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In this paper we present a reformulation--framed as a constrained optimization problem--of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper develops an adaptive tracking controller for a class of nonlinear systems with parametric uncertainty subject to state constraints. The system is characterized by a strict-feedback structure with unknown parameters entering both…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal…
This paper addresses synthesizing receding-horizon controllers for nonlinear, control-affine dynamical systems under multiple incompatible hard and soft constraints. Handling incompatibility of constraints has mostly been addressed in…
In this paper, we present passivity based convergence analysis of continuous time primal-dual gradient method for convex optimization problems. We first show that a convex optimization problem with only affine equality constraints admit a…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
The problem of steering a particular class of $n$-dimensional continuous-time dynamical systems towards the minima of a function without gradient information is considered. We propose an hybrid controller, implementing a discrete-time…
In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax…
In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…
Optimization-based (OB) alternatives to traditional flux limiters couch preservation of properties such as local bounds and maximum principles into optimization problems, which impose these properties through inequality constraints. In this…
In this paper, we propose a novel approach to synthesize linear feedback controllers for navigating in polygonal environments using noisy measurements and a convex cell decomposition. Our method is based on formulating chance constraints…
This paper presents a perturbation analysis framework for nonsmooth optimization on connected Riemannian manifolds to bridge the gap between the rapid development of algorithmic approaches and a robust theoretical foundation. Using…
In this paper, a novel robust tracking control law is proposed for constrained robots under unknown stiffness environment. The stability and the robustness of the controller are proved using a Lyapunov-based approach where the relationship…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…