Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

Predictive Control for Linear and Hybrid Systems

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control

Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

Optimal Discrete Rate Adaptation for Distributed Real-Time Systems with End-to-End Tasks

Many distributed real-time systems face the challenge of dynamically maximizing system utility in response to fluctuations in system workload. We present the MultiParametric Rate Adaptation (MPRA) algorithm for discrete rate adaptation in distributed real-time systems with end-to-end tasks. The key novelty and advantage of MPRA is that it can efficiently produce optimal solutions in response to workload changes such as dynamic task arrivals. Through oline preprocessing MPRA transforms a NP-hard utility optimization problem to a set of simple linear functions in different regions expressed in term of CPU utilization changes caused by workload variations. At run time MPRA produces optimal solutions by evaluating the linear function for the current region. Analysis and simulation results show that MPRA maximizes system utility in the presence of varying workloads, while reducing the online computation complexity to polynomial time

Multi-parametric Analysis for Mixed Integer Linear Programming: An Application to Transmission Planning and Congestion Control

Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance

A FUZZY BI-LEVEL PROJECT PORTFOLIO PLANNING CONSIDERING THE DECENTRALIZED STRUCTURE OF PHARMACY HOLDINGS

Research and development (R&D) in the pharmaceutical industry requires proper and optimal planning and management because of its critical role in public health. Taking into account a decentralized decision-making structure in R&D management in pharmaceutical holding companies, this study introduces a new fuzzy bi-level multi-follower mathematical optimization model to address budget allocation and project portfolio planning. Specifically, the holding company's head office, as the leader, and the subsidiaries, as followers, make strategic and operational decisions concerning important issues such as budget allocation and portfolio selection and scheduling. Since the lower level represents multiple mixed-integer programming problems with uncooperative reference relationships between followers, solving the resulting bi-level model is challenging. Therefore, our model is based on an effective hybrid solution methodology, which converts the bi-level model, including multiple followers, into a single-level model. In order to validate the proposed model, we conducted a case study and analyzed the strategies of each actor within the conglomerate. Based on the results of experiments, it is evident that a strategy that focuses on one level of operations profoundly affects decisions at the other level

Algoritma Criss-crosss dan Branch and Bound dalam Pemrograman Linier Integer, Studi Kasus: Produksi Pangan

Dalam laporan analisis situasi pangan dan gizi tahun 2014 oleh badan ketahanan pangan dan penyuluhan Daerah Istimewa Yogyakarta terdapat 16 desa yang resiko pangan dan gisi tergolong waspada dan 26 desa yang resiko pangan dan gisi tergolong rawan, efisiensi penggunaan bahan baku pangan menjadi sangat penting peranannya. Efisiensi bahan baku bisa digunakan juga untuk mencapai keuntungan dalam industry makanan.Dalam penelitian ini masalah pangan tersebut dipandan dan diformulasikan dengan menggunakan pemrograman linier yang diselesaikan dengan model integer. Algoritma criss-crosss yang dikombinasikan dengan algoritma branch and bound diusulkan dalam penyelesaian masalah integer linier programming. Penelitian ini berfokus pada penerapan kedua algoritma tersebut dalam studi kasus produksi makanan dan pencarian kondisi batasan yang sesuai.Penelitian ini berhasil menerapkan penggabungan algoritma criss-crosss dan branch and bound. Penelitian ini mendefinisikan 4 batasan yang dapat diperhatikan untuk mengurangi pencabangan dalam pencarian nilai intege