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This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
In this paper, we establish a connection between model predictive control (MPC) techniques and Control Barrier Functions (CBFs). Recognizing the similarity between CBFs and Control Lyapunov Functions (CLFs), we propose a MPC formulation…
In the present paper, a fluid-particle coupling method is directly derived from the Navier-Stokes equations (NSE) by applying the concept of volume-filtering, yielding a physically consistent methodology to incorporate solid wall boundary…
We propose integrating an approximation of a predictive control barrier function (PCBF) in a safety filter framework, resulting in a prediction horizon independent formulation. The PCBF is defined through the value function of an optimal…
Control systems operating in the real world face countless sources of unpredictable uncertainties. These random disturbances can render deterministic guarantees inapplicable and cause catastrophic safety failures. To overcome this, this…
In this paper, we consider a formulation of nonlinear constrained optimization problems. We reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system for tracking the optimal…
Safely navigating around obstacles while respecting the dynamics, control, and geometry of the underlying system is a key challenge in robotics. Control Barrier Functions (CBFs) generate safe control policies by considering system dynamics…
Control barrier functions (CBFs) have emerged as a popular topic in safety critical control due to their ability to provide formal safety guarantees for dynamical systems. Despite their powerful capabilities, the determination of feasible…
In this draft article, we consider the problem of achieving safe control of a dynamic system for which the safety index or (control barrier function (loosely)) has relative degree equal to two. We consider parameter affine nonlinear dynamic…
Achieving high-precision control for robotic systems is hindered by the low-fidelity dynamical model and external disturbances. Especially, the intricate coupling between internal uncertainties and external disturbances further exacerbates…
Blind System Identification (BSI) is used to extract a system model whenever input data is not attainable. Therefore, the input data and system model should be estimated simultaneously. Because of nonlinearities in a large number of…
Control barrier functions guarantee safety but typically require accurate system models. Parametric uncertainty invalidates these guarantees. Existing robust methods maintain safety via worst-case bounds, limiting performance, while modular…
This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…
Design and analysis of stabilizing controllers with safety guarantees for nonlinear systems have received considerable attention in recent years. Control Lyapunov-barrier functions (CLBFs) provide a powerful framework for simultaneously…
Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in tight spaces. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization…
Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points $\boldsymbol{\gamma} \subset P$, are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental…
Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…
Control barrier function (CBF)-based safety filters provide a systematic way to enforce state constraints, but they can significantly alter the closed-loop dynamics induced by a nominal, stabilizing controller. In particular, the resulting…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
We study the problem of co-designing control barrier functions (CBF) and linear state feedback controllers for continuous-time linear systems. We achieve this by means of a single semi-definite optimization program. Our formulation can…