we study the effect of discretization on forecast error We use the results of the first part to motivate the design of a controller for an autonomous vehicle using model predictive control (MPC) and a simple kinematic bicycle model The proposed approach is less computationally expensive than existing methods which use vehicle tire models Moreover it can be implemented at low vehicle speeds where tire models become singular Experimental results show the effectiveness of the proposed approach at various speeds on windy roads

Kinematic and dynamic vehicle models for autonomous driving control design

This paper considers the efficient operation of shared mobility systems via the combination of intelligent routing decisions for staff-based vehicle redistribution and real-time price incentives for customers. The approach is applied to London's Barclays Cycle Hire scheme, which the authors have simulated based on historical data. Using model-based predictive control principles, dynamically varying rewards are computed and offered to customers carrying out journeys, based on the current and predicted state of the system. The aim is to encourage them to park bicycles at nearby underused stations, thereby reducing the expected cost of redistributing them using dedicated staff. In parallel, routing directions for redistribution staff are periodically recomputed using a model-based heuristic. It is shown that it is possible to trade off reward payouts to customers against the cost of hiring staff to redistribute bicycles, in order to minimize operating costs for a given desired service level.

Dynamic Vehicle Redistribution and Online Price Incentives in Shared Mobility Systems

The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations

Automated Driving The Role of Forecasts and Uncertainty - A Control Perspective

The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled outcomes of the uncertainty (`scenarios'). A key merit of this approach is that it neither assumes knowledge of the uncertainty set, as it is common in robust optimization, nor of its probability distribution, as it is usually required in stochastic optimization. Moreover, the scenario approach is computationally efficient as its solution is based on a deterministic optimization program that is canonically convex, even when the original chance-constrained problem is not. Recently, researchers have obtained theoretical foundations for the scenario approach, providing a direct link between the number of scenarios and bounds on the constraint violation probability. These bounds are tight in the general case of an uncertain optimization problem with a single chance constraint. However, this paper shows that these bounds can be improved in situations where the constraints have a limited `support rank', a new concept that is introduced for the first time. This property is typically found in a large number of practical applications---most importantly, if the problem originally contains multiple chance constraints (e.g. multi-stage uncertain decision problems), or if a chance constraint belongs to a special class of constraints (e.g. linear or quadratic constraints). In these cases the quality of the scenario solution is improved while the same bound on the constraint violation probability is maintained, and also the computational complexity is reduced.

Georg Schildbach

Papers

Kinematic and dynamic vehicle models for autonomous driving control design

Dynamic Vehicle Redistribution and Online Price Incentives in Shared Mobility Systems

The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations

Automated Driving The Role of Forecasts and Uncertainty - A Control Perspective

Randomized Solutions to Convex Programs with Multiple Chance Constraints