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Enrique Mallada - IEEE Xplore Author Profile

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One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spectral structure of a system have been used to characterize the well-posedness of this problem, without assumptions on the inputs. However, certain struc...Show More
Minimax problems have attracted much attention due to various applications in constrained optimization problems and zero-sum games. Identifying saddle points within these problems is crucial, and saddle flow dynamics offer a straightforward yet useful approach. This study focuses on a class of bilinearly coupled minimax problems with strongly convex-linear objective functions. We design an acceler...Show More
Barrier functions constitute an effective tool for assessing and enforcing safety-critical constraints on dynamical systems. To this end, one is required to find a function $h$ that satisfies a Lyapunov-like differential condition, thereby ensuring the invariance of its zero super-level set $h\geq 0$, This methodology, however, does not prescribe a general method for finding the function $h$ that ...Show More
This paper presents a decentralized stability analysis of power systems comprising grid-forming (GFM) inverters. We leverage a decentralized stability framework capable of ensuring the stability of the entire interconnection through individual assessments at each bus. The key novelty lies in incorporating voltage dynamics and their coupling with reactive power, in addition to the angle dynamics an...Show More
We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as...Show More
Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized sadd...Show More
The inability to naturally enforce safety in Reinforcement Learning (RL), with limited failures, is a core challenge impeding its use in real-world applications. One notion of safety of vast practical relevance is the ability to avoid (unsafe) regions of the state space. Though such a safety goal can be captured by an action-value-like function, a.k.a. safety critics, the associated operator lacks...Show More
The study of theoretical conditions for recovering sparse signals from compressive measurements has received a lot of attention in the research community. In parallel, there has been a great amount of work characterizing conditions for the recovery of both the state and the input to a linear dynamical system (LDS), including a handful of results on recovering sparse inputs. However, existing suffi...Show More
Lyapunov's direct method is a powerful tool that provides a rigorous framework for stability analysis and control design for dynamical systems. A critical step that enables the application of the method is the existence of a Lyapunov function $V-\mathrm{a}$ function whose value monotonically decreases along the trajectories of the dynamical system. Unfortunately, finding a Lyapunov function is oft...Show More
Two-stage settlement electricity markets, which include day-ahead and real-time markets, often observe undesirable price manipulation due to the price difference across stages, inadequate competition, and unforeseen circumstances. To mitigate this, some Independent System Operators (ISOs) have proposed system-level market power mitigation (MPM) policies in addition to existing local policies. Thes...Show More
We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the network feedback. Then, a reduced network is built, where each node represents the aggregate dynamics of each coherent group, and the reduced network captures the...Show More
This article puts forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials. This is indeed possible, provided that one is willing to navigate tradeoffs between optimality, level of exposure to unsafe events, and the maximum detection time of unsafe actions. We...Show More
We consider the problem of controlling the frequency of low-inertia power systems via inverter-based resources (IBRs) that are weakly connected to the grid. We propose a novel grid-forming control strategy, the so-called frequency shaping control, that aims to shape the frequency response of synchronous generators (SGs) to load perturbations so as to efficiently arrest sudden frequency drops. Our ...Show More
In constrained reinforcement learning (C-RL), an agent seeks to learn from the environment a policy that maximizes the expected cumulative reward while satisfying minimum requirements in secondary cumulative reward constraints. Several algorithms rooted in sampled-based primal-dual methods have been recently proposed to solve this problem in policy space. However, such methods are based on stochas...Show More
We consider the problem of learning an inner approximation of the region of attraction (ROA) of an asymptotically stable equilibrium point without an explicit model of the dynamics. Rather than leveraging approximate models with bounded uncertainty to find a (robust) invariant set contained in the ROA, we propose to learn sets that satisfy a more relaxed notion of containment known as recurrence. ...Show More
With the decrease in system inertia, frequency security becomes an issue for power systems around the world. Energy storage systems (ESS), due to their excellent ramping capabilities, are considered as a natural choice for the improvement of the frequency response following major contingencies. In this paper, we propose a new strategy for energy storage – frequency shaping control – that allows to...Show More
Motion planning methods for autonomous systems based on nonlinear programming offer great flexibility in incorporating various dynamics, objectives, and constraints. One limitation of such tools is the difficulty of efficiently repre-senting obstacle avoidance conditions for non-trivial shapes. For example, it is possible to define collision avoidance constraints suitable for nonlinear programming...Show More
This article provides a quantitative and qualitative evaluation of the role of interconnection directionality in a general class of quadratic performance metrics for double-integrator networks. We first develop an analysis framework that can be used to evaluate the quadratic performance metrics of networks defined over a general class of directed graphs. A comparison between systems whose directed...Show More
This paper tackles online scheduling of electric vehicles (EVs) in an adaptive charging network (ACN) with local and global peak constraints. Given the aggregate charging demand of the EVs and the peak constraints of the ACN, it might be infeasible to fully charge all the EVs according to their charging demand. Two alternatives in such resource-limited scenarios are to maximize the social welfare ...Show More
We investigate the problem of finding inner approximations of positive semidefinite (PSD) cones. We develop a novel decomposition framework of the PSD cone by means of conical combinations of smaller dimensional sub-cones. We show that many inner approximation techniques could be summarized within this framework, including the set of (scaled) diagonally dominant matrices, Factor-width k matrices, ...Show More
We study the problem of finding closed-form outer approximations of Minkowski sums and products of sets in the complex plane. Using polar coordinates, we pose this as an optimization problem in which we find a pair of contours that give lower and upper bounds on the radial distance at a given angle. Through a series of variable transformations we rewrite this as a sum-of-squares optimization probl...Show More
As power systems transit to a state of high renewable penetration, little or no presence of synchronous generators makes the prerequisite of well-regulated frequency for grid-following inverters unrealistic. Thus, there is a trend to resort to grid-forming inverters which set frequency directly. We propose a novel grid-forming frequency shaping control that is able to shape the aggregate system fr...Show More
This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further b...Show More
This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one is willing to relax its optimality requirements mildly. We focus on the canonical multi-armed bandit problem and seek to study the exploration-preservation trade...Show More
In this paper, we formulate a cycling cost aware economic dispatch problem that co-optimizes generation and storage dispatch while taking into account cycle based storage degradation cost. Our approach exploits the Rainflow cycle counting algorithm to quantify storage degradation for each charging and discharging half-cycle based on its depth. We show that the dispatch is optimal for individual pa...Show More