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Ultrasonic motors used in high-precision mechatronics are characterized by strong frictional effects, which are among the main problems in precision motion control. The traditional methods apply model-based nonlinear feedforward to…
In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the \emph{percentile criterion}. The percentile criterion is approximately solved by constructing an…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown…
We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…
The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization…
The constrained linear quadratic regulation problem is solved by a continuous piecewise affine function on a set of state space polytopes. It is an obvious question whether this solution can be built up iteratively by increasing the…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
One of the most basic, longstanding open problems in the theory of dynamical systems is whether reachability is decidable for one-dimensional piecewise affine maps with two intervals. In this paper we prove that for injective maps, it is…
In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically…
We survey the main results of approximation theory for adaptive piecewise polynomial functions. In such methods, the partition on which the piecewise polynomial approximation is defined is not fixed in advance, but adapted to the given…
Parametric optimization solves a family of optimization problems as a function of parameters. It is a critical component in situations where optimal decision making is repeatedly performed for updated parameter values, but computation…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
The ability to compute reward-optimal policies for given and known finite Markov decision processes (MDPs) underpins a variety of applications across planning, controller synthesis, and verification. However, we often want policies (1) to…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
Multi-stage problems with uncertain parameters and integer decisions variables are among the most difficult applications of robust optimization (RO). The challenge in these problems is to find optimal here-and-now decisions, taking into…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…
Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty - weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous…