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B. Jeckelmann - IEEE Xplore Author Profile

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This article presents a sum of squares (SOS)-based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by \ell ^\infty bounded input, measurement, and process noise (error in variable setting). Certificates of full-state-feedback robust performance, superstabilization or quadratic stabilization of...Show More
This paper formulates algorithms to upper-bound the maximum Value-at-Risk (VaR) of a state function along trajectories of stochastic processes. The VaR is upper bounded by two methods: minimax tail-bounds (Cantelli/Vysochanskij-Petunin) and Expected Shortfall/Conditional Value-at-Risk (ES). Tail-bounds lead to an infinite-dimensional Second Order Cone Program (SOCP) in occupation measures, while t...Show More
Solving image and video jigsaw puzzles poses the chal-lenging task of rearranging image fragments or video frames from unordered sequences to restore meaningful images and video sequences. Existing approaches often hinge on discriminative models tasked with predicting either the absolute positions of puzzle elements or the permutation actions applied to the original data. Unfortunately, these meth...Show More
This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and in actuated input. The observed data are composed of tuples of current state, input, and the next state's interval ranges based on sensor quantization. Using an established characterization of input-logarithmically-quantized stabilization based on robustness to sector-boun...Show More
This letter proposes a framework to perform verifiably safe control of all discrete-time non-linear systems that are compatible with collected data. Most safety-maintaining control synthesis algorithms (e.g., control barrier functions, density functions) are limited to obtaining theoretical guarantees of safety in continuous-time, even while their implementation on real systems is typically in dis...Show More
The Errors-in-Variables model of system identification/control involves nontrivial input and measurement corruption of observed data, resulting in generically nonconvex optimization problems. This letter performs full-state-feedback stabilizing control of all discrete-time linear systems that are consistent with observed data for which the input and measurement noise obey quadratic bounds. Instanc...Show More
In this letter, we introduce novel tractable approximations for robust Linear Matrix Inequality (LMI) problems. We present various Quadratic Matrix Inequalities (QMIs) that enable us to characterize the effect of ellipsoidal uncertainty in the robust problem. These formulations are expressed in terms of a set of auxiliary decision variables, which facilitate the derivation of a generalized S-proce...Show More
This article considers the problem of error in variables identification for switched affine models. Since it is well known that this problem is generically NP-hard, several relaxations have been proposed in the literature. However, while these approaches work well for low-dimensional systems with few subsystems, they scale poorly with both the number of subsystems and their memory. To address this...Show More
This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Value-at-Risk (VaR) of a state function along SDE state distributions. The VaR problem is upper-bounded by an infinite-dimensional Second-Order Co...Show More
This work proposes a method to compute the maximum value obtained by a state function along trajectories of a Delay Differential Equation (DDE). An example of this task is finding the maximum number of infected people in an epidemic model with a nonzero incubation period. The variables of this peak estimation problem include the stopping time and the original history (restricted to a class of admi...Show More
This paper presents a linear-programming based algorithm to perform data-driven stabilizing control of linear positive systems. A set of state-input-transition observations is collected up to magnitude-bounded noise. A state feedback controller and dual linear copositive Lyapunov function are created such that the set of all data-consistent plants is contained within the set of all stabilized syst...Show More
Inspired by the work of Tsiamis et al. [1], in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a learning task with a given probability. The work in [1] shows that there exist system classes that are hard to learn to stabilize with the core reason being the hardness of identificat...Show More
This letter presents a tractable framework for data-driven synthesis of robustly safe control laws. Given noisy experimental data and some priors about the structure of the system, the goal is to synthesize a state feedback law such that the trajectories of the closed loop system are guaranteed to avoid an unsafe set even in the presence of unknown but bounded disturbances (process noise). The mai...Show More
We present a novel approach to the problem of learning the behavior of dynamical systems for the purpose of robust control design. The approach is centered around the derivation of stable predictors of potentially unstable systems and using them to identify plant models that can be ranked by their complexity (order) vs. empirical Nu -gap value.Show More
This work proposes an algorithm to bind the minimum distance between points on trajectories of a dynamical system and points on an unsafe set. Prior work on certifying safety of trajectories includes barrier and density methods, which do not provide a margin of proximity to the unsafe set in terms of distance. The distance estimation problem is relaxed to a Monge–Kantorovich-type optimal transport...Show More
This letter synthesizes a gain-scheduled controller to stabilize all possible Linear Parameter-Varying (LPV) plants that are consistent with measured input/state data records. Inspired by prior work in data informativity and LTI stabilization, a set of Quadratic Matrix Inequalities is developed to represent the noise set, the class of consistent LPV plants, and the class of stabilizable plants. Th...Show More
This paper presents a method to lower-bound the distance of closest approach between points on an unsafe set and points along system trajectories. Such a minimal distance is a quantifiable and interpretable certificate of safety of trajectories, as compared to prior art in barrier and density methods which offers a binary indication of safety/unsafety. The distance estimation problem is converted ...Show More
This paper considers the problem of learning models to be used for controller design. Using a simple example, it argues that in this scenario the objective should reflect the closed-loop, rather than open-loop distance between the learned model and the actual plant, a task that can be accomplished by using a gap metric motivated approach. This is particularly important when identifying open-loop u...Show More
This paper proposes a method to find super-stabilizing controllers for discrete-time linear systems that are consistent with a set of corrupted observations. The L-infinity bounded measurement noise introduces a bilinearity between the unknown plant parameters and noise terms. A super-stabilizing controller may be found by solving a feasibility problem involving a set of polynomial nonnegativity c...Show More
Peak estimation bounds extreme values of a function of state along trajectories of a dynamical system. This paper focuses on extending peak estimation to continuous and discrete settings with time-independent and time-dependent uncertainty. Techniques from optimal control are used to incorporate uncertainty into an existing occupation measure-based peak estimation framework, which includes special...Show More
Recently, there has been renewed interest in data-driven control, that is, the design of controllers directly from observed data. In the case of linear time-invariant (LTI) systems, several approaches have been proposed that lead to tractable optimization problems. On the other hand, the case of nonlinear dynamics is considerably less developed, with existing approaches limited to at most rational...Show More
Semidefinite programs (SDP) are a staple of today’s systems theory, with applications ranging from robust control to systems identification. However, current state-of-the art solution methods have poor scaling properties, and thus are limited to relatively moderate size problems. Recently, several approximations have been proposed where the original SDP is relaxed to a sequence of lower complexity...Show More
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem has been previously cast as a convex infinite-dimensional linear program on occupation measures, which can be approximately solved by a converging hierarchy of moment relaxations. In this paper, we present an algorithm to approximate optimal trajectories if the solutions to these relaxat...Show More
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem has been previously cast as a convex infinite-dimensional linear program on occupation measures, which can be approximately solved by a converging hierarchy of moment relaxations. In this letter, we present an algorithm to approximate optimal trajectories if the solutions to these relaxa...Show More
Recent advances in control, coupled with an exponential growth in data gathering capabilities, have made feasible a wide range of applications that can profoundly impact society. Yet, achieving this vision requires addressing the challenge of extracting control relevant information from large amounts of data, a problem that has proven to be surprisingly difficult. While modern machine learning tec...Show More