Related papers: Controller design and value function approximation…
Motivated by perception-based control problems in autonomous systems, this paper addresses the problem of developing feedback controllers to regulate the inputs and the states of a dynamical system to optimal solutions of an optimization…
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…
This paper offers a direct data-driven approach for learning robust control barrier certificates (R-CBCs) and robust safety controllers (R-SCs) for discrete-time input-affine polynomial systems with unknown dynamics under…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
A learning approach for optimal feedback gains for nonlinear continuous time control systems is proposed and analysed. The goal is to establish a rigorous framework for computing approximating optimal feedback gains using neural networks.…
This paper considers the synthesis of optimal safe controllers based on density functions. We present an algorithm for robust constrained optimal control synthesis using the duality relationship between the density function and the value…
We consider the problem of approximating discrete-time plants with finite-valued sensors and actu- ators by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. Building on ideas from robust…
For linear infinite systems the approximate controllability problem by control constraints is considered. Controllability conditions represented via system parameters are obtained. Partial differential control systems and control systems…
Several theorems on the volume computing of the polyhedron spanned by a n-dimensional vector set with the finite-interval parameters are presented and proved firstly, and then are used in the analysis of the controllable regions of the…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
We propose the {\alpha}-suboptimal covering number to characterize multi-task control problems where the set of dynamical systems and/or cost functions is infinite, analogous to the cardinality of finite task sets. This notion may help…
We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with constraint, and…
Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H{\"o}lder…
This paper proposes a method to compute lower performance bounds for discrete-time infinite-horizon min-max control problems with input constraints and bounded disturbances. Such bounds can be used as a performance metric for control…
For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator…