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Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs). The method transforms the IHOCs into finite-horizon optimal…

In order for autonomous vehicles to become a part of the Intelligent Transportation Ecosystem, they are required to guarantee a particular level of safety. For that to happen a safe vehicle control algorithms need to be developed, which…

In this paper, we focus on a class of robust vector polynomial optimization problems (RVPOP in short) without any convex assumptions. By combining/improving the utopia point method (a nonlinear scalarization) for vector optimization and…

Model Predictive Control (MPC)-based trajectory planning has been widely used in robotics, and incorporating Control Barrier Function (CBF) constraints into MPC can greatly improve its obstacle avoidance efficiency. Unfortunately,…

This research introduces two efficient methods to estimate the collision risk of planned trajectories in autonomous driving under uncertain driving conditions. Deterministic collision checks of planned trajectories are often inaccurate or…

This article proposes a novel control architecture using a centralized nonlinear model predictive control (CNMPC) scheme for controlling multiple micro aerial vehicles (MAVs). The control architecture uses an augmented state system to…

Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…

Computationally efficient nonlinear model predictive control relies on elaborate discrete-time optimal control problem (OCP) formulations trading off accuracy with respect to the continuous-time problem and associated computational burden.…

Optimization-based approaches such as Model Predictive Control (MPC) are promising approaches in proactive control for safety-critical applications with changing environments such as automated driving systems. However, the computational…

The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not…

In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to…

Optimal control (OC) using inverse dynamics provides numerical benefits such as coarse optimization, cheaper computation of derivatives, and a high convergence rate. However, to take advantage of these benefits in model predictive control…

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…

We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…

Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…

Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…