9,483 research outputs found
Distributed control design for underwater vehicles
The vast majority of control applications are based on non-interacting decentralized control designs. Because of their single-loop structure, these controllers cannot suppress interactions of the system. It would be useful to tackle the undesirable effects of the interactions at the design stage. A novel model predictive control scheme based on Nash optimality is presented to achieve this goal. In this algorithm, the control problem is decomposed into that of several small-coupled mixed integer optimisation problems. The relevant computational convergence, closed-loop performance and the effect of communication failures on the closed-loop behaviour are analysed. Simulation results are presented to illustrate the effectiveness and practicality of the proposed control algorithm
Distributed Model Predictive Control Based on Dynamic Games
Model predictive control (MPC) is widely recognized as a high performance, yet practical,control technology. This model-based control strategy solves at each sample a discrete-timeoptimal control problem over a finite horizon, producing a control input sequence. Anattractive attribute of MPC technology is its ability to systematically account for systemconstraints. The theory of MPC for linear systems is well developed; all aspects suchas stability, robustness,feasibility and optimality have been extensively discussed in theliterature (see, e.g., (Bemporad & Morari, 1999; Kouvaritakis & Cannon, 2001; Maciejowski, 2002; Mayne et al., 2000)). The effectiveness of MPC depends on model accuracy and the availability of fast computational resources. These requirements limit the application base for MPC. Even though, applications abound in process industries (Camacho & Bordons, 2004), manufacturing (Braun et al., 2003), supply chains (Perea-Lopez et al., 2003), among others, are becoming more widespread.Two common paradigms for solving system-wide MPC calculations are centralised anddecentralised strategies. Centralised strategies may arise from the desire to operate thesystem in an optimal fashion, whereas decentralised MPC control structures can result fromthe incremental roll-out of the system development. An effective centralised MPC can bedifficult, if not impossible to implement in large-scale systems (Kumar & Daoutidis, 2002;Lu, 2003). In decentralised strategies, the system-wide MPC problem is decomposed intosubproblems by taking advantage of the system structure, and then, these subproblemsare solved independently. In general, decentralised schemes approximate the interactionsbetween subsystems and treat inputs in other subsystems as external disturbances. Thisassumption leads to a poor systemperformance (Sandell Jr et al., 1978; ?iljak, 1996). Therefore, there is a need for a cross-functional integration between the decentralised controllers, in which a coordination level performs steady-state target calculation for decentralised controller (Aguilera & Marchetti, 1998; Aske et al., 2008; Cheng et al., 2007; 2008; Zhu & Henson, 2002).Several distributed MPC formulations are available in the literature. A distributed MPCframework was proposed by Dumbar and Murray (Dunbar & Murray, 2006) for the classof systems that have independent subsystem dynamic but link through their cost functionsand constraints. Then, Dumbar (Dunbar, 2007) proposed an extension of this framework thathandles systemswith weakly interacting dynamics. Stability is guaranteed through the use ofa consistency constraint that forces the predicted and assumed input trajectories to be close toeach other. The resulting performance is different from centralised implementations in mostof cases. Distributed MPC algorithms for unconstrained and LTI systems were proposed in(Camponogara et al., 2002; Jia & Krogh, 2001; Vaccarini et al., 2009; Zhang & Li, 2007). In (Jia & Krogh, 2001) and (Camponogara et al., 2002) the evolution of the states of each subsystem is assumed to be only influenced by the states of interacting subsystems and local inputs, while these restrictions were removed in (Jia & Krogh, 2002; Vaccarini et al., 2009; Zhang & Li, 2007). This choice of modelling restricts the system where the algorithm can be applied, because inmany cases the evolution of states is also influenced by the inputs of interconnected subsystems. More critically for these frameworks is the fact that subsystems-based MPCs only know the cost functions and constraints of their subsystem. However, stability and optimality as well as the effect of communication failures has not been established.The distributed model predictive control problem from a game theory perspective for LTIsystems with general dynamical couplings, and the presence of convex coupled constraintsis addressed. The original centralised optimisation problem is transformed in a dynamicgame of a number of local optimisation problems, which are solved using the relevantdecision variables of each subsystem and exchanging information in order to coordinatetheir decisions. The relevance of proposed distributed control scheme is to reduce thecomputational burden and avoid the organizational obstacles associated with centralisedimplementations, while retains