To mitigate the problems of demand-supply mismatch in the future grid the solution of renewable energy source (RES) integration results in a bidirectional flow of information and transactions, which are prone to different kinds of cyber attacks, especially in energy trading where the security of financial transactions is of most concern. Electric vehicle (EV) having the advantage of mobility can play a significant role in maintaining demand-supply balance at any location unlike their peers (conventional compensator). For deciding entire system security, securing EVs charging-discharging transactions at all charging stations or connecting points is most important. The system can be made more secure against cyber-attacks with the introduction of the blockchain framework. Hence, in view of secured transactions, the paper focuses on the energy trading process between EVs and distribution network (DN) in a Byzantine based blockchain consensus framework. During peak load period DN initiates the energy trading process by demanding additional power from the EVs. This process of energy trading results in energy and information exchange which needs to be secured through blockchain from vulnerable attacks and threats. Possible scenarios of various cyber-attacks on different nodes of the system are visualized in the form of false data. To highlight the application of blockchain, the Byzantine general problem framework is used which states that for successful attack 33% of information is to be manipulated, in other words, decreasing the probability of attack confirms the system security. Numerical results based on various operating scenarios for the standard IEEE 33 bus system are in agreement with the Byzantine consensus problem indicating improvement in system security.

This letter proposes a control algorithm as a stepping stone for the stabilization and control of structured and unstructured systems discussed in the literature. The foundation behind this proposed controller design theory utilizes an invariant target manifold giving rise to a non-degenerate form, through which the definition of certain passive outputs and storage functions provide the control law for stabilizing the system. The proposed control framework is developed by integrating the notions of immersion and passivity hence labeled as the “Passivity and Immersion (P&I) approach”. Immersing the system dynamics into the user-defined lower order target dynamics and using the concept of attractivity of the manifold based upon the passivity theory results in encompassing various design paradigms under a single roof of the P&I approach. The benchmark examples are solved to show the effectiveness of the proposed P&I approach in confirming how the various design paradigms can be unified.

The virtual derivatives computation and successive derivations of virtual inputs in an adaptive backstepping controller cause the explosion of complexity. Moreover, the feedback linearization has poor robustness features and necessitates exact estimation of the feedback control law’s coefficients. Due to measurement noise, the model-based estimation techniques for identifying uncertainties result in inaccurate gradient and Hessian calculations. Such limitations lead to model and measurement uncertainties that prevent effective stabilization and control of nonlinear systems. Machine learning-based data-driven approaches offer effective tools for identifying dynamical systems and uncertainties with minimal prior knowledge of the model structure. Therefore, the contribution of this research is two-fold: First, the general controller design theory is proposed which utilizes the idea of an invariant target manifold giving rise to a non-degenerate two form, through which the definition of certain passive outputs and storage functions leads to a generation of control law for stabilizing the system. Since the above concepts are linked with the Immersion and Invariance (I&I) design policy and the passivity theory of controller design, the proposed methodology is labeled as the "Passivity and Immersion (P&I) based approach". Second, the proposed P&I approach is integrated with a Bayesian nonparametric approach, particularly the Gaussian Process for stabilization and control of the partially unknown nonlinear systems. The effectiveness of the proposed methodologies has been evaluated on an inverted pendulum using MATLAB in the presence of input-output uncertainties.

Nesterov’s Accelerated Gradient (NAG) algorithm is a popular algorithm that provides a faster convergence to the optimal solution of an optimization problem. Despite its popularity, the origin of this algorithm is still a conceptual mystery that has motivated the proposed control theoretic perspective. This letter has derived the second-order ODE for Nesterov’s Accelerated Gradient algorithm for strongly convex functions (NAG-SC) through the notions of manifold stabilization achieved with the recently introduced P&I approach and persistence of an invariant manifold. Furthermore, the contraction of the Nesterov’s flows under the control actions (i.e., Controlled Contraction (CC)) is also proved. The contraction of Nesterov’s flows not only ensures a stable numerical integration but also reveals the multiple potentials of the NAG-SC method that motivate its usefulness in machine learning and deep learning applications.

This article deals with the embedding framework of Markov decision processes (MDPs) with discrete state and action space to find optimal actions. The optimal control problem of MDPs can be efficiently tackled by restructuring the same into an equivalent linearly-solvable Markov decision processes (LMDPs) through the method called embedding. However, state costs under the embedding may not exactly match the original costs and even assume unrealistic values. In this work, we derive a constructive sufficient condition to devise an exact embedding solution rendering the embedded state cost to match the original system. Furthermore, since, in this case, the embedding implies a transition from the discrete to continuous action space, the correlation between the obtained continuous action and an equivalent desired discrete action is investigated using a maximum a posteriori probability-based method. Finally, some examples, including mammalian cell-cycle network, are presented to demonstrate the effectiveness of the proposed method.