Search

This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min–max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush–Kuhn–Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption. [ABSTRACT FROM AUTHOR]

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a solution can be based on prior functions. We show that the problem is well-posed when formulated in a parametric fashion, and that the solution parameter depends continuously on the prior function. In this way, we are able to obtain a smooth parametrization of admissible spectral densities. Based on this result, the problem is reparametrized via a bijective change of variables out of a numerical consideration, and then a continuation method is used to compute the unique solution parameter. Numerical aspects, such as convergence of the proposed algorithm and certain computational procedures are addressed. A simple example is provided to show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper considers the set membership fusion estimation problem for the general multisensor dynamic systems with unknown but bounded noises. In order to achieve the ellipsoidal fusion formulae, we divide the set membership filter problem into two steps: the prediction step and the fusion update step. The proposed method has the following nice properties. First, each step can be converted into a semidefinite programming problem, which can be efficiently computed. Second, part-analytical formulae of the shape matrix and the center of the bounding ellipsoid can be derived by using a decoupled technique, which can significantly reduce the computational complexity. Moreover, the relationship between the fusion center and local sensors can be clearly revealed based on the ellipsoidal fusion formula. Finally, it is interesting that the ellipsoidal fusion formula is similar in form to the classic mean-squared error filter fusion, although they are of the different optimization frameworks. However, the fusion weights of the information matrix provided by the different sensors are different and the optimal fusion weights can be calculated by solving a convex optimization problem. A typical numerical example in target tracking demonstrates the effectiveness of the proposed centralized and distributed fusion formula. [ABSTRACT FROM AUTHOR]

We consider the problem of resilient state estimation in the presence of integrity attacks. There are $m$ sensors monitoring the state and $p$ of them are under attack. The sensory data collected by the compromised sensors can be manipulated arbitrarily by the attacker. The classical estimators, such as the least squares estimator, may not provide a reliable estimate under the so-called $(p,m)$ -sparse attack. In this paper, we are not restricting our efforts to studying whether any specific estimator is resilient to the attack or not, but instead we aim to present some generic sufficient and necessary conditions for resilience by considering a general class of convex optimization based estimators. The sufficient and necessary conditions are shown to be tight, with a trivial gap. We further specialize our result to the scalar sensor measurements case and extend our framework to incorporate estimators with correlated cost function optimization. Experimental results tested on the IEEE 14-bus test system validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with a general class of distributed constrained optimization problems over a multiagent network, where the global objective function is represented by the sum of all local objective functions. Each agent in the network only knows its own local objective function, and is restricted to a global nonempty closed convex set. We discuss the scenario where the communication of the whole multiagent network is expressed as a sequence of time-varying general unbalanced directed graphs. The directed graphs are required to be uniformly jointly strongly connected and the weight matrices are only row-stochastic. To collaboratively deal with the optimization problems, existing distributed methods mostly require the communication graph to be fixed or balanced, which is impractical and hardly inevitable. In contrast, we propose a new distributed projection subgradient algorithm which is applicable to the time-varying general unbalanced directed graphs and does not need each agent to know its in-neighbors’ out-degree. When the objective functions are convex and Lipschitz continuous, it is proved that the proposed algorithm exactly converges to the optimal solution. Simulation results on a numerical experiment are shown to substantiate feasibility of the proposed algorithm and correctness of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization, given in terms of the all-pass divisors of a certain all-pass function, is established in the most general setting: after several partial results, mostly in the continuous-time case, this is indeed the first complete parametrization obtained without resorting to any facilitating assumption. This result provides a positive answer to a conjecture raised in 2016. [ABSTRACT FROM AUTHOR]

Given a set of target detections over several time periods, this paper addresses the multitarget tracking (MTT) problem of optimally assigning detections to targets and estimating the trajectory of the targets over time. MTT has been studied in the literature via predominantly probabilistic methods. In contrast, we propose the use of mixed integer optimization (MIO) along with relaxations and local-search-based heuristic algorithms that are: scalable, as they provide near optimal solutions for six targets and ten time periods in milliseconds to seconds; general, as they make no probabilistic assumptions on the detection process; robust, as they can accommodate missed and false detections of the targets; and easily implementable, as they use at most two tuning parameters. We evaluate the performance of the new methods using a novel metric for the complexity of an instance, and find that they provide high quality solutions both reliably and quickly for a large range of scenarios, resulting in a promising approach to the area of MTT. [ABSTRACT FROM AUTHOR]

This paper develops a new sampling-based method for stability verification of piecewise continuous nonlinear systems via Lyapunov functions. Depending on the nonlinear system dynamics, the candidate Lyapunov function and the set of states of interest, verifying stability requires solving complex, possibly non-convex or infeasible optimization problems. To avoid such problems, the proposed approach firstly distributes the verification of Lyapunov's inequality on a finite sampling of a bounded set of states of interest. Secondly, it extends the validity of Lyapunov's inequality to an infinite, bounded set of states by automatically exploiting local continuity properties. A sampling-based method for estimating the domain of attraction (DOA) via level sets of a validated Lyapunov function is also presented. Efficient state-space exploration is achieved using multi-resolution sampling and hyper-rectangles as basic sampling blocks. The operations that need to be performed for each sampling point in the state-space can be carried out in parallel, which improves scalability. The proposed methodology is illustrated for various benchmark examples from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting, where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function, and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of controlling a network of mobile sensors so that a set of hidden states are estimated up to a user-specified accuracy. The sensors take measurements and fuse them online using an information consensus filter (ICF). At the same time, the local estimates guide the sensors to their next best configuration. This leads to an LMI-constrained optimization problem that we solve by means of a new distributed random approximate projections method. The new method is robust to the state disagreement errors that exist among the robots as the ICF fuses the collected measurements. Assuming that the noise corrupting the measurements is zero-mean and Gaussian and that the robots are self-localized in the environment, the integrated system converges to the next best positions from where new observations will be taken. This process is repeated with the robots taking a sequence of observations until the hidden states are estimated up to the desired user-specified accuracy. We present simulations of sparse landmark localization, where the robotic team achieves the desired estimation tolerances while exhibiting interesting emergent behavior. [ABSTRACT FROM PUBLISHER]

Subspace-based methods have been effectively used to estimate multi-input/multi-output, discrete-time, linear-time invariant systems from uniformly spaced spectrum samples. A critical step in these methods is the splitting of causal and noncausal invariant subspaces of a Hankel matrix built from spectrum measurements via singular-value decomposition in order to determine model order. Quite often, in particular when signal-to-noise ratio is low, unmodelled dynamics is present, and the number of measurements is small, this step is inconclusive since the assumed mirror image symmetry with respect to the unit circle between the eigenvalues of the invariant spaces is lost. In this paper, we propose a new model order selection and invariant space splitting scheme based on the regularized nuclear norm optimization in combination with a particular subspace method that is insensitive to noise and undermodelling. By a detailed numerical study, efficacy of the proposed scheme is shown for a broad range of signal-to-noise ratio and short data records. [ABSTRACT FROM AUTHOR]