its properties (stability, optimality, feasibility). In this context,the type of coordination that can be achieved is determined by the connectivity and capacity of the communication network as well as the information available of system?s cost function and constraints. In this work we will assume that the connectivity of the communication network is sufficient for the subsystems to obtain information of all variables that appear in their local problems. We will show that when system?s cost function and constraints are known by all distributed controllers, the solution of the iterative process converge to the centralised MPC solution. This means that properties (stability, optimality, feasibility) of the solution obtained using the distributed implementation are the same ones of the solution obtained using the centralised implementation. Finally, the effects of communication failures on the system?s properties (convergence, stability and performance) are studied. We will show the effect of the system partition and communication on convergence and stability, and we will find a upper bound of the system performance.Fil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de InvestigaciĂłn en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de IngenierĂa y Ciencias HĂdricas. Instituto de InvestigaciĂłn en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Sanchez, Guido Marcelo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de InvestigaciĂłn en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de IngenierĂa y Ciencias HĂdricas. Instituto de InvestigaciĂłn en Señales, Sistemas e Inteligencia Computacional; ArgentinaFil: Murillo, Marina Hebe. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de Desarrollo TecnolĂłgico para la Industria QuĂmica. Universidad Nacional del Litoral. Instituto de Desarrollo TecnolĂłgico para la Industria QuĂmica; ArgentinaFil: Limache, Alejandro Cesar. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - Santa Fe. Instituto de Desarrollo TecnolĂłgico para la Industria QuĂmica. Universidad Nacional del Litoral. Instituto de Desarrollo TecnolĂłgico para la Industria QuĂmica; Argentin
Resilient Distributed Energy Management for Systems of Interconnected Microgrids
In this paper, distributed energy management of interconnected microgrids,
which is stated as a dynamic economic dispatch problem, is studied. Since the
distributed approach requires cooperation of all local controllers, when some
of them do not comply with the distributed algorithm that is applied to the
system, the performance of the system might be compromised. Specifically, it is
considered that adversarial agents (microgrids with their controllers) might
implement control inputs that are different than the ones obtained from the
distributed algorithm. By performing such behavior, these agents might have
better performance at the expense of deteriorating the performance of the
regular agents. This paper proposes a methodology to deal with this type of
adversarial agents such that we can still guarantee that the regular agents can
still obtain feasible, though suboptimal, control inputs in the presence of
adversarial behaviors. The methodology consists of two steps: (i) the
robustification of the underlying optimization problem and (ii) the
identification of adversarial agents, which uses hypothesis testing with
Bayesian inference and requires to solve a local mixed-integer optimization
problem. Furthermore, the proposed methodology also prevents the regular agents
to be affected by the adversaries once the adversarial agents are identified.
In addition, we also provide a sub-optimality certificate of the proposed
methodology.Comment: 8 pages, Conference on Decision and Control (CDC) 201
On linear convergence of a distributed dual gradient algorithm for linearly constrained separable convex problems
In this paper we propose a distributed dual gradient algorithm for minimizing
linearly constrained separable convex problems and analyze its rate of
convergence. In particular, we prove that under the assumption of strong
convexity and Lipshitz continuity of the gradient of the primal objective
function we have a global error bound type property for the dual problem. Using
this error bound property we devise a fully distributed dual gradient scheme,
i.e. a gradient scheme based on a weighted step size, for which we derive
global linear rate of convergence for both dual and primal suboptimality and
for primal feasibility violation. Many real applications, e.g. distributed
model predictive control, network utility maximization or optimal power flow,
can be posed as linearly constrained separable convex problems for which dual
gradient type methods from literature have sublinear convergence rate. In the
present paper we prove for the first time that in fact we can achieve linear
convergence rate for such algorithms when they are used for solving these
applications. Numerical simulations are also provided to confirm our theory.Comment: 14 pages, 4 figures, submitted to Automatica Journal, February 2014.
arXiv admin note: substantial text overlap with arXiv:1401.4398. We revised
the paper, adding more simulations and checking for typo
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