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6th IFAC Conference on Maneuvering and Control of Marine Craft

作者： Johansen, Tor A. Fugseth, Thomas P. Tondel, Petter Fossen, Thor I. Norwegian Univ Sci & Technol Dept Engn Cybernet NO-7491 Trondheim Norway

A propeller with a rudder can produce a thrust vector within a range of directions and magnitudes in the horizontal plane for low-speed maneuvering and dynamic positioning. The set of attainable thrust vectors is non-convex because significant lift can be produced by the rudder only with forward thrust. It is suggested to decompose the attainable thrust region into a finite union of convex polyhedral sets and a mixed-integer-like convex quadratic programming formulation of the optimal control allocation problem for marine vessels with any number of rudders as well as thrusters and other propulsion devices is derived. Actuator rate and position constraints are explicitly taken into account. Using multi-parametric quadratic programming software, an explicit piecewise linear representation of the least-squares optimal control allocation law is pre-computed. It can therefore be implemented with low computational complexity and high software reliability without the use of real-time optimization. The method is illustrated using a scale model ship in a basin. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： ship control multi-parametric programming disjunctive programming quadratic programming constrained control control allocation

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multilevel multi-leader multiple-follower games with nonseparable objectives and shared constraints

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COMPUTATIONAL MANAGEMENT SCIENCE 2021年第4期18卷 455-475页

作者： Zewde, Addis Belete Kassa, Semu Mitiku Addis Ababa Univ Dept Math Addis Ababa Ethiopia Botswana Int Univ Sci & Technol Dept Math & Stat Sci P Bag 16 Palapye Botswana

multi-leader multi-follower (MLMF) games are hierarchical games in which a collection of players in the upper-level, called leaders, compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the players in the lower-level, called followers. MLMF games serve as an important model in game theory to address compromises among multiple interacting decision units within a hierarchical system where multiple decision makers are involved at each level of the hierarchy. Such problems arise in a variety of contexts in economics, engineering, operations research and other fields and are of great importance in strategic decision making. In this paper, MLMF games with multiple hierarchical levels are considered. A reformulation of some class of multilevel-MLMF games into multilevel single-leader single-follower games is proposed, and equivalence between the original problem and the reformulated one is established. Using this equivalent reformulation, a solution procedure is proposed for such games. The proposed solution approach can effectively solve some class of multilevel-MLMF games whose objective functions at each level have non-separable terms where the shared constraints at each level are polyhedral. Our results improve previous works of Kulkarni and Shanbhag (IEEE Trans Autom Control 60(12):3379-3384, 2015) and that of Kassa and Kassa (J Glob Optim 68(4):729-747, 2017).

关键词： multilevel multi-leader multi-follower game multilevel programming multi-parametric programming Equivalent reformulation Solution Method

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Robust multi-parametric Control of Continuous-Time Linear Dynamic Systems

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IFAC-PapersOnLine 2017年第1期50卷 4660-4665页

作者： Sun M. Villanueva M.E. Pistikopoulos E.N. Chachuat B. Centre for Process Systems Engineering Department of Chemical Engineering Imperial College London London SW7 2AZ United Kingdom Artie McFerrin Department of Chemical Engineering Texas A&M University College StationTX 77843 United States

We extend a recent methodology called multi-parametric NCO-tracking for the design of parametric controllers for continuous-time linear dynamic systems in the presence of uncertainty The approach involves backing-off the path and terminal state constraints based on a worst-case uncertainty propagation determined using either interval analysis or ellipsoidal calculus. We address the case of additive uncertainty and we discuss approaches to handling multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservatism. These developments are illustrated with the case study of a fluidized catalytic cracking (FCC) unit operated in partial combustion mode. © 2017

关键词： Constrained linear-quadratic regulation multi-parametric NCO-tracking multi-parametric programming Robust model predictive control

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Optimal controllers for hybrid systems: Stability and piecewise linear explicit form

Optimal controllers for hybrid systems: Stability and piecew...

