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We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…
This paper develops a fast numerical dual control for exploration and exploitation (DCEE) method to address auto-optimization problems in unknown environments. In auto-optimization problems, the optimal operating condition is unknown a…
Recent work have shown how the optimal state-feedback, obtained as the solution to the Hamilton-Jacobi-Bellman equations, can be approximated for several nonlinear, deterministic systems by deep neural networks. When imitation (supervised)…
Designing spacecraft trajectories remains challenging in the presence of stochastic effects such as maneuver execution errors and observation uncertainties. Although covariance control and belief-space planning provide useful tools for…
The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric…
The present work deals with an improved back-propagation algorithm based on Gauss-Newton numerical optimization method for fast convergence. The steepest descent method is used for the back-propagation. The algorithm is tested using various…
Automated synthesis of correct-by-construction controllers for autonomous systems is crucial for their deployment in safety-critical scenarios. Such autonomous systems are naturally modeled as stochastic dynamical models. The general…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
Recent efforts in the development of autonomous driving technology have induced great advancements in perception, planning and control systems. Model predictive control is one of the most popular advanced control methods, but its…
We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…
Achieving real-time capability is an essential prerequisite for the industrial implementation of nonlinear model predictive control (NMPC). Data-driven model reduction offers a way to obtain low-order control models from complex digital…
This work focuses on optimizing the gates of a quantum circuit with a given topology to approximate the unitary time evolution governed by a Hamiltonian. Recognizing that unitary matrices form a mathematical manifold, we employ Riemannian…
We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where…
Differentiable programming is revolutionizing computational science by enabling automatic differentiation (AD) of numerical simulations. While first-order gradients are well-established, second-order derivatives (Hessians) for implicit…
Safe trajectory planning for high-performance automated vehicles in an environment with both static and moving obstacles is a challenging problem. Part of the challenge is developing a formulation that can be solved in real-time while…
Nonlinear Model Predictive Control (NMPC) is a powerful and widely used technique for nonlinear dynamic process control under constraints. In NMPC, the state and control weights of the corresponding state and control costs are commonly…
This paper introduces a new algorithm for trajectory optimization, Decoupled Reduced-space and Adaptive Feasibility-repair Trajectory Optimization (DRAFTO). It first constructs a constrained objective that accounts for smoothness, safety,…
Even though mobile robots have been around for decades, trajectory optimization and continuous time collision avoidance remain subject of active research. Existing methods trade off between path quality, computational complexity, and…