Related papers: Reach-avoid Verification Based on Convex Optimizat…
We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of…
In this paper, we extend our previous results and formally propose the SCvx-fast algorithm, a new addition to the Successive Convexification algorithmic framework. The said algorithm solves non-convex optimal control problems with specific…
We study the problem of ellipsoidal bounding of convex set-valued data, where the convex set is obtained by the $p$-sum of finitely many ellipsoids, for any real $p\geq 1$. The notion of $p$-sum appears in the Brunn-Minkowski-Firey theory…
This paper concerns a class of constrained difference-of-convex (DC) optimization problems in which, the constraint functions are continuously differentiable and their gradients are strictly continuous. For such nonconvex and nonsmooth…
We analyze the convergence properties of a modified barrier method for solving bound-constrained optimization problems where evaluations of the objective function and its derivatives are affected by bounded and non-diminishing noise. The…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…
We propose a continuous feedback control strategy that steers a point-mass vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds. The main idea consists in avoiding each obstacle via the shortest path on the cone's…
This paper presents converse theorems for safety in terms of barrier functions for unconstrained continuous-time systems modeled as differential inclusions. Via a counterexample, we show the lack of existence of autonomous and continuous…
We study online inverse linear optimization, also known as contextual recommendation, where a learner sequentially infers an agent's hidden objective vector from observed optimal actions over feasible sets that change over time. The learner…
When a system's constraints change abruptly, the system's reachability safety does no longer sustain. Thus, the system can reach a forbidden/dangerous value. Conventional remedy practically involves online controller redesign (OCR) to…
Unsafe memory accesses in programs written using popular programming languages like C/C++ have been among the leading causes for software vulnerability. Prior memory safety checkers such as SoftBound enforce memory spatial safety by…
The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
In this work, we propose a control scheme for linear systems subject to pointwise in time state and input constraints that aims to minimize time-varying and a priori unknown cost functions. The proposed controller is based on online convex…