Chance-constrained model predictive control for drinking water networks

On the Assessment of Tree-Based and Chance-Constrained Predictive Control Approaches applied to Drinking Water Networks

This paper focuses on water demand forecasting for predictive control of Drinking Water Networks (DWN) in the short term by using Gaussian Process (GP). For the predictive control strategy, system states in a finite horizon are generated by a DWN model and demands are regarded as system disturbances. The goal is to provide a demand estimation within a given confidence interval. For the sake of obtaining a desired forecasting performance, the forecasting process is carried out in two parts: the expected part is forecasted by Double-Seasonal Holt-Winters (DSHW) method and the stochastic part is forecasted by GP method. The mean value of water demand is firstly estimated by DSHW while GP provides estimations within a confidence interval. GP is applied with random inputs to propagate uncertainty at each step. Results of the application of the proposed approach to a real case study based on the Barcelona DWN have shown that the general goal has been successfully reached.

This paper considers the problem of supply-demand imbalances in Mobility-on-Demand (MoD) services. These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high. To achieve this, we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing. More precisely, first travel demand is predicted using Gaussian Process Regression (GPR) which provides uncertainty bounds on the prediction. We then formulate a stochastic model predictive control (MPC) for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds. In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction, we employ a probabilistic constraining method with user-defined confidence interval, using Chance Constrained MPC (CCMPC). The benefits of the proposed method are twofold. First, travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework, allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability. Second, CCMPC can be relaxed into a Mixed-Integer-Linear-Program (MILP) and the MILP can be solved as a corresponding Linear-Program, which always admits an integral solution. Our transportation simulations show that by tuning the confidence bound on the chance constraint, close to optimal oracle performance can be achieved, with a median customer wait time reduction of 4% compared to using only the mean prediction of the GPR.

This paper proposes the application of a distributed command governor (DCG) strategy for the operational control of drinking water networks (DWN). This approach is very suitable to this kind of management problems given the large-scale and complex nature of DWNs, the relevant effect of persistent disturbances (water demands) over the network evolutions and their marginal stability feature. The performance improvement offered by DCG is compared with the consideration of two non-centralized model predictive control (MPC) approaches already proposed for the same management purposes and within the same context. The paper also discusses the effectiveness of all strategies and highlights the advantages of each approach. The Barcelona DWN is considered as the case study for the assessment analysis.

Trabajo presentado a la 3rd Conference on Control and Fault Tolerant Systems, celebrada en Barcelona (España) del 7 al 9 de septiembre de 2016.

Stochastic linear Model Predictive Control with chance constraints – A review

Recent research shows that non-convex AC OPF problem can be recast as a convex Semidefinite (SD) problem or Second Order Cone Programming (SOCP) problem. This paper presents a stochastic SOCP OPF (SSOCP-OPF) model for power systems connected to the wind farms. This is performed by reformulating the original non-convex OPF problem using more practical parameters of the power system. Finally, we obtain a convex optimization problem through some well-known approximations and an exact relaxation incorporating the stochastic nature of wind power. One of the advantage of convex SOCP problems, which are a general form of linear problems, is that they can be efficiently solved through Interior Point Methods (IPMs). The proposed OPF model takes advantage of both DC-OPF models (solution efficiency) and full AC-OPF models (solution accuracy). As an application of SSOCP-OPF model, we study the impact of wind power uncertainty on the transmission loss in the power systems. To evaluate the proposed stochastic model modified IEEE 30-bus test system is used. The optimization problem is coded in GAMS platform and solved using its embedded interior point optimizer MOSEK.

The Sharpe ratio is a measure based on the theory of mean variance, it is the measure of the performance of a portfolio when the risk can be measured through the standard deviation. This paper suggests a Sharpe-ratio portfolio solution using a second order cone programming (SOCP). We use the penalty-regularized method to represent the nonlinear portfolio problem. We present a computationally tractable way to determining the Sharpe-ratio portfolio. A Markov chain structure is employed to represent the underlying asset price process. In order to determine the optimal portfolio in Markov chains, a new hybrid optimization programming method for SOCP is proposed. The suggested method’s efficiency and efficacy are demonstrated using a numerical example.

Nonlinear Model Predictive Control often suffers from excessive computational complexity, which becomes critical when fast plants are to be controlled. This papers presents an approach to NMPC that exploits the quasi-LPV framework. For quasi-LPV systems, the scheduling variables are determined by the state variables and/or inputs. By calculating an estimate of the state variables during prediction, the prediction model can be adapted to the estimated state evolution in each step. Stability of the proposed algorithm is enforced by the offline solution of an optimization problem with Linear Matrix Inequality (LMI) constraints. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs (QP) or Second Order Cone Programs (SOCP) in each time step, which leads to computational efficiency. The algorithm is tested in simulation to highlight convergence of the prediction and stability of the closed-loop under contraints.

