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Convex Analysisの二,三の進展について

Computational geometry

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.

Predictive Control for Linear and Hybrid Systems

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].

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

Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult-to-access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.

Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: A survey

Solutions to constrained linear model predictive control problems can be precomputed off-line in an explicit form as a piecewise linear state feedback on a polyhedral partition of the state-space, avoiding real-time optimization. We suggest an algorithm that can determine an approximate explicit piecewise linear state feedback by imposing an orthogonal search tree structure on the partition. This leads to a real-time computational complexity that is logarithmic in the number of regions in the partition, and the algorithm yields guarantees on the suboptimality, asymptotic stability and constraint fulfillment.

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Approximate explicit constrained linear model predictive control via orthogonal search tree

https://folk.ntnu.no/torarnj/Paper-Combustion_7.pdf

Explicit stochastic predictive control of combustion plants based on Gaussian process models

It has recently been shown that the feedback solution to linear and quadratic constrained Model Predictive Control (MPC) problems has an explicit representation as a piecewise linear (PWL) state feedback. For nonlinear MPC the prospects of explicit solutions are even higher than for linear MPC, since the benefits of computational efficiency and verifiability are even more important. Preliminary studies on approximate explicit PWL solutions of convex nonlinear MPC problems, based on multi-parametric Nonlinear Programming (mp-NLP) ideas show that sub-optimal PWL controllers of practical complexity can indeed be computed off-line. However, for non-convex problems there is a need to investigate practical computational methods that not necessarily lead to guaranteed properties, but when combined with verification and analysis methods will give a practical tool for development and implementation of explicit NMPC. The present paper focuses on the development of such methods. As a case study, the application of the developed approaches to compressor surge control is considered.

Computational Aspects of Approximate Explicit Nonlinear Model Predictive Control

Multi-parametric Programming.- Nonlinear Model Predictive Control.- Explicit NMPC Using mp-QP Approximations of mp-NLP.- Explicit NMPC via Approximate mp-NLP.- Explicit MPC of Constrained Nonlinear Systems with Quantized Inputs.- Explicit Min-Max MPC of Constrained Nonlinear Systems with Bounded Uncertainties.- Explicit Stochastic NMPC.- Explicit NMPC Based on Neural Network Models.- Semi-Explicit Distributed NMPC.

Explicit Nonlinear Model Predictive Control: Theory and Applications

In this paper, a distributed linear MPC approach to solve the trajectory planning problem for rotary-wing UAVs is proposed, where the objective of the UAV system is to form a communication network to multiple targets with given radio communication capacities. The approach explicitly incorporates constraints on radio communication path losses, computed by using SPLAT! that is able to take into account terrain models and antenna locations. In order to enhance the online optimization, at each time sample the terrain below each UAV and the communication path losses are approximated with linear functions of the spatial coordinates. This leads to linear MPC sub-problems, which are solved by using convex quadratic programming. An algorithm for automatic initialization and optimal reconfiguration of the communication topology in case of failures or severe radio path loss due to e.g. channel fading, is proposed. The communication network that is provided by the UAVs is considered to be a payload communication capacity that is normally independent of the command and control datalink used to control the UAVs. The performance of the distributed linear MPC trajectory planning and the reconfiguration algorithm is studied on two simulation cases with four UAVs and two targets.

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Alexandra Grancharova

Papers

Approximate explicit constrained linear model predictive control via orthogonal search tree

Explicit stochastic predictive control of combustion plants based on Gaussian process models

Computational Aspects of Approximate Explicit Nonlinear Model Predictive Control

Explicit Nonlinear Model Predictive Control: Theory and Applications

UAVs Trajectory Planning by Distributed MPC under Radio Communication Path Loss Constraints