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This paper deals with the problem of robust fault estimation for the Lipschitz nonlinear systems under the influence of sensor faults and actuator faults. In the proposed methodology, a descriptor system is formulated by augmenting sensor fault vectors with the states of the system. A novel fast adaptive unknown input observer (FAUIO) structure is proposed for the simultaneous estimation of both faults and states of a class of nonlinear systems. A new LMI condition is established by utilizing the $\mathcal{H}_\infty$ criterion to ensure the asymptotic convergence of the estimation error of the developed observer. This derived LMI condition is deduced by incorporating the reformulated Lipschitz property, a new variant of Young inequality, and the well-known linear parameter varying (LPV) approach. It is less conservative than the existing ones in the literature, and its effectiveness is compared with the other proposed approaches. Further, the proposed observer methodology is extended for the disturbance-affected nonlinear system for the purpose of the reconstruction of states and faults with optimal noise attenuation. Later on, both designed approaches are validated through an application of a single-link robotic arm manipulator in MATLAB Simulink.

In this paper, a constructive and systematic strategy with more apparent degrees of freedom to achieve the accurate estimation of unknown parameters via a control perspective is proposed. By adding a virtual control in the final equation of the gradient dynamics, the Gradient Estimator (GE) and Memory Regressor and Extension (MRE) approaches are extended. The solution of the virtual control law is identified by the P&I approach. The P&I approach is based on the choice of an appropriate implicit manifold and the generation of a suitable passive output and a related storage function. This facilitates the virtual control law being obtained in a way that the parametric error converges asymptotically to zero. Because the above ideas connect with the P&I approach and GE, the developed methodology is labeled the passivity and immersion-based modified gradient estimator (MGE). The proposed P&I-based modified gradient estimator is extended via the MRE approach. This modification provides improved transient response and fast convergence. Based on certain PE and non-PE examples, a comparative analysis is carried out to show the efficacy of the proposed approaches.

The dynamic mode decomposition (DMD) technique extracts the dominant modes characterizing the innate dynamical behavior of the system within the measurement data. For appropriate identification of dominant modes from the measurement data, the DMD algorithm necessitates ensuring the quality of the input measurement data sequences. On that account, for validating the usability of the dataset for the DMD algorithm, the paper proposed two conditions: Persistence of excitation (PE) and the Granger Causality Test (GCT). The virtual data sequences are designed with the hankel matrix representation such that the dimensions of the subspace spanning the essential system modes are increased with the addition of new state variables. The PE condition provides the lower bound for the trajectory length, and the GCT provides the order of the model. Satisfying the PE condition enables estimating an approximate linear model, but the predictability with the identified model is only assured with the temporal causation among data searched with GCT. The proposed methodology is validated with the application for coherency identification (CI) in a multi-machine power system (MMPS), an essential phenomenon in transient stability analysis. The significance of PE condition and GCT is demonstrated through various case studies implemented on 22 bus six generator system.

The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework is proposed wherein we begin by framing the proposed dynamics in a fiber-bundle setting endowed with a Riemannian metric that captures the geometry of the gradient (of the Lagrangian function). A strongly monotone gradient vector field is obtained by using the natural gradient adaptation on the Riemannian manifold. The Lyapunov stability analysis proves that this adaption leads to a globally exponentially stable saddle-point solution. Further, with numeric simulations we show that the scaling a key parameter in the Riemannian metric results in an accelerated convergence to the saddle-point solution., Comment: arXiv admin note: text overlap with arXiv:1905.04521

The constrained multi-agent optimization problem of distributed resource allocation is addressed using the evolutionary game theoretic framework. The issue of building temperature control is analyzed in which the controller is to devise a scheme to distribute available scarce power to every room to regulate their temperature as per the comfort of user in the best possible manner. The paper correlates the global constraint of fixed resource amount with the constant population size. The respective population game is evaluated by means of a dynamical model of the evolutionary game theory to find the necessary control action. The robustness of optimal solution with respect to minor fluctuations in the temperature distribution is characterized using evolutionary stable strategy ( ESS ). Along with the global constraint, the problem formulation constitutes local constraint over an individual control unit located in every room. The classical dynamical models of evolutionary game theory such as replicator dynamics, logit dynamics, etc. fail to incorporate respective constraints. With the escort evolutionary dynamical (ED) model it is possible to address these local constraints through the concept of the intersection of simplices. However, evaluation of these classical dynamics along with ED is driven by expected payoff obtained by the overall population, which renders a centralized implementation approach. To mitigate this central dependency a distributed version of the ED model referred to as distributed escort dynamics (DED) is proposed. The control action devised adopting DED approach is shown to provide smooth trajectory tracking along with the low start-up transience when compared with distributed interior point (DIP) method.