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39th IEEE Conference on Decision and Control

作者： Bemporad, A Borrelli, F Morari, M ETH Zentrum Automat Control Lab CH-8092 Zurich Switzerland

ISBN: (纸本)0780366387

In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closed-loop stability. Hybrid systems are modeled in discrete-time within the mixed logical dynamical (MLD) framework [8], or, equivalently [7], as piecewise affine (PWA) systems. A stabilizing controller is obtained by designing a model predictive controller (MPC), which is based on the minimization of a weighted 1/infinity -norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixed-integer linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NP-hard problems, which may prevent their on-line solution if the sampling-time is too small for the available computation power. Rather than solving the MILP on line, in this paper we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP (mp-MILP). As the resulting control law is piecewise affine, on-line computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of the heat exchange system [16] shows the potential of the method.

关键词： hybrid systems model predictive control mixed-integer programming multi-parametric programming

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Relations between Model Predictive Control and Reinforcement Learning

Relations between Model Predictive Control and Reinforcement...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Goerges, Daniel Univ Kaiserslautern Electromobil Erwin Schrodinger Str 12 D-67663 Kaiserslautern Germany

In this paper relations between model predictive control and reinforcement learning are studied for discrete-time linear time-invariant systems with state and input constraints and a quadratic value function. The principles of model predictive control and reinforcement learning are reviewed in a tutorial manner. From model predictive control theory it is inferred that the optimal value function is piecewise quadratic on polyhedra and that the optimal policy is piecewise affine on polyhedra. Various ideas for exploiting the knowledge on the structure and the properties of the optimal value function and the optimal policy in reinforcement learning theory and practice are presented. The ideas can be used for deriving stability and feasibility criteria and for accelerating the learning process which can facilitate reinforcement learning for systems with high order, fast dynamics, and strict safety requirements. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Model predictive control multi-parametric programming reinforcement learning approximate dynamic programming actor-critic structure

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An explicit MPC for quadrotor trajectory tracking 34

An explicit MPC for quadrotor trajectory tracking

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34th Chinese Control Conference (CCC)

作者： Liu, Cunjia Lu, Hao Chen, Wen-Hua Univ Loughborough Dept Aeronaut & Automot Engn Loughborough LE11 3TU Leics England Beihang Univ Sch Instrumentat Sci & Optoelect Engn Beijing Peoples R China

ISBN: (纸本)9789881563897

This paper intends to provide an explicit solution of model predictive control (MPC) for trajectory tracking of quadrotors. This kind of MPC can be designed in a conventional way where a nonlinear optimisation problem needs to be solved online. In this paper by using the differential flatness property of the quadrotor, the reference trajectory, system outputs and inputs can be represented using Bezier curves. Thus, the formulated optimisation problem can be parameterised and converted into standard quadratic programming. The resulted quadratic programming problem can be further formulated into multiparametric quadratic programming which is then solved off-line as a piecewise affine function. The involved manipulations including the reduction of the number of optimisation variables and constraints are detailed in this paper. The performance of the proposed control scheme is demonstrated in a simulation study.

关键词： Model predictive control multi-parametric programming flight control trajectory tracking

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Some Necessary and Sufficient Conditions for Correctness of Linear Machine in Presence of Numerical Errors 21st

Some Necessary and Sufficient Conditions for Correctness of ...

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21st IFAC World Congress on Automatic Control - Meeting Societal Challenges

作者： Sharma, Aditi Bhushan, Mani Indian Inst Technol Dept Chem Engn Bombay Maharashtra India

Linear machine (LM) has been recently proposed (Airan et al., 2017) for solving the point location problem which arises in explicit model predictive control (e-MPC). LM associates a linear discriminant function with each critical region identified in the offline phase in e-MPC. The solution to the online point location problem in the LM approach then simply corresponds to the region whose discriminant function attains the largest value amongst all the discriminant functions. LM involves two steps: (i) identification of neighbouring critical regions, and (ii) finding the discriminant functions by writing constraints involving discriminant functions of neighbouring pairs of regions. Both these steps involve solving linear programming (LP) problems. Similar to any other optimization problem, the constraints of the LP are satisfied with some tolerances. Even though theoretically sound, the resulting LM may not accurately identify the critical region due to the numerical errors arising from these tolerances. In the current work, we identify some conditions which can be used as an aid by the user to judge the accuracy of LM results. In particular, we give a necessary condition for step (i) whose violation will yield incorrect misclassification for some point location problems. We also propose a sufficient condition whose satisfaction guarantees the accuracy of linear machine solution despite numerical errors which may have crept in during step (ii) of the LM design. This condition needs to be evaluated for each specified point during the point location phase. We illustrate thee ideas on the well known quadruple tank system. Copyright (C) 2020 The Authors.