This paper adopts one kind of classical predictive control, namely model algorithmic control, to control the distillation process. Due to finite cognition degree for the distillation system and existence noise in the chemical industry, we present a chance constrained model predictive control algorithm to eliminate the effect of parameter pertubation and noise. In view of the linear impulse response model, we introduce set-valued optimal algorithm and orthogonal standardization method to transform the chance constrained model predictive control to a general model predictive control problem. For the determinate MPC, efficient quadratic programming exsits to solve such problem. Applying such controller to a distillation system, output constraint condition will be satisfied with a predefined probability.

In this paper, we consider chance-constrained Stochastic Model Predictive Control problems for uncertain linear systems subject to additive disturbance. A popular method for solving the associated chance-constrained optimization problem is by means of randomization, in which the chance constraints are replaced by a finite number of sampled constraints, each corresponding to a disturbance realization. Earlier approaches in this direction lead to computationally expensive problems, whose solutions are typically very conservative both in terms of cost and violation probabilities. One way of overcoming this conservatism is to use piecewise affine (PWA) policies, which offer more flexibility than conventional open-loop and affine policies. Unfortunately, the straight-forward application of randomized methods towards PWA policies will lead to computationally demanding problems, that can only be solved for problems of small sizes. To address this issue, we propose an alternative method based on a combination of randomized and robust optimization. We show that the resulting approximation can greatly reduce conservatism of the solution while exhibiting favorable scaling properties with respect to the prediction horizon.

Several types of relaxations for binary quadratic polynomial programs can be obtained using linear, second-order cone, or semidefinite techniques. In this paper, we propose a general framework to construct conic relaxations for binary quadratic polynomial programs based on polynomial programming. Using our framework, we re-derive previous relaxation schemes and provide new ones. In particular, we present three relaxations for binary quadratic polynomial programs. The first two relaxations, based on second-order cone and semidefinite programming, represent a significant improvement over previous practical relaxations for several classes of nonconvex binary quadratic polynomial problems. From a practical point of view, due to the computational cost, semidefinite-based relaxations for binary quadratic polynomial problems can be used only to solve small to midsize instances. To improve the computational efficiency for solving such problems, we propose a third relaxation based purely on second-order cone programming. Computational tests on different classes of nonconvex binary quadratic polynomial problems, including quadratic knapsack problems, show that the second-order-cone-based relaxation outperforms the semidefinite-based relaxations that are proposed in the literature in terms of computational efficiency, and it is comparable in terms of bounds.

Purpose – This paper aims to find an objects representation scheme with high precision and to compute the objects’ separation distance effectively in final analysis. Proximity queries have been used widely in robot trajectory planning, automatic assembly planning, virtual surgery and many other applications. The core of proximity query is the precise computation of (minimum) separation distance in narrow phase, and specific object representation scheme corresponds to different methods of separation distance computation. Design/methodology/approach – In this paper, a second-order cone programming (SOCP)-based (minimum) separation distance computation algorithm was proposed. It treats convex superquadrics, descriptive primitives of complex object as the study objects. The separation distance between two convex superquadrics was written as a general nonlinear programming (NLP) problem with superquadric constraints and then transformed into an SOCP problem with the method of conic formulation of superquadric constraints. Finally, a primal-dual interior point method embedded in MOSEK was used for solving the SOCP problem. Findings – The proposed algorithm achieved exact separation distance computation between convex superquadrics, with a relative error of 10-6. It is particularly suitable for proximity queries in narrow phase of static collision detection algorithms. Further, the proposed algorithm achieved continuous collision detection between rectilinear translation superquadrics. Originality/value – The proposed algorithm in narrow phase of static collision detection algorithms makes objects’ separation distance effectively computed. Proximity queries are easy and more accurate to perform in this way.

A directional constant beamwidth (DCB) beamforming algorithm is introduced, which keeps the beamwidth unchanged when the mainlobe is steered to a large range of angles. The algorithm is based on the optimization theory that minimizing the sidelobe level subjects to the minimum mean square error between the designed mainlobe under all directions and the corresponding reference mainlobe. The introduced algorithm can be written in the form of second order cone programming (SOCP) and can be solved by some certain matlab toolboxes. It is shown by simulation that the new algorithm can form the directional constant beamwidth beampattern effectively under the designed mainlobe direction from -60° to +60°.

Locating the position of a remote node on a wireless network is becoming more relevant, as we move forward in the Internet of things and in autonomous vehicles. This paper proposes a new system to implement the location of remote nodes. A new prototype Android application has been developed to collect real measurements and to study the performance of several smartphone’s sensors and location algorithms, including an innovative one, based on the second order cone programming (SOCP) relaxation. The application collects the WiFi access points information and the terminal location. An internal odometry module developed for the prototype is used when Android’s service is unavailable. This paper compares the performance of existing location estimators given in closed form, an existing SOCP one, and the new SOCP location estimator proposed, which has reduced complexity. An algorithm to merge measurements from non-identical terminals is also proposed. Cooperative and terminal stand-alone operations are compared, showing a higher performance for SOCP-based ones, that are capable of estimating the path loss exponent and the transmission power. The heterogeneous terminals were also used in the tests. Our results show that the accurate positioning of static remote entities can be achieved using a single smartphone. On the other hand, the accurate real-time positioning of the mobile terminal is provided when three or more scattered terminal nodes cooperate sharing the samples taken synchronously.