The literature available on disturbance decoupling (DD) of Boolean control network (BCN) is built on a restrictive notion of what constitutes as disturbance decoupling. The results available on necessary and sufficient conditions are of limited applicability because of their stringent requirements. This work tries to expand the notion of DD in BCN to incorporate a larger number of systems deemed unsuitable for DD. The methods available are further restrictive in the sense that system is forced to follow trajectory unaffected by the disturbances rather than decoupling disturbances while the system follows its natural course. Some sufficient conditions are provided under which the problem can be addressed. This work tries to establish the notion of disturbance decoupling via feedback control,analogous to the classical control theory. This approach though, is not limited to DD problems and can be extended to the general control problems of BCNs. Determination of observability, which is sufficient for the fault detection, is proven to be NP-hard for Boolean Control Network. Algorithms based on reconstructability, a necessary condition, of BCN turn out to be of exponential complexity in general.In such cases it makes sense to search for the availability of some special structure in BCN that could be utilized for fault detection with minimal computational efforts. An attempt is made to address this problem by introducing instantaneous fault detection (IFD) and providing necessary and sufficient conditions for the same. Later necessary and sufficient conditions are proposed for solving the problem of instantaneous fault detection along with disturbance decoupling using a single controller.

Equivalence of convex optimization, saddle-point problems, and variational inequalities is a well-established concept. The variational inequality (VI) is a static problem which is studied under dynamical settings using a framework called the projected dynamical system, whose stationary points coincide with the static solutions of the associated VI. VI has rich properties concerning the monotonicity of its vector-valued map and the uniqueness of its solution, which can be extended to convex optimization and saddle-point problems. Moreover, these properties also extend to the representative projected dynamical system. The objective of this paper is to harness rich monotonicity properties of the representative projected dynamical system to develop the solution concepts of the convex optimization problem and the associated saddle-point problem. To this end, this paper studies a linear inequality constrained convex optimization problem and models its equivalent saddle-point problem as a VI. Further, the VI is studied as a projected dynamical system\cite{friesz1994day} which is shown to converge to the saddle-point solution. By considering the monotonicity of the gradient of Lagrangian function as a key factor, this paper establishes exponential convergence and stability results concerning the saddle-points. Our results show that the gradient of the Lagrangian function is just monotone on the Euclidean space, leading to only Lyapunov stability of stationary points of the projected dynamical system. To remedy the situation, the underlying projected dynamical system is formulated on a Riemannian manifold whose Riemannian metric is chosen such that the gradient of the Lagrangian function becomes strongly monotone. Using a suitable Lyapunov function, the stationary points of the projected dynamical system are proved to be globally exponentially stable and convergent to the unique saddle-point.

Models of multi-agent systems can be found all around us. One of the objectives of multi-agent systems is to define local control laws in order to achieve a desired global state of the system. This paper utilises the concept of Distributed Resource Allocation (DRA) approach for successful incorporation of a large number of Plug-in Electric Vehicles (PEVs) with the power grid. DRA approach is implemented using the concept of achieving output consensus. A fixed number of PEVs are considered which are connected to the grid for a certain time interval. The PEV batteries can be charged as well discharged during this time interval. Charging and discharging of PEVs from the grid is further divided into time slots and are coined as strategies. The goal of this paper is to obtain a well-inclined charging strategy for each PEV connected to the grid such that it satisfies the power grid objective in terms of the smoothening factor of grid load profile.

This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal variables of the coupled agents, the given law accelerates the convergence of the proposed dynamics to the saddle-point solution. The resulting dynamics is represented as a feedback interconnected networked system that proves to be passive. The passivity properties of the proposed dynamics are exploited along with the LaSalle's invariance principle for hybrid systems, to establish asymptotic convergence and stability of the saddle-point solution. Further, the primal dynamics is analyzed for the rate of convergence and stronger convergence bounds are established, it is proved that the primal dynamics achieve accelerated convergence under the adaptive synchronization. The robustness of the proposed dynamics is quantified using L2-gain analysis and the correlation between the rate of convergence and robustness of the proposed dynamics is presented. The effectiveness of the proposed dynamics is demonstrated by applying it to solve distributed least squares and distributed support vector machines problems.

In this paper, we investigate the nature of the singularity in the spherically symmetrical, shear-free, gravitational collapse of a star with heat flux using a separable metric [cqg1]. For any non-singular, regular, radial density profile for a star described by this metric, eq. (2.1), the singularity of the gravitational collapse is not naked locally. Our results here unequivocally support the Strong Cosmic Censorship Hypothesis., Comment: Submitted to General Relativity and Gravitation

In this paper, we find all the Conformal Killing Vectors (CKVs) and their Lie Algebra for the recently reported [cqg1] spherically symmetric, shear-free separable metric spacetimes with non-vanishing energy or heat flux. We also solve the geodesic equatios of motion for the spacetime under consideration., Comment: submitted to Classical and Quantum Gravity

We investigate the formation of a locally naked singularity in the collapse of radiation shells in an expanding Vaidya-deSitter background. This is achieved by considering the behaviour of non-spacelike and radial geodesics originating at the singularity. A specific condition is determined for the existence of radially outgoing, null geodesics originating at the singularity which, when this condition is satisfied, becomes locally naked. This condition turns out to be the same as that in the collapse of radiation shells in an asymptotically flat background. Therefore, we have, at least for the case considered here, established that the asymptotic flatness of the spacetime is not essential for the development of a locally naked singularity. Our result then unequivocally supports the view that no special role be given to asymptotic observers (or, for that matter, any set of observers) in the formulation of the Cosmic Censorship Hypothesis., Comment: submitted Oct. 1997, Revised Version, to be published Gen. Rel. Grav., Latex file, 9 pages