Large-scale convex optimal control problems: time decomposition, incentive coordination, and parallel algorithm

Chang, Ting-Wei; Jin, Xiao-xuan; Luh, Peter B.; Miao, Xinyuan

doi:10.1109/9.45157

Cited by 9 publications

(10 citation statements)

References 4 publications

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“…In fact, to resolve these conflicts, we consider a second level of control which takes into account the interactions and modifies, if necessary, the objective of the controller and coordinates between different subsystems (Singh et al, 1975;Singh and Titli, 1978). Several works have been presented in the literature and have been interested in the control of large-scale systems (see, e.g., Salman and Cruz, 1984;Gahutu and Looze, 1985;Munack and Thoma, 1986;Chang et al, 1990;Lin and Wonham, 1990;Tang et al, 1991;Mahmoud, 1995;Tang et al, 1995;Chen et al, 2009;Peng et al, 2009). Rekik et al (2005Rekik et al ( , 2007 have considered the determination of sub-optimal control laws of large-scale nonlinear continuous systems which can be decomposed into interconnected subsystems.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical control for discrete large-scale complex systems by intelligent controllers

Masmoudi

Rekik

Djemel

et al. 2011

IJCAT

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This paper presents a new method to approximate optimal control strategies of discrete time large-scale nonlinear systems using intelligent approaches. The idea is based on the decomposition principle of the global system into interconnected subsystems for which nonlinearities are located in the interconnection terms. Then, the mixed coordination procedure between different subsystems is formulated as a hierarchical method for the solution of large-scale optimal control problems. So, for each subsystem, local optimal feedback gains are expressed in terms of the interconnection vector. For this purpose, neural networks and fuzzy logic controllers have been constructed in order to identify these gains. A comparison with the differential dynamic programming procedure as a reference method is done. Simulation results of two numerical examples show that the proposed method yields to satisfactory performances, and the robustness of the proposed approaches has been tested.

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Section: Introductionmentioning

confidence: 99%

Hierarchical control for discrete large-scale complex systems by intelligent controllers

Masmoudi

Rekik

Djemel

et al. 2011

IJCAT

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“…Two conceptually different ways to do so when solving CFTOC problems are to apply a parallel algorithm directly to the CFTOC problem, or to parallelize the computations of the search directions in the solver used to solve the CFTOC problem. Examples where the parallelism is applied directly to the CFTOC problem are [10], [11], [12], and [13]. In this paper, parallel algorithms for solving the UFTOC problems which correspond to computing the secondorder search directions are presented.…”

Section: Introductionmentioning

confidence: 99%

Direct Parallel Computations of Second-Order Search Directions for Model Predictive Control

Nielsen

Axehill

2019

IEEE Trans. Automat. Contr.

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Model Predictive Control (MPC) is one of the most widely spread advanced control schemes in industry today. In MPC, a constrained finite-time optimal control (CFTOC) problem is solved at each iteration in the control loop. The CFTOC problem can be solved using for example second-order methods such as interior-point (IP) or active-set (AS) methods, where the computationally most demanding part often consists of computing the sequence of second-order search directions. These can be computed by solving a set of linear equations which corresponds to solving a sequence of unconstrained finite-time optimal control (UFTOC) problems. In this paper, different direct (non-iterative) parallel algorithms for solving UFTOC problems are presented. The parallel algorithms are all based on a recursive reduction and solution propagation of the UFTOC problem. Numerical evaluations of the proposed parallel algorithms indicate that a significant boost in performance can be obtained, which can facilitate high performance second-order MPC solvers.

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“…Some attempts have been performed to apply optimal control problems on parallel computers, including the approach presented in [3] using dynamic programming and a space decomposition scheme in which the global optimal control problem is reduced to the optimization of subproblems. In [4] and [5], parallel algorithms are presented for optimal control problems with long prediction horizon using time decomposition techniques. A two-phase parallel computing method is presented in [6] to obtain the solution of receding horizon controller for constrained nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamic processor allocation for multiple RHC systems in multi-core computing environments

Azimi

Gordon

2009

2009 American Control Conference

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This paper develops a new dynamic processor allocation algorithm for multiple receding horizon controllers (RHC) executing on a multi-core parallel computer. The proposed formulation accounts for bounded model uncertainty, sensor noise, and computation delay. A cost function appropriate for control of multiple coupled vehicle systems on multiple processors is used and an upper bound on the cost as a function of the execution horizon is employed. A parallel processing adaptation of the SNOPT optimization package is used and the efficiency factor of the parallel optimization routine is estimated through simulation benchmarks. Minimization of the cost function upper bound combined with the efficiency factor information results in a combinatorial optimization problem for dynamically allocating the optimal number of logical processors for each RHC subsystem. The new approach is illustrated through simulation of a leaderfollower control system for two 3DOF helicopters running on a computer with two quad-core processors.

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Large-scale convex optimal control problems: time decomposition, incentive coordination, and parallel algorithm

Cited by 9 publications

References 4 publications

Hierarchical control for discrete large-scale complex systems by intelligent controllers

Hierarchical control for discrete large-scale complex systems by intelligent controllers

Direct Parallel Computations of Second-Order Search Directions for Model Predictive Control

Dynamic processor allocation for multiple RHC systems in multi-core computing environments

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