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We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems.…
This paper is concerned with impulse approximate controllability for stochastic evolution equations with impulse controls. As direct applications, we formulate captivating minimal norm and time optimal control problems; The minimal norm…
In this paper, we study a class of finite-time control problems for discrete-time positive linear systems with time-varying state parameters. Although several interesting control problems appearing in population biology, economics, and…
This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a…
The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets…
This paper addresses two minimum reaching time control problems within the context of finite stable systems. The well-known Variable Structure Control (VSC) and Unity Vector Control (UVC) strategies are analyzed, with the primary objective…
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…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
Given a stable linear time-invariant (LTI) system subject to output constraints, we present a method to compute a set of disturbances such that the reachable set of outputs matches as closely as possible the output constraint set, while…
Brockett's minimum attention functional \cite{Brockett} has been proposed as one means of capturing the cost of control implementation--regarded here as the rate of change of the control with respect to both state and time--for general…
In this paper, we focus on batch state estimation for linear systems. This problem is important in applications such as environmental field estimation, robotic navigation, and target tracking. Its difficulty lies on that limited operational…
We present a method that allows efficient and safe approximation of model predictive controllers using kernel interpolation. Since the computational complexity of the approximating function scales linearly with the number of data points, we…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety…
This work presents a method to obtain inner and outer approximations of the region of attraction of a given target set as well as an admissible controller generating the inner approximation. The method is applicable to constrained…
This paper is concerned with minimizing a sum of rational functions over a compact set of high-dimension. Our approach relies on the second Lasserre's hierarchy (also known as the upper bounds hierarchy) formulated on the pushforward…
We present a controller synthesis algorithm for reach-avoid problems for piecewise linear discrete-time systems. Our algorithm relies on SMT solvers and in this paper we focus on piecewise constant control strategies. Our algorithm…
In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the…
This paper presents an approach for approximating the reachable space of robotic manipulators based on convex polytopes. The proposed approach predicts the reachable space over a given time horizon based on the robot's actuation limits and…
We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice…