Related papers: Toeplitz matrices in the Boundary Control method

Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…

The inverse linear-quadratic optimal control problem is a system identification problem whose aim is to recover the quadratic cost function and hence the closed-loop system matrices based on observations of optimal trajectories. In this…

We are interested in fast and stable iterative regularization methods for image deblurring problems with space invariant blur. The associated coefficient matrix has a Block Toeplitz Toeplitz Blocks (BTTB) like structure plus a small rank…

Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that…

We expose in full detail a constructive procedure to invert the so--called "finite Markov moment problem". The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce…

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…

In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…

We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…

We show how the solution to NMPC problems for a special type of input-affine discrete-time systems can be obtained by reformulating the underlying non-convex optimal control problem in terms of a finite number of convex subproblems. The…

This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under additive disturbances and state-estimation errors. We enforce forward invariance of static and dynamic safe sets and convergence…

We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…

Implementing obstacle avoidance in dynamic environments is a challenging problem for robots. Model predictive control (MPC) is a popular strategy for dealing with this type of problem, and recent work mainly uses control barrier function…

We investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. The equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as…

Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via…

We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coefficients from dynamic response operator and answer a…

In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…

In this paper we explore the use of block coordinate descent (BCD) to optimize the centroidal momentum dynamics for dynamically consistent multi-contact behaviors. The centroidal dynamics have recently received a large amount of attention…