相关论文: Infinite-Dimensional Sums-of-Squares for Optimal C…
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
This work considers the problem of approximating initial condition and time-dependent optimal control and trajectory surfaces using multivariable Fourier series. A modified Augmented Lagrangian algorithm for translating the optimal control…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
The mathematical framework of hybrid system is a recent and general tool to treat control systems involving control action of heterogeneous nature. In this paper, we construct and test a semi-Lagrangian numerical scheme for solving the…
We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on monotone interpolation. These schemes converge under very weak…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…
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…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and…
The behaviour of the moment-sums-of-squares (moment-SOS) hierarchy for polynomial optimal control problems on compact sets has been explored to a large extent. Our contribution focuses on the case of non-compact control sets. We describe a…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
We present a control design procedure for nonlinear control systems in which we represent a potentially high dimensional system with a low dimensional continuous-state abstraction. The abstraction generates a reference which the original…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…