9,489 research outputs found
Optimality condition decomposition approach to distributed model predictive control
International audienceThis paper presents a new methodology for distributed model predictive control of large-scale systems. The methodology involves two distinct stages, i.e., the decomposition of large-scale systems into subsystems and the design of subsystem controllers. Two procedures are used: in the first stage, the structure of the Karush-Kuhn-Tucker matrix resulting from the necessary optimality conditions is exploited to yield a decomposition of the large-scale system into several subsystems. In the second stage, a particular technique, the so-called optimality condition decomposition makes it possible to synthesize distributed coordinated subcontrollers thus achieving an optimal distributed control of the large-scale system. The convergence of the proposed approach is stated
On feasibility, stability and performance in distributed model predictive control
In distributed model predictive control (DMPC), where a centralized
optimization problem is solved in distributed fashion using dual decomposition,
it is important to keep the number of iterations in the solution algorithm,
i.e. the amount of communication between subsystems, as small as possible. At
the same time, the number of iterations must be enough to give a feasible
solution to the optimization problem and to guarantee stability of the closed
loop system. In this paper, a stopping condition to the distributed
optimization algorithm that guarantees these properties, is presented. The
stopping condition is based on two theoretical contributions. First, since the
optimization problem is solved using dual decomposition, standard techniques to
prove stability in model predictive control (MPC), i.e. with a terminal cost
and a terminal constraint set that involve all state variables, do not apply.
For the case without a terminal cost or a terminal constraint set, we present a
new method to quantify the control horizon needed to ensure stability and a
prespecified performance. Second, the stopping condition is based on a novel
adaptive constraint tightening approach. Using this adaptive constraint
tightening approach, we guarantee that a primal feasible solution to the
optimization problem is found and that closed loop stability and performance is
obtained. Numerical examples show that the number of iterations needed to
guarantee feasibility of the optimization problem, stability and a prespecified
performance of the closed-loop system can be reduced significantly using the
proposed stopping condition
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
A Parametric Non-Convex Decomposition Algorithm for Real-Time and Distributed NMPC
A novel decomposition scheme to solve parametric non-convex programs as they
arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of
a fixed number of alternating proximal gradient steps and a dual update per
time step. Hence, the proposed approach is attractive in a real-time
distributed context. Assuming that the Nonlinear Program (NLP) is
semi-algebraic and that its critical points are strongly regular, contraction
of the sequence of primal-dual iterates is proven, implying stability of the
sub-optimality error, under some mild assumptions. Moreover, it is shown that
the performance of the optimality-tracking scheme can be enhanced via a
continuation technique. The efficacy of the proposed decomposition method is
demonstrated by solving a centralised NMPC problem to control a DC motor and a
distributed NMPC program for collaborative tracking of unicycles, both within a
real-time framework. Furthermore, an analysis of the sub-optimality error as a
function of the sampling period is proposed given a fixed computational power.Comment: 16 pages, 9 figure
Rate analysis of inexact dual first order methods: Application to distributed MPC for network systems
In this paper we propose and analyze two dual methods based on inexact
gradient information and averaging that generate approximate primal solutions
for smooth convex optimization problems. The complicating constraints are moved
into the cost using the Lagrange multipliers. The dual problem is solved by
inexact first order methods based on approximate gradients and we prove
sublinear rate of convergence for these methods. In particular, we provide, for
the first time, estimates on the primal feasibility violation and primal and
dual suboptimality of the generated approximate primal and dual solutions.
Moreover, we solve approximately the inner problems with a parallel coordinate
descent algorithm and we show that it has linear convergence rate. In our
analysis we rely on the Lipschitz property of the dual function and inexact
dual gradients. Further, we apply these methods to distributed model predictive
control for network systems. By tightening the complicating constraints we are
also able to ensure the primal feasibility of the approximate solutions
generated by the proposed algorithms. We obtain a distributed control strategy
that has the following features: state and input constraints are satisfied,
stability of the plant is guaranteed, whilst the number of iterations for the
suboptimal solution can be precisely determined.Comment: 26 pages, 2 figure
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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