关键词： point location explicit model predictive control multi-parametric programming

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Constrained model predictive control: Applications to multi-vehicle formation and an autonomous blimp

Constrained model predictive control: Applications to multi-...

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SICE-ICASE International Joint Conference

作者： Fukushima, Hiroaki Kon, Kazuyuki Matsuno, Fumtoshi Hada, Yasushi Kawabata, Kuniaki Asama, Hajime Univ Electrocommun 1-5-1 Chofugaoka Chofu Tokyo 1828585 Japan RIKEN 2-1 Hirosawa Wako Saitama 3510198 Japan Univ Tokyo Res Artifacts Ctr Engn Kashiwa Chiba 2778568 Japan

ISBN: (纸本)9788995003848

Model predictive control (MPC) is one of the few ways to handle input and output constraints explicitly. Although MPC has been widely applied to chemical process control, the effectiveness for mechanical systems with shorter time constants has not been fully investigated. The goal of this paper is to investigate the applicability of model predictive control to mechanical systems based on experimental examples of multi-vehicle formation and autonomous blimp control.

关键词： constrained system mixed integer programming multi-parametric programming

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Weak Factors Identification Method for Renewable Energy Accommodation 5

Weak Factors Identification Method for Renewable Energy Acco...

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5th Asia Conference on Power and Electrical Engineering (ACPEE)

作者： Huang, Zonghong Wen, Shiyang Yan, Zhibin Dai, Wei Ge, Pengjiang Yu, Juan State Grid Ningxia Elect Power Co Econ & Technol Res Inst Yinchuan Ningxia Peoples R China Chongqing Univ Sch Elect Engn Chongqing Peoples R China Ningxia Elect Power Co Dev Dept State Grid Yinchuan Ningxia Peoples R China

ISBN: (纸本)9781728152813

With the integration of large-scale renewable energy, the insufficiency of the regulation ability and transmission capacity of the power system leads to mass curtailment of renewable energies. To alleviate the problem of renewable energy curtailment and promote the development of renewable generation, this paper proposes a weak factor identification method to capture the critical factors restricting the operational security region of renewable generation. Based on the optimal power flow (OPF) model and the multi-parametric programming technology, the operational security region characterization method of renewable generation is proposed considering the operational constraints of the power system. Based on the operational security region, the weak factors identification method is proposed based on the active constraints obtained through extreme feasible points on the security region boundary. Using the proposed method, the weak factors including the critical transmission capacity constraints of lines and minimum output constraints of generators are identified. The effectiveness of the proposed method is demonstrated in the modified IEEE 30 bus system.

关键词： multi-parametric programming renewable generation security region weak factors identification

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Robust multi-parametric Control of Continuous-Time Linear Dynamic Systems

Robust Multi-Parametric Control of Continuous-Time Linear Dy...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Sun, Muxin Villanueva, Mario E. Pistikopoulos, Efstratios N. Chachuat, Benoit Imperial Coll London Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA

We extend a recent methodology called multi-parametric NCO-tracking for the design of parametric controllers for continuous-time linear dynamic systems in the presence of uncertainty. The approach involves backing-off the path and terminal state constraints based on a worst-case uncertainty propagation determined using either interval analysis or ellipsoidal calculus. We address the case of additive uncertainty, and we discuss approaches to handling multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservatism. These developments are illustrated with the case study of a fluidized catalytic cracking (FCC) unit operated in partial combustion mode. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Robust model predictive control Constrained linear-quadratic regulation multi-parametric programming multi-parametric NCO-tracking

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